I have just discovered a new proof of the existence of God.
Consider the following sentence:
(S) If this sentence is true, then God exists.
Suppose sentence S is true. Then the first clause is satisfied, so the second clause is true. Thus, God exists.
What the preceding paragraph proves is that if sentence S is true, then God exists. But that is exactly what sentence S asserts. So that means we have proved that sentence S is true! And therefore God really does exist.
As a result of this proof I am longer an atheist. Sorry to disappoint everyone.*
* Note this proof also works for unicorns. Yay, unicorns exist!
Showing posts with label philosophy. Show all posts
Showing posts with label philosophy. Show all posts
Sunday, April 5, 2015
Monday, March 17, 2014
Facts, Brute and Otherwise
Prof. Feser has responded at length to some comments I made on one of his posts. As usual, I thank him for his time and attention to my comments.
In those comments, I proposed the example of lightning striking a tree and starting a forest fire. I claimed that the lightning is still an explanation for the fire, even if the lightning itself was a brute fact (i.e. a fact having no explanation).
I realized (eventually) that my example was not the sort of explanation Feser had in mind in his original post. My example was a horizontal causal chain, in which one event causes another, which causes another, and so on, while Feser's original claim was about vertical explanatory chains: one level of explanation is in turn given a more detailed description by a lower-level explanation, which is in turn given a still-lower-level explanation. (The picture I have in mind is, for example, of a broken window that is explained at one level by the rock that hit it, but at a lower level by the fracturing properties of glass and the stresses imposed by the rock, and those properties are in turn explained by the properties of the molecules of which the glass and the rock are made, and so on.) So my example wasn't really relevant to Feser's point.
In his new post, though, Feser clearly does intend his point to apply to horizontal causal chains, so perhaps the forest fire example is relevant after all. Let me add a few more remarks.
For some reason, I'm more sympathetic to the idea that the brutishness of facts propagates vertically. I'm not sure why my intuition differentiates between the horizontal and vertical explanatory chains. The goal of physics is to describe the way the universe is in as simple and efficient a manner as possible. We physicists suppose that everything physical can be explained at bottom by the Standard Model of elementary particles, but we are content to take that theory as a brute fact. (Well, not really "content": we are always striving for a deeper explanation which will explain the structure and parameters of the Standard Model. But if we found such a theory, we would take that as a brute fact.) So in some sense the answer to any physical question is, "That's just the way the universe is." But that doesn't mean such explanations aren't useful.
Any explanation of a fact A will necessarily be in terms of other facts B, C, and D. (Unless A is self-explanatory, whatever that might mean.) B, C, and D, in turn, are either self-explanatory, or brute facts, or they are explained in terms of some further facts E, F, and G. So the whole thing can only bottom out in facts that are either self-explanatory or brute. (It seems to me that this much is true of both vertical and horizontal chains.)
If I read the professor's remarks correctly, he is saying that something can only be a real explanation if it bottoms out in only self-explanatory facts. (And that this is true of both vertical and horizontal explanatory chains.)
My response is that, if this is true, then there are hardly any examples of real explanations. In fact, maybe there has never been a real explanation in the history of humanity. For (nearly?) all actual explanations leave something else unexplained.
For instance:
What I'm saying is, any actual example of an explanation always leaves some loose ends. The regularities themselves are enough for us to claim we have an explanation: heat boils water, rock breaks window, ice makes sidewalks slippery.
Now, what Feser seems to be saying is that, though we might not know what the explanation is for the explaining facts B, C, and D, we must at least believe that there is an explanation for those facts. Otherwise we don't really have an explanation.
To this I can only respond as Keith Parsons did: I don't see why I should think this. If all actual examples of explanations leave something else unexplained, why should I deny that these are true explanations? It makes more sense to me to provide an account of explanation that reflects how we actually use explanations than to provide an account which declares by fiat that no real-world examples of explanation are true explanations.
Feser challenged me to provide an alternative account of explanation. I have done so before in previous discussions, and have not to my recollection had a response, but I am happy to repeat it here.
Consider the D-N model of scientific explanation. According to this model, an explanation of an event A consists of two things:
Let's return to the boiling pot. I can, in principle, carry my explanatory chain vertically downward, explaining the molecular properties of water in terms of the quantum mechanical properties of the atoms, and the properties of the atoms in terms of the Standard Model. There I bottom out in brute facts, from my physicist's point of view.
So here's my counter-challenge for Professor Feser: give a real explanation - in his own sense - of why the water is boiling: an explanation that bottoms out only in self-explaining facts or necessary truths.
Finally let me note that scientific explanations of the kind I've been talking about have a stunning record of success. Engines, TVs, computers, cell phones - all of modern technology stems from our ability to explain things in terms of unifying regularities. In contrast, Aristotelian explanation has been around for more than 2000 years: what practical successes can it claim?
In those comments, I proposed the example of lightning striking a tree and starting a forest fire. I claimed that the lightning is still an explanation for the fire, even if the lightning itself was a brute fact (i.e. a fact having no explanation).
I realized (eventually) that my example was not the sort of explanation Feser had in mind in his original post. My example was a horizontal causal chain, in which one event causes another, which causes another, and so on, while Feser's original claim was about vertical explanatory chains: one level of explanation is in turn given a more detailed description by a lower-level explanation, which is in turn given a still-lower-level explanation. (The picture I have in mind is, for example, of a broken window that is explained at one level by the rock that hit it, but at a lower level by the fracturing properties of glass and the stresses imposed by the rock, and those properties are in turn explained by the properties of the molecules of which the glass and the rock are made, and so on.) So my example wasn't really relevant to Feser's point.
In his new post, though, Feser clearly does intend his point to apply to horizontal causal chains, so perhaps the forest fire example is relevant after all. Let me add a few more remarks.
For some reason, I'm more sympathetic to the idea that the brutishness of facts propagates vertically. I'm not sure why my intuition differentiates between the horizontal and vertical explanatory chains. The goal of physics is to describe the way the universe is in as simple and efficient a manner as possible. We physicists suppose that everything physical can be explained at bottom by the Standard Model of elementary particles, but we are content to take that theory as a brute fact. (Well, not really "content": we are always striving for a deeper explanation which will explain the structure and parameters of the Standard Model. But if we found such a theory, we would take that as a brute fact.) So in some sense the answer to any physical question is, "That's just the way the universe is." But that doesn't mean such explanations aren't useful.
Any explanation of a fact A will necessarily be in terms of other facts B, C, and D. (Unless A is self-explanatory, whatever that might mean.) B, C, and D, in turn, are either self-explanatory, or brute facts, or they are explained in terms of some further facts E, F, and G. So the whole thing can only bottom out in facts that are either self-explanatory or brute. (It seems to me that this much is true of both vertical and horizontal chains.)
If I read the professor's remarks correctly, he is saying that something can only be a real explanation if it bottoms out in only self-explanatory facts. (And that this is true of both vertical and horizontal explanatory chains.)
My response is that, if this is true, then there are hardly any examples of real explanations. In fact, maybe there has never been a real explanation in the history of humanity. For (nearly?) all actual explanations leave something else unexplained.
For instance:
- I can explain why that pot of water is boiling by noting that it has been on a hot burner for 15 minutes.
- I can explain why the window broke by noting the rock that hit it.
- I can explain why I slipped and fell by noting the ice on the sidewalk.
What I'm saying is, any actual example of an explanation always leaves some loose ends. The regularities themselves are enough for us to claim we have an explanation: heat boils water, rock breaks window, ice makes sidewalks slippery.
Now, what Feser seems to be saying is that, though we might not know what the explanation is for the explaining facts B, C, and D, we must at least believe that there is an explanation for those facts. Otherwise we don't really have an explanation.
To this I can only respond as Keith Parsons did: I don't see why I should think this. If all actual examples of explanations leave something else unexplained, why should I deny that these are true explanations? It makes more sense to me to provide an account of explanation that reflects how we actually use explanations than to provide an account which declares by fiat that no real-world examples of explanation are true explanations.
Feser challenged me to provide an alternative account of explanation. I have done so before in previous discussions, and have not to my recollection had a response, but I am happy to repeat it here.
Consider the D-N model of scientific explanation. According to this model, an explanation of an event A consists of two things:
- A list of natural laws L1, L2, L3....
- A list of conditions C1, C2, C3.... that guarantee the laws apply in the case A.
- L1: Lightning causes fires.
- C1: There was a lightning strike.
Let's return to the boiling pot. I can, in principle, carry my explanatory chain vertically downward, explaining the molecular properties of water in terms of the quantum mechanical properties of the atoms, and the properties of the atoms in terms of the Standard Model. There I bottom out in brute facts, from my physicist's point of view.
So here's my counter-challenge for Professor Feser: give a real explanation - in his own sense - of why the water is boiling: an explanation that bottoms out only in self-explaining facts or necessary truths.
Finally let me note that scientific explanations of the kind I've been talking about have a stunning record of success. Engines, TVs, computers, cell phones - all of modern technology stems from our ability to explain things in terms of unifying regularities. In contrast, Aristotelian explanation has been around for more than 2000 years: what practical successes can it claim?
Tuesday, March 4, 2014
Bicycles and Universes
I have often imagined debating William Lane Craig myself, and thought out the ways I would respond to his arguments. I have often, while listening to Craig's debates, wondered why his opponent didn't call him on some claim that was simply untrue. Were they just being polite, or did they not realize the falsity of the claim?
I think I may be cured of these fantasies. Sean Carroll did brilliantly in the debate - far better than I could ever have done. He didn't hesitate to say outright, "That's just false!" And his deep expertise in cosmology was the perfect counterpoint to Craig's quote-mining of partially-understood physics papers.
I have only a couple of comments on style and content. I thought Sean did a good job of pointing out where Craig failed to respond to the argument. (This is an area where Craig usually excels.) But instead of merely pointing it out, he ought to have taken the opportunity to summarize his argument again, for those who might not have understood it completely the first time.
Craig, as usual, excelled in his logical organization and presentation of his argument. His concluding summary nicely recalled his original point: not that he was out to prove God's existence, but that modern cosmology lends support to one of his premises.
Here Carroll really missed an opportunity. He ought to have said, briefly and succinctly, that modern cosmology lends no support at all the premise that the universe had a beginning. What we can say for sure is that the universe was a very different place 13.7 billion years ago. But any statement about what happened before that is very speculative and unfounded in established science. There are models in which time has a beginning, and there are models in which it doesn't: none of these models are established science, and so nothing can be deduced from them about a beginning.
One final missed opportunity: when Craig asked, quite reasonably, "If universes can just pop into existence, why not bicycles? What's the difference?" (from memory, not an exact quote) Sean could have responded that there is an obvious and crucial difference: bicycles are things that exist within time, while universes are not. On the contrary, time exists within a universe. For all Craig's bluster about simultaneous causation in the Q&A session, causality has to do with what brings about a change. And for there to be change, there must be time. Since a universe is not something that happens in time, the causality issue doesn't apply.
I think Sean probably had something like this in mind in his argument about the a cosmological model as a self-contained description needing no outside cause, but it would have been nice to respond to Craig's question with a specific difference that clearly matters.
I think I may be cured of these fantasies. Sean Carroll did brilliantly in the debate - far better than I could ever have done. He didn't hesitate to say outright, "That's just false!" And his deep expertise in cosmology was the perfect counterpoint to Craig's quote-mining of partially-understood physics papers.
I have only a couple of comments on style and content. I thought Sean did a good job of pointing out where Craig failed to respond to the argument. (This is an area where Craig usually excels.) But instead of merely pointing it out, he ought to have taken the opportunity to summarize his argument again, for those who might not have understood it completely the first time.
Craig, as usual, excelled in his logical organization and presentation of his argument. His concluding summary nicely recalled his original point: not that he was out to prove God's existence, but that modern cosmology lends support to one of his premises.
Here Carroll really missed an opportunity. He ought to have said, briefly and succinctly, that modern cosmology lends no support at all the premise that the universe had a beginning. What we can say for sure is that the universe was a very different place 13.7 billion years ago. But any statement about what happened before that is very speculative and unfounded in established science. There are models in which time has a beginning, and there are models in which it doesn't: none of these models are established science, and so nothing can be deduced from them about a beginning.
One final missed opportunity: when Craig asked, quite reasonably, "If universes can just pop into existence, why not bicycles? What's the difference?" (from memory, not an exact quote) Sean could have responded that there is an obvious and crucial difference: bicycles are things that exist within time, while universes are not. On the contrary, time exists within a universe. For all Craig's bluster about simultaneous causation in the Q&A session, causality has to do with what brings about a change. And for there to be change, there must be time. Since a universe is not something that happens in time, the causality issue doesn't apply.
I think Sean probably had something like this in mind in his argument about the a cosmological model as a self-contained description needing no outside cause, but it would have been nice to respond to Craig's question with a specific difference that clearly matters.
Monday, March 3, 2014
Craig, Carroll, and Cause
Since I've been reading about causes, one part of the debate that stood out for me was the fact that neither Carroll nor Craig tried to define "cause." In terms of the debate, this was undoubtedly wise: a long digression on the different definitions of "cause" would probably have lost most of the audience. But it was bad philosophy. Carroll tried to explain that, for a physicist, having a consistent mathematical model that comports with the experimental evidence is all we need. Any discussion of causes and effects will proceed from that model. Craig simply kept repeating his argument from incredulity: a universe can't just pop into being without a reason.
But certainly, how we think about causation affect our ideas on whether a self-contained universe needs a cause.
(By the way, this issue is independent of whether the universe in question has a beginning or not. While it might seem intuitively that a universe that begins is more guilty of "just popping" into existence, it has often been argued that a universe that is infinite in time is no less in need of some sort of external cause or explanation.)
On Hume's regularity view, causation is a matter of constant conjunction: to know that A causes B, we need to know that A is always followed by B. So what we need to do is to make lots of observations of deities, and if "Let there be light!" is always followed by a universe popping into existence, then we can conclude that gods cause universes.
On Wesley Salmon's analysis, a causal process is one that can carry some sort of a mark that transmits from the cause to the effect. It would seem, though, that if God is perfect, God is impossible to mark. Thus, we could never tell if a mark can be passed to the universe.
Another modern approach is to take causation to involve the transmission of a conserved quantity, like energy or momentum. But neither the theist not the atheist would claim that a universe that has a beginning in time was initiated by a transfer of pre-existing energy, so in this case there is no possibility of a cause.
On the Aristotelian-Thomian analysis, causation involves a potentiality becoming actuality, and an external cause is necessary to tip something into actuality. A universe is obviously possible (if it were impossible we wouldn't be here), so on this analysis an external cause is needed to make the universe actual.
So it seems possible, in principle at least, that both Craig and Carroll are right: differing definitions of "cause" may yield different conclusions about whether a self-contained universe requires a cause.
But certainly, how we think about causation affect our ideas on whether a self-contained universe needs a cause.
(By the way, this issue is independent of whether the universe in question has a beginning or not. While it might seem intuitively that a universe that begins is more guilty of "just popping" into existence, it has often been argued that a universe that is infinite in time is no less in need of some sort of external cause or explanation.)
On Hume's regularity view, causation is a matter of constant conjunction: to know that A causes B, we need to know that A is always followed by B. So what we need to do is to make lots of observations of deities, and if "Let there be light!" is always followed by a universe popping into existence, then we can conclude that gods cause universes.
On Wesley Salmon's analysis, a causal process is one that can carry some sort of a mark that transmits from the cause to the effect. It would seem, though, that if God is perfect, God is impossible to mark. Thus, we could never tell if a mark can be passed to the universe.
Another modern approach is to take causation to involve the transmission of a conserved quantity, like energy or momentum. But neither the theist not the atheist would claim that a universe that has a beginning in time was initiated by a transfer of pre-existing energy, so in this case there is no possibility of a cause.
On the Aristotelian-Thomian analysis, causation involves a potentiality becoming actuality, and an external cause is necessary to tip something into actuality. A universe is obviously possible (if it were impossible we wouldn't be here), so on this analysis an external cause is needed to make the universe actual.
So it seems possible, in principle at least, that both Craig and Carroll are right: differing definitions of "cause" may yield different conclusions about whether a self-contained universe requires a cause.
Saturday, February 8, 2014
Against Cause
In an attempt to gain a better understanding of modern views of causation, I've been reading Causation and Explanation, by Stathis Psillos. So far what I've learned is this: modern views of causation are a mess. There are intrinsic and extrinsic views, reductive and non-reductive views, the "marker" view, and the "conserved quantity" view. There is no agreement on whether Hume's regularity view of causation needs to be improved upon, or abandoned and replaced with something quite different.
Over at The Edge, there is the annual Edge Question event. This year's question: What scientific idea is ready for retirement? Go read the responses, they're very interesting and very short.
Among the responses, W. Daniel Hillis suggests we retire the concept of cause and effect. Causes, he suggests, are just parts of a story we tell about the world.
So maybe the reason philosophers can't find a decent characterization of causes is that they are not really a part of the universe. Rather, they are something we invent - maybe in a rather haphazard and inconsistent manner - to help us track important aspects of the world around us.
Over at The Edge, there is the annual Edge Question event. This year's question: What scientific idea is ready for retirement? Go read the responses, they're very interesting and very short.
Among the responses, W. Daniel Hillis suggests we retire the concept of cause and effect. Causes, he suggests, are just parts of a story we tell about the world.
Science is a rich source of powerful explanatory stories. For example, Newton explained how a force causes a mass to accelerate. This gives us a story of how an apple drops from a tree or a planet circles around the Sun. It allows us to decide how hard the rocket engine needs to push to get it to the Moon. Models of causation allow us to design complex machines like factories and computers that have fabulously long chains of causes and effects. They convert inputs into the outputs that we want.These stories can be very useful, but they can also be misleading.
It is tempting to believe that our stories of causes and effects are how the world works. Actually, they are just a framework that we use to manipulate the world and to construct explanations for the convenience of our own understanding.
So maybe the reason philosophers can't find a decent characterization of causes is that they are not really a part of the universe. Rather, they are something we invent - maybe in a rather haphazard and inconsistent manner - to help us track important aspects of the world around us.
Sunday, December 22, 2013
Physics Lies!
I've been bashing the theists for a while, so I'm going to take a break and bash an atheist for a change.
Nancy Cartwright is the author of How the Laws of Physics Lie, and is apparently an influential philosopher. Kitcher mentions her in his Mind and Cosmos review, she is regularly included in anthologies of important papers in the philosophy of science, and her term "Dappled World" (borrowed from Manley Hopkins, according to Kitcher) seems to have become a sort of rallying point for modern philosophical views of science.
I think her work is shoddy and unconvincing.
OK, choosing that title for her book is like waving a cape in front of a bull, I suppose. But I really tried to give her a fair hearing, honest I did. Readers of this blog can, I suppose, judge how good I am at giving a fair hearing to views I disagree with. But let me try to present her argument before I tear it apart.
The Laws of Physics Lie
In Essay 3 of the book, Cartwright lays out the case that the laws of physics are not true, or, to the extent they are true, they are not interesting. In fact, they are not even approximately true. Why?
She illustrates with Newton's law of universal gravitation. For the definition of this law she quotes Feynman:
For instance, in an atom, the law of gravitation is swamped by the Coulomb force and so the former is not even approximately true.
Notice that she is not complaining about extreme cases where Newtonian gravitation must be replaced by General Relativity. Her complaint is that the law doesn't state a fact: except, perhaps, in a universe completely empty except for two uncharged objects.
She considers an alternate version of NG1 that uses a prefatory clause to correct the deficiency:
This, she allows, may be a true law, but it is not a very interesting one, for in reality objects have both kinds of properties (mass and electric charge) and so NG2 has no (or very few) applications in reality.
From a physicist's point of view, this is all very wrong-headed. First of all, since she is talking about combining different influences, the law she ought to be talking about is Newton's second law of motion:
With this change, I submit, we have a law that is at least approximately true, with no further need of ceteris paribus clauses.
This is such a simple solution to Cartwright's difficulty that it's hard to believe she missed it. However, she does go on to discuss the law of vector composition of forces, and then to consider a suggestion of Lewis Creary that is similar to NG3. Let's consider what she has to say about these issues.
Vector Addition
Cartwright admits that physicists have an answer to the question of combining forces: she calls it the "vector addition story."
But this is quite obviously false. Consider, for example, a spring that is subject to equal and opposite forces on its two ends:
The net force is zero, so the center of mass of the spring doesn't accelerate. But the spring is compressed - the component forces have a real, physical effect.
Try telling this guy that the component forces aren't real:
Cartwright is essentially saying "'two apples plus one apple equals three apples' can't be true, because if the two apples and the one apple are real, and the three apples are real, then I would have six apples, not three." But this is just silly: two apples plus one apple equals three apples because that's simply what addition means, when applied to apples. Similarly, in the vector addition of forces, two real, occurrent forces can be added to make a real net force, because that's simply what it means to combine two forces.
For this, Cartwright deserves an award for Worst Misuse of Mathematics By a Professional Philosopher Not Named Craig.
Causal Action
Cartwright then turns to Creary, who claims that there are two types of physical laws: laws of causal influence and laws of causal action. Though she doesn't say so, in Newton's mechanics, the law of causal action is good old F = ma (NA).
Apparently Cartwright doesn't know about quantum mechanics, where Schroedinger's equation gives a general law, or quantum field theory, where the Lagrangian path integral does the same.
Anyway, it makes no sense to claim that there are no true fundamental laws of physics, except for those few cases where the laws are both fundamental and true. Naturally, if there are general laws of action, and if physics is a more or less unified subject, then we would expect the general laws to be few. The fact that there are only a few such fundamental laws actually shows the strength of the reductionist thesis rather than the opposite.
On the other hand, if her point is just that most of the time, working physicists are not dealing with the fundamental laws, but with some approximations to them, or phenomenological laws that are not fundamental, then I would agree with her, but find the point trite and uninteresting. These physicists wouldn't ever claim that their approximations are true in all cases.
Actually, Cartwright does know about quantum mechanics, because in the very next section she discusses a quantum example: the spectrum of a carbon atom. What she says here is so pathetic that I can't bear to grind through it point by point. Essentially, she again ignores the general law of action (Schroedinger's equation) in order to make her point that there is no general law of action.
At first I thought Cartwright had simply not bothered to understand the physics before she began drawing philosophical conclusions. But later in the book she shows a detailed understanding of some much more difficult areas of physics, so that doesn't seem to be the problem.
The only other explanation I can think of for these egregious errors is that Cartwright is working with a pre-conceived agenda, such that all the examples are contorted so as to support her thesis.
This is no way to ground a philosophical world view.
Nancy Cartwright is the author of How the Laws of Physics Lie, and is apparently an influential philosopher. Kitcher mentions her in his Mind and Cosmos review, she is regularly included in anthologies of important papers in the philosophy of science, and her term "Dappled World" (borrowed from Manley Hopkins, according to Kitcher) seems to have become a sort of rallying point for modern philosophical views of science.
I think her work is shoddy and unconvincing.
OK, choosing that title for her book is like waving a cape in front of a bull, I suppose. But I really tried to give her a fair hearing, honest I did. Readers of this blog can, I suppose, judge how good I am at giving a fair hearing to views I disagree with. But let me try to present her argument before I tear it apart.
The Laws of Physics Lie
In Essay 3 of the book, Cartwright lays out the case that the laws of physics are not true, or, to the extent they are true, they are not interesting. In fact, they are not even approximately true. Why?
She illustrates with Newton's law of universal gravitation. For the definition of this law she quotes Feynman:
(NG1) The Law of Gravitation is that two bodies exert a force between each other which varies inversely as the square of the distance between them, and varies directly as the product of their masses.Then she asks, and answers:
Does this law truly describe how bodies behave?Why not? Well, she says, two bodies may have electric charges, and so the force exerted by one on the other is given neither by NG1 nor by Coulomb's law of electric force, but by a combination of the two. Therefore
Assuredly not.
These two laws are not true: worse, they are not even approximately true.
For instance, in an atom, the law of gravitation is swamped by the Coulomb force and so the former is not even approximately true.
Notice that she is not complaining about extreme cases where Newtonian gravitation must be replaced by General Relativity. Her complaint is that the law doesn't state a fact: except, perhaps, in a universe completely empty except for two uncharged objects.
She considers an alternate version of NG1 that uses a prefatory clause to correct the deficiency:
(NG2) If there are no forces other than gravitational forces at work, then two bodies exert a force between each other which varies inversely as the square of the distance between them, and varies directly as the product of their masses.
This, she allows, may be a true law, but it is not a very interesting one, for in reality objects have both kinds of properties (mass and electric charge) and so NG2 has no (or very few) applications in reality.
From a physicist's point of view, this is all very wrong-headed. First of all, since she is talking about combining different influences, the law she ought to be talking about is Newton's second law of motion:
(NA) The acceleration of an object is proportional to the net force and inversely proportional to its mass.Somehow, she completely avoids mentioning this law anywhere in the chapter (though she mentions it obliquely in considering a related objection, as we will see below). Since she doesn't mention NA, I don't know whether she considers this one of laws that is not even approximately true. But you can't talk about gravitational and electric forces combining without it. With this framework in mind, there is an obvious alternative to NG1 and NG2:
(NG3) For two massive bodies, there is a contribution to the net force that varies inversely as the square of the distance between them, and varies directly as the product of their masses.
With this change, I submit, we have a law that is at least approximately true, with no further need of ceteris paribus clauses.
This is such a simple solution to Cartwright's difficulty that it's hard to believe she missed it. However, she does go on to discuss the law of vector composition of forces, and then to consider a suggestion of Lewis Creary that is similar to NG3. Let's consider what she has to say about these issues.
Vector Addition
Cartwright admits that physicists have an answer to the question of combining forces: she calls it the "vector addition story."
The vector addition story is, I admit, a nice one. But it is just a metaphor. We add forces... when we do calculations. Nature does not 'add' forces.For the component forces are not there, in any but a metaphorical sense, to be added....For Cartwright, the individual component forces are not real. Only the net force is real.
But this is quite obviously false. Consider, for example, a spring that is subject to equal and opposite forces on its two ends:
The net force is zero, so the center of mass of the spring doesn't accelerate. But the spring is compressed - the component forces have a real, physical effect.
Try telling this guy that the component forces aren't real:
Cartwright is essentially saying "'two apples plus one apple equals three apples' can't be true, because if the two apples and the one apple are real, and the three apples are real, then I would have six apples, not three." But this is just silly: two apples plus one apple equals three apples because that's simply what addition means, when applied to apples. Similarly, in the vector addition of forces, two real, occurrent forces can be added to make a real net force, because that's simply what it means to combine two forces.
For this, Cartwright deserves an award for Worst Misuse of Mathematics By a Professional Philosopher Not Named Craig.
Causal Action
Cartwright then turns to Creary, who claims that there are two types of physical laws: laws of causal influence and laws of causal action. Though she doesn't say so, in Newton's mechanics, the law of causal action is good old F = ma (NA).
On Creary's account, Coulomb's law and the law of gravity come out true because they correctly describe what influences are produced.... The vector addition law then combines the separate influences to predict what motions will occur.
This seems to me to be a plausible account of how a lot of causal explanation is structured. But as a defence of the truth of fundamental laws, it has two important drawbacks. First, in many cases there are no general laws of interaction... In fact, classical mechanics may well be the only discipline where a general law of action is always available.
Apparently Cartwright doesn't know about quantum mechanics, where Schroedinger's equation gives a general law, or quantum field theory, where the Lagrangian path integral does the same.
Anyway, it makes no sense to claim that there are no true fundamental laws of physics, except for those few cases where the laws are both fundamental and true. Naturally, if there are general laws of action, and if physics is a more or less unified subject, then we would expect the general laws to be few. The fact that there are only a few such fundamental laws actually shows the strength of the reductionist thesis rather than the opposite.
On the other hand, if her point is just that most of the time, working physicists are not dealing with the fundamental laws, but with some approximations to them, or phenomenological laws that are not fundamental, then I would agree with her, but find the point trite and uninteresting. These physicists wouldn't ever claim that their approximations are true in all cases.
Actually, Cartwright does know about quantum mechanics, because in the very next section she discusses a quantum example: the spectrum of a carbon atom. What she says here is so pathetic that I can't bear to grind through it point by point. Essentially, she again ignores the general law of action (Schroedinger's equation) in order to make her point that there is no general law of action.
At first I thought Cartwright had simply not bothered to understand the physics before she began drawing philosophical conclusions. But later in the book she shows a detailed understanding of some much more difficult areas of physics, so that doesn't seem to be the problem.
The only other explanation I can think of for these egregious errors is that Cartwright is working with a pre-conceived agenda, such that all the examples are contorted so as to support her thesis.
This is no way to ground a philosophical world view.
Thursday, December 19, 2013
A Natural Reduction
One of the great advantages of the naturalist world view is how it all hangs together. The workings of the mind can be explained in terms of the workings of the brain, which can be explained in terms of the workings of the brain cells, which can be explained in terms of the electrical and chemical properties of molecules, which can be explained in terms of the physical properties of the particles of which those molecules are composed. And the same goes for anything else in the universe: stars, moons, clovers....
Now, I will admit that some of the links in that proposed chain of explanation are not as strong as others: the mind-brain link, for example. But the overall scheme seems sound, and the naturalistic world view can count innumerable successes as evidence of its truth: the technologies of transportation, agriculture, communication, medicine, and psychiatry, to mention just a few. Put this against the abject failure of alternative ways of thinking: what did Christianity (just to pick on one alternative) accomplish in the 1500 years before scientific thinking arose?
At any rate, even when precise explanations are lacking, there doesn't seem to be any strong argument why the gaps cannot be filled out in a naturalistic way.
It seems, though, that many atheist philosophers are no longer satisfied with this reductionistic picture. The recent book Mind and Cosmos, by atheist philosopher Thomas Nagel, argues that there are aspects of subjective experience that can't be explained by reductionistic means. (Short version here.) Another atheist philosopher, Philip Kitcher, whom I have the greatest respect for, disagrees with Nagel but seems to agree that the reductionist program has not accomplished the task it set out to do. "Unity fails at both ends," writes Kitcher.
For once, I agree with Professor Feser: if naturalism fails to give us a unified picture of everything, then it is time to abandon naturalism and seek a different explanation, rather than to cling to a failed program.
But I am not as pessimistic as these philosophers. Perhaps that's merely ignorance on my part. But some of the anti-reductionist arguments I've come across seem just silly, and, as I already said, there don't seem to be any good arguments for the impossibility of naturalistic explanation. I remain a hard-core reductionist, and I'm going to try to defend that view.
Next: Do the laws of physics lie?
Now, I will admit that some of the links in that proposed chain of explanation are not as strong as others: the mind-brain link, for example. But the overall scheme seems sound, and the naturalistic world view can count innumerable successes as evidence of its truth: the technologies of transportation, agriculture, communication, medicine, and psychiatry, to mention just a few. Put this against the abject failure of alternative ways of thinking: what did Christianity (just to pick on one alternative) accomplish in the 1500 years before scientific thinking arose?
At any rate, even when precise explanations are lacking, there doesn't seem to be any strong argument why the gaps cannot be filled out in a naturalistic way.
It seems, though, that many atheist philosophers are no longer satisfied with this reductionistic picture. The recent book Mind and Cosmos, by atheist philosopher Thomas Nagel, argues that there are aspects of subjective experience that can't be explained by reductionistic means. (Short version here.) Another atheist philosopher, Philip Kitcher, whom I have the greatest respect for, disagrees with Nagel but seems to agree that the reductionist program has not accomplished the task it set out to do. "Unity fails at both ends," writes Kitcher.
For once, I agree with Professor Feser: if naturalism fails to give us a unified picture of everything, then it is time to abandon naturalism and seek a different explanation, rather than to cling to a failed program.
But I am not as pessimistic as these philosophers. Perhaps that's merely ignorance on my part. But some of the anti-reductionist arguments I've come across seem just silly, and, as I already said, there don't seem to be any good arguments for the impossibility of naturalistic explanation. I remain a hard-core reductionist, and I'm going to try to defend that view.
Next: Do the laws of physics lie?
Saturday, November 23, 2013
Guest Post: Purity of Form and Function
While I'm gearing up for my assault on Mount Kripke, here's a guest post from Richard Wein.
Hi everyone. Robert's invited me to make a guest post on the subject of James Ross's paper "Immaterial Aspects of Thought". The resulting post is rather long, partly because there's a lot of linguistic confusion to be cleared up. I hope I can dispel a little of that confusion.
At the core of Ross's argument is his insistence that our logical thinking must involve "pure forms". He then argues that physical processes can't have such forms, and so logical thinking must involve more than just physical processes. I see no good reason to accept that we need any such forms.
Ross's concept of "pure forms" is hardly explained, and remains mysterious to me. He says, for example, that squaring involves thinking in the form "N X N = N^2". He doesn't seem to mean that we must think such words to ourselves. He seems to have in mind some unseen form, possibly Platonistic. In Section III, he talks briefly about "Platonistic definitions", and perhaps this example is one such.
It may help here if I briefly give my own physicalist view, so that I can consider Ross's in contrast to it. I say that the only verbal forms that exist are the sorts that we observe, such as those in writing, speech and conscious thought. These observed verbal forms are produced by non-conscious, non-verbal physical cognitive processes. Of course there's a lot more to be said about how this happens, and particularly about consciousness, but these are not issues that Ross raises. He is not, for example, making an argument from consciousness. Nor is he making an inference to the best explanation, where we must consider the relative merits of his explanation and a physicalist one. He is making a purely eliminative argument, and so the onus is on him to eliminate physicalist alternatives, not on me to elaborate on them.
The claim that our thinking must take the form of definitions in this sense seems to lead to a problem of infinite regress. If squaring is defined in terms of a more basic operation, multiplying, then how is multiplying defined? And so on. But I won't dwell on this point, because Ross's "pure forms" are so mysterious that I doubt I could make any specific positive criticism stick. My point is that we just don't need anything of the sort Ross is insisting on. He gives us no reason to think that the sorts of physical processes I've mentioned are incapable of producing everything that we actually observe. I don't think he even tries to show that. His only response to views like mine seems to be that, on such views, the actual processes we currently call "squaring" wouldn't be "real" squaring, but only "simulated" squaring.
This response is a confused use of language, mistaking an empty verbal distinction for a substantive one. First, regardless of whether we call such operations "real" or "simulated", if they're sufficient to deliver everything we actually observe--and Ross doesn't seem to argue the contrary--then there's no reason to think we need anything more. That in itself should suggest some confusion on Ross's part.
The distinction Ross was originally making was between processes that involve "pure forms" and those that don't. If the distinction he's now making between "real" and "simulated" processes is just a translation of the original distinction into different words, then the translation achieves nothing. He's just re-asserting his unsupported claim that we need such pure forms, but doing it in confusing new words. If, on the other hand, the new distinction were genuinely different from the original one, Ross would actually have to demonstrate that denying pure forms entails denying real squaring. He would have to make a substantive argument, and he wouldn't be able to do that without clarifying the meaning of his new distinction. In fact he makes no such argument (or clarification). He simply puts the words "we only simulate" into the mouth of the denier, as if it's indisputable that denying pure forms entails denying real squaring. So it's pretty clear that this is just a confusing terminological switch, masquerading as a substantive argument. The appearance of having achieved something arises through conflation of a weaker sense of the words (in which they are just a translation of the original claim) with a stronger sense (which has the appearance of a more irresistible claim). To accept Ross's conclusion on this basis is to commit a fallacy of equivocation.
Unlike Ross's denier, I don't say that we don't "really" square. Neither do I say that we do "really" square. The word "really" is misleading here. If denying that we "really" square is to be taken as just another way of saying that we don't think in "pure forms", then I prefer to say--more directly--that we don't think in pure forms.
There ends my main response to Ross's argument. But I'd likely briefly to address some other aspects of his paper which are liable to cause confusion.
Ross uses the term "pure forms" interchangeably with "pure functions", and I'm afraid this translation may have led to a conflation of these concepts of his own with the concept of a mathematical function in the ordinary sense of that term. Mathematical functions are purely abstract, and don't exist in anything like the sense that physical objects do. Pairs of mathematical functions like addition and quaddition are correctly called "non-equivalent". To call them "incompossible" would be a kind of category error, mistakenly implying that it makes any sense to ask whether they can co-exist. Ross's talk of incompossible pure forms/functions is further support for the conclusion that he sees these as having a more real sort of existence than do mathematical functions (in the ordinary sense).
I have no idea what it could mean for the process of squaring to take the form of a mathematical function. The messy, fallible real-world processes that we call "squaring" are quite a different thing from the abstract function that mathematicians call "f(x)=x^2". Talk of a process taking the form of a mathematical function seems to me like a category error, an attempt to transfer properties inappropriately between pure abstractions and real processes. Of course, during the process of performing an arithmetic operation, some definition of a function (some form of words) might be produced, e.g. in conscious thought. But that's a production of the process, and not the process itself or the form of the process. Moreover, simple arithmetic doesn't always involve giving ourselves any definitions, rules or instructions for how to proceed. The answers can come to mind (or speech) as the result of non-verbal non-conscious processes, without any verbal reasoning. That's why there's no infinite regress of definitions, rules or instructions.
You may have noticed that I haven't mentioned determinacy. Ross's argument is primarily made in terms of pure forms. But at times he translates into the language of determinacy, and his summary argument is expressed in such language. This translation into the language of determinacy serves no useful purpose, but creates further opportunities for confusion, because Ross's "indeterminacy" is easily conflated with other senses of the word, and Ross himself encourages such conflation by appealing to work on other sorts of indeterminacy (and even "underdetermination") which have little to do with his argument.
Since I don't think we need any "realization" of "pure forms", and I would question whether the the concept is even coherent, there's no point in my addressing Section II of the paper in detail. But I think it would be useful briefly to give a clearer account of the addition/quaddition scenario and "indeterminacy". Ross employs a variant of Kripke's quaddition function, where the differentiating point (instead of 57) is set to a number of years greater than the lifetime of the universe. That example seems peculiar to me, as I can see no reason why a system can't calculate a number of years greater than that lifetime. So I'll take a slightly different example of my own. Let the differentiating point be a number greater than any that can be represented by a given calculator. Then there's a sense in which the calculator equally well "realizes" addition and quaddition. That sense is that the calculator gives the answers for quaddition as well as it gives them for addition. As long as we don't confuse ourselves with talk of "pure forms", there's nothing remarkable about this. Ross wants to say that the calculator can't realize two different functions, so it must realize neither. But in the sense of "realize" that I've just used, there's no problem with saying that it realizes both, and the fact that it realizes both has no substantive significance.
Given that we're not talking about epistemological or quantum indeterminacy, any indeterminacy lies just in the fact that often our categories are not sufficiently well-defined for us to be able to assign a given state of affairs to a single category. For example, for some people there is no fact of the matter as to whether they are best described as children or adults. That's just a limitation of language. Indeterminacy is significant for our understanding of how language works, and for making sure we use language in ways that don't cause confusion, but it doesn't have any substantive, non-linguistic significance. Some people are reading far too much into indeterminacy.
Hi everyone. Robert's invited me to make a guest post on the subject of James Ross's paper "Immaterial Aspects of Thought". The resulting post is rather long, partly because there's a lot of linguistic confusion to be cleared up. I hope I can dispel a little of that confusion.
At the core of Ross's argument is his insistence that our logical thinking must involve "pure forms". He then argues that physical processes can't have such forms, and so logical thinking must involve more than just physical processes. I see no good reason to accept that we need any such forms.
Ross's concept of "pure forms" is hardly explained, and remains mysterious to me. He says, for example, that squaring involves thinking in the form "N X N = N^2". He doesn't seem to mean that we must think such words to ourselves. He seems to have in mind some unseen form, possibly Platonistic. In Section III, he talks briefly about "Platonistic definitions", and perhaps this example is one such.
It may help here if I briefly give my own physicalist view, so that I can consider Ross's in contrast to it. I say that the only verbal forms that exist are the sorts that we observe, such as those in writing, speech and conscious thought. These observed verbal forms are produced by non-conscious, non-verbal physical cognitive processes. Of course there's a lot more to be said about how this happens, and particularly about consciousness, but these are not issues that Ross raises. He is not, for example, making an argument from consciousness. Nor is he making an inference to the best explanation, where we must consider the relative merits of his explanation and a physicalist one. He is making a purely eliminative argument, and so the onus is on him to eliminate physicalist alternatives, not on me to elaborate on them.
The claim that our thinking must take the form of definitions in this sense seems to lead to a problem of infinite regress. If squaring is defined in terms of a more basic operation, multiplying, then how is multiplying defined? And so on. But I won't dwell on this point, because Ross's "pure forms" are so mysterious that I doubt I could make any specific positive criticism stick. My point is that we just don't need anything of the sort Ross is insisting on. He gives us no reason to think that the sorts of physical processes I've mentioned are incapable of producing everything that we actually observe. I don't think he even tries to show that. His only response to views like mine seems to be that, on such views, the actual processes we currently call "squaring" wouldn't be "real" squaring, but only "simulated" squaring.
This response is a confused use of language, mistaking an empty verbal distinction for a substantive one. First, regardless of whether we call such operations "real" or "simulated", if they're sufficient to deliver everything we actually observe--and Ross doesn't seem to argue the contrary--then there's no reason to think we need anything more. That in itself should suggest some confusion on Ross's part.
The distinction Ross was originally making was between processes that involve "pure forms" and those that don't. If the distinction he's now making between "real" and "simulated" processes is just a translation of the original distinction into different words, then the translation achieves nothing. He's just re-asserting his unsupported claim that we need such pure forms, but doing it in confusing new words. If, on the other hand, the new distinction were genuinely different from the original one, Ross would actually have to demonstrate that denying pure forms entails denying real squaring. He would have to make a substantive argument, and he wouldn't be able to do that without clarifying the meaning of his new distinction. In fact he makes no such argument (or clarification). He simply puts the words "we only simulate" into the mouth of the denier, as if it's indisputable that denying pure forms entails denying real squaring. So it's pretty clear that this is just a confusing terminological switch, masquerading as a substantive argument. The appearance of having achieved something arises through conflation of a weaker sense of the words (in which they are just a translation of the original claim) with a stronger sense (which has the appearance of a more irresistible claim). To accept Ross's conclusion on this basis is to commit a fallacy of equivocation.
Unlike Ross's denier, I don't say that we don't "really" square. Neither do I say that we do "really" square. The word "really" is misleading here. If denying that we "really" square is to be taken as just another way of saying that we don't think in "pure forms", then I prefer to say--more directly--that we don't think in pure forms.
There ends my main response to Ross's argument. But I'd likely briefly to address some other aspects of his paper which are liable to cause confusion.
Ross uses the term "pure forms" interchangeably with "pure functions", and I'm afraid this translation may have led to a conflation of these concepts of his own with the concept of a mathematical function in the ordinary sense of that term. Mathematical functions are purely abstract, and don't exist in anything like the sense that physical objects do. Pairs of mathematical functions like addition and quaddition are correctly called "non-equivalent". To call them "incompossible" would be a kind of category error, mistakenly implying that it makes any sense to ask whether they can co-exist. Ross's talk of incompossible pure forms/functions is further support for the conclusion that he sees these as having a more real sort of existence than do mathematical functions (in the ordinary sense).
I have no idea what it could mean for the process of squaring to take the form of a mathematical function. The messy, fallible real-world processes that we call "squaring" are quite a different thing from the abstract function that mathematicians call "f(x)=x^2". Talk of a process taking the form of a mathematical function seems to me like a category error, an attempt to transfer properties inappropriately between pure abstractions and real processes. Of course, during the process of performing an arithmetic operation, some definition of a function (some form of words) might be produced, e.g. in conscious thought. But that's a production of the process, and not the process itself or the form of the process. Moreover, simple arithmetic doesn't always involve giving ourselves any definitions, rules or instructions for how to proceed. The answers can come to mind (or speech) as the result of non-verbal non-conscious processes, without any verbal reasoning. That's why there's no infinite regress of definitions, rules or instructions.
You may have noticed that I haven't mentioned determinacy. Ross's argument is primarily made in terms of pure forms. But at times he translates into the language of determinacy, and his summary argument is expressed in such language. This translation into the language of determinacy serves no useful purpose, but creates further opportunities for confusion, because Ross's "indeterminacy" is easily conflated with other senses of the word, and Ross himself encourages such conflation by appealing to work on other sorts of indeterminacy (and even "underdetermination") which have little to do with his argument.
Since I don't think we need any "realization" of "pure forms", and I would question whether the the concept is even coherent, there's no point in my addressing Section II of the paper in detail. But I think it would be useful briefly to give a clearer account of the addition/quaddition scenario and "indeterminacy". Ross employs a variant of Kripke's quaddition function, where the differentiating point (instead of 57) is set to a number of years greater than the lifetime of the universe. That example seems peculiar to me, as I can see no reason why a system can't calculate a number of years greater than that lifetime. So I'll take a slightly different example of my own. Let the differentiating point be a number greater than any that can be represented by a given calculator. Then there's a sense in which the calculator equally well "realizes" addition and quaddition. That sense is that the calculator gives the answers for quaddition as well as it gives them for addition. As long as we don't confuse ourselves with talk of "pure forms", there's nothing remarkable about this. Ross wants to say that the calculator can't realize two different functions, so it must realize neither. But in the sense of "realize" that I've just used, there's no problem with saying that it realizes both, and the fact that it realizes both has no substantive significance.
Given that we're not talking about epistemological or quantum indeterminacy, any indeterminacy lies just in the fact that often our categories are not sufficiently well-defined for us to be able to assign a given state of affairs to a single category. For example, for some people there is no fact of the matter as to whether they are best described as children or adults. That's just a limitation of language. Indeterminacy is significant for our understanding of how language works, and for making sure we use language in ways that don't cause confusion, but it doesn't have any substantive, non-linguistic significance. Some people are reading far too much into indeterminacy.
Tuesday, November 19, 2013
Grue Some More
The second point Ross brings up in support of the indeterminacy of the physical is Goodman's Grue Argument. This one is easily dealt with.
Goodman defines something as "grue" if it is first observed before Jan1, 2025 (say) and is green, or is first observed after Jan 1, 2025 and is blue. He uses this to make a point about induction: any evidence we cite as evidence for the proposition "all emeralds are green" is also evidence for the proposition "all emeralds are grue." Thus, the grue problem casts doubt on the rationality of inductive conclusions.
So we see that Goodman's point was about induction, not indeterminacy. But this is really unimportant for Ross's argument, because Ross doesn't actually use the grue argument in any essential way. Rather, he either cites grue as an example of the problem of limited data, or as an analogy to Kripke's quaddition argument. For instance, Ross writes:
Goodman defines something as "grue" if it is first observed before Jan1, 2025 (say) and is green, or is first observed after Jan 1, 2025 and is blue. He uses this to make a point about induction: any evidence we cite as evidence for the proposition "all emeralds are green" is also evidence for the proposition "all emeralds are grue." Thus, the grue problem casts doubt on the rationality of inductive conclusions.
So we see that Goodman's point was about induction, not indeterminacy. But this is really unimportant for Ross's argument, because Ross doesn't actually use the grue argument in any essential way. Rather, he either cites grue as an example of the problem of limited data, or as an analogy to Kripke's quaddition argument. For instance, Ross writes:
A decisive reason why a physical process cannot be determinate among incompossible abstract functions is "amplified grueness": a physical process, however short or long, however few or many outputs, is compatible with counterfactually opposed predicates; even the entire cosmos is. Since such predicates can name functions from "input to output" for every change, any physical process is indeterminate among opposed functions. This is like the projection of a curve from a finite sample of points: any choice has an incompatible competitor.But the problem of limited data, as we have seen, is irrelevant for the indeterminacy question. So the grue point devolves onto the Kripke/quaddition point, which I will consider next.
Friday, November 15, 2013
A Pointless Point about Data Points
I've been, and continue to be, busy with my real work, so I have to apologize if these posts dribble out slowly, a bit at a time, rather than in one long, well-thought-out post the way Prof. Feser does. But maybe it will actually be an advantage to try to clear up one point at a time.
Ross gives three main arguments to support his claim B: "No physical system is determinate." These are:
The problem of limited data (PLD) is pretty easy to state. Suppose I have some system from which I can take data, and I am trying to determine what function the system is following in order to produce the data. If I take a limited number (say a finite number) of input-output pairs, there will be an infinite number of functions which fit the given data points. For example, suppose I have only three data points. Then there is exactly one quadratic function that will exactly fit those three points. But I could also fit the data with a cubic function, or a quartic function, or a polynomial of any higher degree, or an exponential function times an appropriate polynomial, etc.
Now, how does this help Ross establish his (B)? Actually, it doesn't help at all. The mere fact that I have a limited amount of data doesn't tell me anything about the process that is producing that data. Since the PLD applies equally to determinate and indeterminate systems, it can't. This seems completely obvious to me, but since it seems to be a point of contention, I will spell it out.
Suppose I get some set of N input-output pairs from a determinate process. (For Ross, this means having a human compute them.) Let someone else give me N input-output pairs from an indeterminate process that is simulating (in Ross's sense) the first process. (For Ross, this could be a computer.) Now, since Ross allows that the indeterminate process can simulate the determinate process very closely, the two data sets will be identical. (This is easy to see if we say the process in question is addition: the computer and the human will give the same outputs for the same inputs. Unless, of course, the human makes a mistake.)
Since the N input-output pairs are identical whether I get them from a determinate or an indeterminate process, there is obviously no way I can tell from the data which sort of process produced that data.
Now let's introduce the PLD. Clearly, it applies to both processes. So if (as Ross claims) the PLD provides support for the claim that the purely physical process is indeterminate, then it also provides support for the claim that the human-generated process is indeterminate. So the PLD strengthens Ross's case for B to the exact extent that it weakens his case for A (that humans are capable of determinate processes). In other words, it doesn't help him at all.
This is what I meant when I wrote that Ross's arguments don't go beyond epistemology. The PLD says I can have only limited knowledge about the process that produced the data. But it says nothing at all about the metaphysical properties of that process.
Ross gives three main arguments to support his claim B: "No physical system is determinate." These are:
- Kripke's addition/quaddition argument.
- Goodman's grue argument.
- The problem of limited data.
The problem of limited data (PLD) is pretty easy to state. Suppose I have some system from which I can take data, and I am trying to determine what function the system is following in order to produce the data. If I take a limited number (say a finite number) of input-output pairs, there will be an infinite number of functions which fit the given data points. For example, suppose I have only three data points. Then there is exactly one quadratic function that will exactly fit those three points. But I could also fit the data with a cubic function, or a quartic function, or a polynomial of any higher degree, or an exponential function times an appropriate polynomial, etc.
Now, how does this help Ross establish his (B)? Actually, it doesn't help at all. The mere fact that I have a limited amount of data doesn't tell me anything about the process that is producing that data. Since the PLD applies equally to determinate and indeterminate systems, it can't. This seems completely obvious to me, but since it seems to be a point of contention, I will spell it out.
Suppose I get some set of N input-output pairs from a determinate process. (For Ross, this means having a human compute them.) Let someone else give me N input-output pairs from an indeterminate process that is simulating (in Ross's sense) the first process. (For Ross, this could be a computer.) Now, since Ross allows that the indeterminate process can simulate the determinate process very closely, the two data sets will be identical. (This is easy to see if we say the process in question is addition: the computer and the human will give the same outputs for the same inputs. Unless, of course, the human makes a mistake.)
Since the N input-output pairs are identical whether I get them from a determinate or an indeterminate process, there is obviously no way I can tell from the data which sort of process produced that data.
Now let's introduce the PLD. Clearly, it applies to both processes. So if (as Ross claims) the PLD provides support for the claim that the purely physical process is indeterminate, then it also provides support for the claim that the human-generated process is indeterminate. So the PLD strengthens Ross's case for B to the exact extent that it weakens his case for A (that humans are capable of determinate processes). In other words, it doesn't help him at all.
This is what I meant when I wrote that Ross's arguments don't go beyond epistemology. The PLD says I can have only limited knowledge about the process that produced the data. But it says nothing at all about the metaphysical properties of that process.
Tuesday, November 5, 2013
Goodbye, Hilda
I'd like to thank Prof. Feser for his continued patience in responding to my critique of Ross's argument. I've been very busy, but I finally had some time to look at his most recent response. He misconstrued the A, B, C, of my previous post (understandably, since I hadn't spelled them out clearly), and I began a long post carefully laying out the logic of my argument and why Feser's response didn't answer it. Then I realized that it did answer it, in spite of the misunderstanding about A, B, and C. The "purely physical" assumption is indeed the critical assumption in Ross's argument that I wasn't taking into account, and it does eliminate the Hilda objection in a non-question-begging way. I apologize to Prof. Feser for the unwarranted and unnecessary snark in my last post. I am hereby giving Hilda the boot.
I hope to return to my original epistemological objection (as time permits), but I wanted to get this apology out in a timely manner.
Crow is a dish best eaten warm.
I hope to return to my original epistemological objection (as time permits), but I wanted to get this apology out in a timely manner.
Crow is a dish best eaten warm.
Monday, October 21, 2013
A Head Scratcher
Ed Feser has responded again, and it's a puzzler.
I will ignore the first part of his post, in which he is once again arguing against some argument that is not the argument I made.
Next, Feser points out that my objection, even if it worked against Ross, was irrelevant against Feser's own version of the argument.
Well, I never said I was arguing against Feser's version of the argument, I explicitly stated I was critiquing Ross's argument. And that is what I will continue to do here, though I may return to Feser's version later if I have the time and inclination.
Feser then goes on to explain why he thinks his version of the argument is actually what Ross intended anyway. Specifically, he addresses what Ross means by saying the calculator is not adding. Now, Ross makes a clear and consistent distinction in his paper between true adding, which he elaborates as carrying out the "pure function" of addition, and what the calculator does, which is only "simulating addition." This is a crucial distinction for him, because his basic claim is that humans can execute pure functions, while any purely physical system cannot.
In my posts I have consistently (I hope) been using "adding" in Ross's first sense. I didn't think it was necessary to spell this out: since I was critiquing Ross's paper, I was using Ross's terminology, except where I explicitly stated otherwise. But to be clear, I will henceforth use ETPFOA ("executing the "pure function" of addition") instead of "adding."
So when I said that Ross denied that the machine was adding, I meant it was not ETPFOA. Feser, on the other hand, wrote,
So how does Feser respond? He quotes Ross's discussion of simulated addition, then writes:
Now it is very strange for Feser, who is a professional philosopher, to sweep aside an crucial distinction like this, as if it were unimportant. It is not true that Ross says the machine can add in the ETPFOA sense that both Ross and I are using. It is true that Ross says the machine can do something like adding - but only something that has the name of adding, and gets that name by analogy to ETPFOA, not because it is actually ETPFOAing.
Moreover, I don't see anywhere Ross says that the machine "adds relative to the intentions of the designers and users," as Feser claims. And what exactly is Feser claiming here? That the machine ETPFOAs relative to the intentions of the designers? Or that it only simulates adding relative them? OK, the machine taken together with the larger context results in addition "of a sort" - but of which sort? Again, Feser glosses over the crucial distinction.
You wouldn't think it possible, but there's actually worse to come. Quoting Feser again:
Later on, he continues in a similar vein:
This is just bizarre. Ed Feser, who revels in pointing out inconsistencies of the naturalists, is arguing that an inconsistency doesn't matter? Nor is this some trivial point of Rossian exegesis, as Feser implies: it's a basic contradiction in Ross's whole scheme.As I pointed out already, the distinction between ETPFOA and simulated adding is crucial to Ross's argument.
The logic of my Hilda example is straightforward. Ross says that humans can ETPFOA. Ross says that A, B, and C entail that a computer cannot ETPFOA. I claim that A, B, and C are true for Hilda, too. So A, B, and C entail that Hilda cannot ETPFOA.
With this contradiction, the whole argument falls to pieces. Now, you can argue that I am wrong: that A, B, and C are not true of Hilda. Or you can argue that there is some D that I missed that is true of the computer but not true of Hilda. But you can't say this example is irrelevant to the soundness of Ross's argument.
I will ignore the first part of his post, in which he is once again arguing against some argument that is not the argument I made.
Next, Feser points out that my objection, even if it worked against Ross, was irrelevant against Feser's own version of the argument.
For another thing, it is not just Ross’s views that are in question here, but mine. And I can assure Oerter that what I am claiming is (2) rather than (1). So, even if what he had to say in his latest post was relevant to the cogency of Ross’s version of the argument in question, it wouldn’t affect my own version of it.
Well, I never said I was arguing against Feser's version of the argument, I explicitly stated I was critiquing Ross's argument. And that is what I will continue to do here, though I may return to Feser's version later if I have the time and inclination.
Feser then goes on to explain why he thinks his version of the argument is actually what Ross intended anyway. Specifically, he addresses what Ross means by saying the calculator is not adding. Now, Ross makes a clear and consistent distinction in his paper between true adding, which he elaborates as carrying out the "pure function" of addition, and what the calculator does, which is only "simulating addition." This is a crucial distinction for him, because his basic claim is that humans can execute pure functions, while any purely physical system cannot.
In my posts I have consistently (I hope) been using "adding" in Ross's first sense. I didn't think it was necessary to spell this out: since I was critiquing Ross's paper, I was using Ross's terminology, except where I explicitly stated otherwise. But to be clear, I will henceforth use ETPFOA ("executing the "pure function" of addition") instead of "adding."
So when I said that Ross denied that the machine was adding, I meant it was not ETPFOA. Feser, on the other hand, wrote,
Ross is not denying, for example, that your pocket calculator is really adding rather than “quadding”....
So how does Feser respond? He quotes Ross's discussion of simulated addition, then writes:
So, Ross plainly does say that there is a sense in which the machine adds -- a sense that involves simulation, analogy, something that is “adding” in the way that what a puppet does is “walking.” How can that be given what he says in the passage Oerter quotes? The answer is obvious: The machine “adds” relative to the intentions of the designers and users, just as a puppet “walks” relative to the motions of the puppeteer. The puppet has no power to walk on its own and the machine has no power to do adding (as opposed to “quadding,” say) on its own. But something from outside the system -- the puppeteer in the one case, the designers and users in the other -- are also part of the larger context, and taken together with the physical properties of the system result in “walking” or “adding” of a sort.
In short, Ross says just what I said he says.
Now it is very strange for Feser, who is a professional philosopher, to sweep aside an crucial distinction like this, as if it were unimportant. It is not true that Ross says the machine can add in the ETPFOA sense that both Ross and I are using. It is true that Ross says the machine can do something like adding - but only something that has the name of adding, and gets that name by analogy to ETPFOA, not because it is actually ETPFOAing.
Moreover, I don't see anywhere Ross says that the machine "adds relative to the intentions of the designers and users," as Feser claims. And what exactly is Feser claiming here? That the machine ETPFOAs relative to the intentions of the designers? Or that it only simulates adding relative them? OK, the machine taken together with the larger context results in addition "of a sort" - but of which sort? Again, Feser glosses over the crucial distinction.
You wouldn't think it possible, but there's actually worse to come. Quoting Feser again:
Oerter insists that I am misunderstanding Ross here. As we will see in a moment, I am not misunderstanding him at all, but it is important to emphasize that even if I were, that would be completely irrelevant to the question of whether the argument for the immateriality of the intellect that we are debating is sound. For one thing, and quite obviously, whether or not I have gotten Ross right on some exegetical matter is irrelevant to whether premises (A) and (B) of the argument in question are true, and whether the conclusion (C) follows from them. So Oerter is, whether he realizes it or not, just changing the subject.
Later on, he continues in a similar vein:
Evidently the reason Oerter thinks all this is worth spilling pixels over is that he thinks his “Hilda” example shows that Ross is being inconsistent, and he needs for me to have gotten Ross wrong in order to make his “Hilda” example work. I have already explained, in my previous post, why Ross is not at all being inconsistent. But even if he were, it wouldn’t matter. The alleged inconsistency, you’ll recall, is that Ross treats Hilda as adding despite the fact that we can’t tell from her physical properties alone whether she is, whereas he does not treat the machine as adding despite the fact that we can’t tell from its physical properties alone whether it is. Suppose he really were inconsistent in this way. How does that show that premise (B) of his argument is false (much less that (A) is false, or that the conclusion doesn’t follow)?
Answer: It doesn’t. The most such an inconsistency would show is that Ross needs to clarify what is going on with Hilda that isn’t going on with the machine. And there are several ways he can do this consistent with the argument. First, he could say what I would say (and what, as I have shown, he does in fact say himself, despite what Oerter thinks) -- namely that the machine does add in a sense, but just not by virtue of its physical properties alone. There is perfect consistency here -- both systems, Hilda and the machine, add (albeit in analogous senses), but neither does so in virtue of its physical properties alone.
This is just bizarre. Ed Feser, who revels in pointing out inconsistencies of the naturalists, is arguing that an inconsistency doesn't matter? Nor is this some trivial point of Rossian exegesis, as Feser implies: it's a basic contradiction in Ross's whole scheme.As I pointed out already, the distinction between ETPFOA and simulated adding is crucial to Ross's argument.
The logic of my Hilda example is straightforward. Ross says that humans can ETPFOA. Ross says that A, B, and C entail that a computer cannot ETPFOA. I claim that A, B, and C are true for Hilda, too. So A, B, and C entail that Hilda cannot ETPFOA.
With this contradiction, the whole argument falls to pieces. Now, you can argue that I am wrong: that A, B, and C are not true of Hilda. Or you can argue that there is some D that I missed that is true of the computer but not true of Hilda. But you can't say this example is irrelevant to the soundness of Ross's argument.
Saturday, October 19, 2013
What Does Ross Say?
Well, no, I'm not making the sort of trivial, "silly" argument that Feser likes to ascribe to me. But before I can clarify this, it is necessary to clarify just what it is that Ross is saying.
Feser writes:
What exactly does Ross claim? Here is Ross from his paper:
I just don't see how Feser can write "Ross is not denying, for example, that your pocket calculator is really adding rather than “quadding”..." for that is exactly what Ross is denying.
It is this denial I had in mind when I said Ross couldn't apply the same reasoning to Hilda without denying that Hilda adds, too. But rather than re-visit that argument I will wait for the professor to (I hope) clarify.
Feser writes:
Part of the problem here might be that Oerter is not carefully distinguishing the following two claims:
(1) There just is no fact of the matter, period, about what function a system is computing.
(2) The physical properties of a system by themselves don’t suffice to determine what function it is computing.
Oerter sometimes writes as if what Ross is claiming is (1), but that is not correct. Ross is not denying, for example, that your pocket calculator is really adding rather than “quadding” (to allude to Kripke’s example). He is saying that the physical facts about the machine by themselves do not suffice to determine this. Something more is needed (in this case, the intentions of the designers and users of the calculator).
What exactly does Ross claim? Here is Ross from his paper:
Adding is not a sequence of outputs; it is summing; whereas if the process were
quadding, all its outputs would be quadditions, whether or not they differed in quantity from additions (before a differentiating point shows up to make the outputs diverge from sums).
For any outputs to be sums, the machine has to add. But the indeterminacy among incompossible functions is to be found in each single case, and therefore in every case. Thus, the machine never adds.
Extending the outputs, even to infinity, is unavailing. If the machine is not really adding in the single case, no matter how many actual outputs seem "right," say, for all even numbers taken pairwise (see the qualifying comments in notes 7 and 10 about incoherent totalities), had all relevant cases been included, there would have been nonsums. Kripke drew a skeptical conclusion from such facts, that it is indeterminate which function the machine satisfies, and thus "there is no fact of the matter" as to whether it adds or not. He ought to conclude, instead, that it is not adding; that if it is indeterminate (physically and logically, not just epistemically) which function is realized among incompossible functions, none of them is. That follows from the logical requirement, for each such function, that any realization of it must be of it and not of an incompossible one. [emphasis added]Ross is quite clear: he is not saying (2) at all. Neither is he saying (1). He is saying something stronger than either (1) or (2): the machine does not add - period. It is not that the physical properties of the system alone don't determine what function it is computing, the system isn't actually computing any function at all. "... if it is indeterminate (physically and logically, not just epistemically) which function is realized among incompossible functions, none of them is."
I just don't see how Feser can write "Ross is not denying, for example, that your pocket calculator is really adding rather than “quadding”..." for that is exactly what Ross is denying.
It is this denial I had in mind when I said Ross couldn't apply the same reasoning to Hilda without denying that Hilda adds, too. But rather than re-visit that argument I will wait for the professor to (I hope) clarify.
Tuesday, October 15, 2013
Feser and Ross and me
Ed Feser has responded to my complaints about Ross's argument - sort of. Once again, I am flattered that Feser thinks my amateur philosophizing worthy of his attention. I always learn a lot from our exchanges, even if I am not ultimately convinced of his point. He (correctly) diagnoses my confusion between indeterminacy of meaning and physical indeterminism. But that confusion doesn't (I think) invalidate my main point: that Ross's argument never gets him beyond epistemological indeterminacy.
Oddly, Feser doesn't specifically respond to my critcism. Instead, he refers back to his American Catholic Philosophical Quarterly article. But in that article, he doesn't specifically respond to the epistemology objection, either. Here's what he wrote:
Here's why. Note that Ross's argument is just as valid when talking about what another person is doing when (say) adding. That is, when I am trying to determine whether Hilda is actually adding, or merely simulating adding, all I can do is investigate her physical actions and responses. If Ross's argument is correct, then from a finite amount of data such as these I cannot determine whether Hilda is adding or not. So (if Ross is right) I can never know whether another person is capable of addition.
But note that from the above it doesn't follow that Hilda is not adding. It may be that Hilda is in fact doing something perfectly determinate. I just can't know whether she is or not. So it is clear that Ross's argument doesn't get us past the epistemological.
This point ties in with my second complaint about Ross: the double standard. If I can't say for sure that another person is not adding, then by the same token I cannot say for sure that a machine is not adding.*
In his article, Feser almost makes the same point. Kripke's original point (if I understand it correctly) was, not only can I not be sure what someone else means when they say something, I cannot even be sure what I mean when I say something. That is, even my own thoughts are indeterminate in meaning. Ross obviously doesn't want this conclusion - his own argument relies on one's own thoughts being determinate. Feser points out that (using Frege's conception of meaning) we cannot infer from the external indeterminacy that there is no internal meaning. He writes:
But establishing that there is "no determinate meaning at all" is precisely what Ross needs for his argument. So the argument fails.
* Though it is not directly relevant to the argument, I want to point out that the situation is actually worse with respect to the machine than it is with respect to another person. We can open up the machine, trace its circuits or it mechanism or whatever, and deduce what it will do for a given input. With another person, we can only investigate the physical outputs: we can't open up Hilda's brain and trace its circuitry. Well, not yet, at any rate.
Oddly, Feser doesn't specifically respond to my critcism. Instead, he refers back to his American Catholic Philosophical Quarterly article. But in that article, he doesn't specifically respond to the epistemology objection, either. Here's what he wrote:
Dillard also suggests that Kripke’s point is epistemological rather than metaphysical—that his argument shows at most only that the claim that someone is thinking in accordance with a certain function (such as addition) is underdetermined by the physical evidence, and not that the physical facts are themselves indeterminate. This is odd given that both Kripke and Ross explicitly insist that the points they are respectively making are metaphysical rather than merely epistemological. Indeed, Kripke says that “not even what an omniscient God would know . . . could establish whether I meant plus or quus,” because for the reasons given above, everything about my past behavior, sensations, and the like is compatible (not just compatible as far as we know, but compatible full stop) with my meaning either plus or quus. Nor does Dillard say anything to show otherwise.That is, Feser merely states that Ross says that his point is metaphysical, not epistemological. But Feser doesn't give any additional reasons for us to believe that Ross has actually established this. Well, I agree that Ross says that - but I don't think he has established it.
Here's why. Note that Ross's argument is just as valid when talking about what another person is doing when (say) adding. That is, when I am trying to determine whether Hilda is actually adding, or merely simulating adding, all I can do is investigate her physical actions and responses. If Ross's argument is correct, then from a finite amount of data such as these I cannot determine whether Hilda is adding or not. So (if Ross is right) I can never know whether another person is capable of addition.
But note that from the above it doesn't follow that Hilda is not adding. It may be that Hilda is in fact doing something perfectly determinate. I just can't know whether she is or not. So it is clear that Ross's argument doesn't get us past the epistemological.
This point ties in with my second complaint about Ross: the double standard. If I can't say for sure that another person is not adding, then by the same token I cannot say for sure that a machine is not adding.*
In his article, Feser almost makes the same point. Kripke's original point (if I understand it correctly) was, not only can I not be sure what someone else means when they say something, I cannot even be sure what I mean when I say something. That is, even my own thoughts are indeterminate in meaning. Ross obviously doesn't want this conclusion - his own argument relies on one's own thoughts being determinate. Feser points out that (using Frege's conception of meaning) we cannot infer from the external indeterminacy that there is no internal meaning. He writes:
Frege emphasized that the sense of an expression is not a private psychological entity such as a sensation or mental image, any more than it is something material. Thus he would hardly take an argument to the effect that meaning cannot be fixed either by sensations and mental images or by bodily behavior to establish that there is no determinate meaning at all.
But establishing that there is "no determinate meaning at all" is precisely what Ross needs for his argument. So the argument fails.
* Though it is not directly relevant to the argument, I want to point out that the situation is actually worse with respect to the machine than it is with respect to another person. We can open up the machine, trace its circuits or it mechanism or whatever, and deduce what it will do for a given input. With another person, we can only investigate the physical outputs: we can't open up Hilda's brain and trace its circuitry. Well, not yet, at any rate.
Saturday, October 12, 2013
Ross's Double Standard
Another problem with Ross's argument is the double standard he employs. It's obvious that humans are not nearly as accurate as machines when it comes to computations. But Ross doesn't take this as evidence that humans are not carrying out a pure function. On the contrary, he suggests that mistakes could be evidence that the human is carrying out the function. He writes:
But when he talks about machine addition, he counts any error, even a potential error many years in the future, as evidence that the machine doesn't truly add.
This is a blatant double standard. Logically, if a mistake is evidence that X is not performing the function, then that is true whether X is a human or a machine.
This is not a claim about how many states we can be in. This is a claim about the ability exercised in a single case, the ability to think in a form that is sum-giving for every sum, a definite thought form distinct from every other. When a person has acquired such an ability is not always transparent from successful answers, and it can be exhibited even by mistakes. [Emphasis added.]
But when he talks about machine addition, he counts any error, even a potential error many years in the future, as evidence that the machine doesn't truly add.
This is a blatant double standard. Logically, if a mistake is evidence that X is not performing the function, then that is true whether X is a human or a machine.
Sunday, October 6, 2013
Against Physicalism
Are humans more than just a complicated physical machine? Physicalism is the idea that the physical is "all there is" - everything that exists is either physical or is reducible to something that is physical. Thanks to Ed Feser's blog, I've come across an interesting argument from James Ross that physicalism cannot be true. Ross takes an approach that draws on Kripke, Goodman, and Quine to build a rather astonishing claim about physical systems. Ross's argument is very subtle and worth a close look. If it succeeds, it's truly an astounding accomplishment: one of the great philosophical debates of all times, solved. I don't think it succeeds, and I'm going to try to suggest why not.
Feser summarizes Ross's argument like this:
Specifically, Ross refers to "pure functions" that humans can define but that cannot be implemented by any purely physical system. He gives examples like adding, squaring a number, and the modus ponens of logic.
Now, what makes Ross think that a physical system cannot add? Of course he knows that mechanical devices and computers are capable of performing sums, but he says they are only simulating addition, not truly adding. He writes:
Now, I can go along with Ross as far as the epistemological aspect of his conclusion: no matter how many input-output pairs we examine, we can never know what function is being computed. But Ross claims much more: he says physical systems are not just epistemologically indeterminate but "physically and logically" indeterminate, too. That is, it's not just that we can't know what function the machine is computing, but there really is no fact of the matter about what the output will be until it actually happens.
The problem is, the argument Ross gives is not up to the task of proving that claim.
First of all, what does Ross mean by "empirically adequate"? He is not using this in the sense of van Fraasen, for whom empirical adequacy means agreement, not just with all past observations, but with all possible observations. For Ross explicitly mentions a "differentiation point", possibly at some remote future time, at which the outcomes disagree. Nor does he mean "agreement with all future observations", for the same reason. So he must mean merely "agreement with all past observations."
But having two hypotheses that agree with all past observations is not enough to tell us that the physical system is actually (physically) indeterminate. It only says that our information is insufficient to distinguish between the two.
Another example Ross gives is the problem of determining a function, knowing only a finite number of data points. He (correctly) points out that there is an infinity of curves that will agree on those finite data. But this just says we don't know what the function is that produced the data. It doesn't follow that there is no such function at all. But that's what Ross needs for his conclusion that physical systems are not just epistemically indeterminate, but physically indeterminate.
Ross's other arguments draw on Goodman's and Quine's work. These, too, also only reach as far as epistemology. Goodman's grue problem suggests that we can never know for sure whether we are inducting on the right categories. But it is a long way from that epistemological claim to the claim that there are no correct categories for induction to work on. Duhem's claim about undertermination says only that we can't know what part of whole complex of assumptions, theories, and practices is at fault when an experiment disagrees with theory. Again, this is only an epistemological claim. True, Quine tried to extend this uncertainty to the whole realm of human knowledge - but this extension hardly helps Ross's claim that humans can add, employ modus ponens, etc. Thus,none of Ross's arguments, either in the article or in his book, Thought and World, take us beyond epistemological indeterminacy.
I have to say it is exceedingly odd to see Feser defending physical indeterminism here. In our discussions of quantum mechanics and causation he argued strenuously that there is no such thing as physical indeterminism - not even in the case of quantum mechanics (where nearly all physicists accept fundamental indeterminism). So I'm wondering how Feser can square real, physical and logical indeterminism with the principle of causality.
Feser summarizes Ross's argument like this:
All formal thinking is determinate.
No physical process is determinate.
Thus, no formal thinking is a physical process.
Specifically, Ross refers to "pure functions" that humans can define but that cannot be implemented by any purely physical system. He gives examples like adding, squaring a number, and the modus ponens of logic.
Now, what makes Ross think that a physical system cannot add? Of course he knows that mechanical devices and computers are capable of performing sums, but he says they are only simulating addition, not truly adding. He writes:
Whatever the discriminable features of a physical process may be, there will always be a pair of incompatible predicates, each as empirically adequate as the other, to name a function the exhibited data or process "satisfies." That condition holds for any finite actual
"outputs," no matter how many. That is a feature of physical process itself, of change. There is nothing about a physical process, or any repetitions of it, to block it from being a case of incompossible forms ("functions"), if it could be a case of any pure form at all. That is because the differentiating point, the point where the behavioral outputs diverge to manifest different functions, can lie beyond the actual, even if the actual should be infinite; e.g., it could lie in what the thing would have done, had things been otherwise in certain ways. For instance, if the function is x(*)y = (x + y, if y < 10^40 years, = x + y + 1, otherwise), the differentiating output would lie beyond the conjectured life of the universe.
Now, I can go along with Ross as far as the epistemological aspect of his conclusion: no matter how many input-output pairs we examine, we can never know what function is being computed. But Ross claims much more: he says physical systems are not just epistemologically indeterminate but "physically and logically" indeterminate, too. That is, it's not just that we can't know what function the machine is computing, but there really is no fact of the matter about what the output will be until it actually happens.
The problem is, the argument Ross gives is not up to the task of proving that claim.
First of all, what does Ross mean by "empirically adequate"? He is not using this in the sense of van Fraasen, for whom empirical adequacy means agreement, not just with all past observations, but with all possible observations. For Ross explicitly mentions a "differentiation point", possibly at some remote future time, at which the outcomes disagree. Nor does he mean "agreement with all future observations", for the same reason. So he must mean merely "agreement with all past observations."
But having two hypotheses that agree with all past observations is not enough to tell us that the physical system is actually (physically) indeterminate. It only says that our information is insufficient to distinguish between the two.
Another example Ross gives is the problem of determining a function, knowing only a finite number of data points. He (correctly) points out that there is an infinity of curves that will agree on those finite data. But this just says we don't know what the function is that produced the data. It doesn't follow that there is no such function at all. But that's what Ross needs for his conclusion that physical systems are not just epistemically indeterminate, but physically indeterminate.
Ross's other arguments draw on Goodman's and Quine's work. These, too, also only reach as far as epistemology. Goodman's grue problem suggests that we can never know for sure whether we are inducting on the right categories. But it is a long way from that epistemological claim to the claim that there are no correct categories for induction to work on. Duhem's claim about undertermination says only that we can't know what part of whole complex of assumptions, theories, and practices is at fault when an experiment disagrees with theory. Again, this is only an epistemological claim. True, Quine tried to extend this uncertainty to the whole realm of human knowledge - but this extension hardly helps Ross's claim that humans can add, employ modus ponens, etc. Thus,none of Ross's arguments, either in the article or in his book, Thought and World, take us beyond epistemological indeterminacy.
I have to say it is exceedingly odd to see Feser defending physical indeterminism here. In our discussions of quantum mechanics and causation he argued strenuously that there is no such thing as physical indeterminism - not even in the case of quantum mechanics (where nearly all physicists accept fundamental indeterminism). So I'm wondering how Feser can square real, physical and logical indeterminism with the principle of causality.
Tuesday, April 16, 2013
Pruss, PSR, and QM
In the discussion of the Leibnizian cosmological argument for God, Tyler mentioned a book by Alexander Pruss (of Prosblogion fame), The Principle of Sufficient Reason, A Reassessment. In particular, Tyler said he thought Pruss had answered all the possible quantum mechanical objections to the Principle of Sufficient Reason (PSR). I have finally gotten a chance to look at Pruss's chapter on QM. It seems to me that he succeeds - much too well.
If the PSR means anything at all, then it needs a more rigorous notion of "reason" and "causality" than Pruss is employing here.
Pruss has a good grasp of the quantum mechanical objection. He even presents a version of the famous EPR-Bell inequality paradox. He goes on to suggest several ways of reconciling QM with the PSR, including non-local causation, or backward-in-time causation, and hidden variable theories. With regard to the latter, he acknowledges that Bohmian theories run into problems with relativity, and are not a really satisfactory replacement for standard quantum field theory. But, he says, it is possible to show that some such theory could, in principle, explain the QM results.
For instance, take a neo-Leibnizian theory that says that every point of space is a monad, and this monad has encoded within it a list of all the events that will happen throughout time at that point and through an internal causal process it goes deterministically through these events as time passes.Now, it seems obvious to me that this solution achieves too much. For this could be said of any conceivable pattern of events in any conceivable universe. No matter how random, lawless, and chaotic, those events could be described in Pruss's monad theory as deterministic and causal. So this solution makes the PSR trivial, and therefore uninteresting. If every possible pattern of events satisfies the PSR, then the PSR has no content.
If the PSR means anything at all, then it needs a more rigorous notion of "reason" and "causality" than Pruss is employing here.
Saturday, April 6, 2013
Supernatural Times Two
Two interesting things I've come across about defining the supernatural:
The first is a paper by Fishman and Boudry that makes the point that methodological naturalism is not an a priori commitment of the scientific enterprise; rather, it is a conclusion arrived at in the same way as other scientific results, namely, by applying the usual criteria of economical explanation of phenomena. They argue that "supernatural," as it is commonly used, is too loose a term to be useful. Instead, they say, we should talk about the "overnatural" - beings or powers that are similar to natural ones, but beyond what is normally possible (like Superman or walking on water) - and the "transnatural" - things that are "categorically different from ‘natural’ ones, so much so that their properties are essentially mysterious, ineffable, and incomprehensible."
The overnatural can be investigated the way we investigate any scientific hypothesis. The transnatural, on the other hand, cannot be scientifically investigated, since it (by definition) is incomprehensible and inexplicable. However, they argue, the transnatural is an empty concept. They quote Martin Mahner:
The second bit is a blog post by Victor Reppert, who argues that the supernatural is a claim that minds are not composed of non-mental things - they are part of the "rock bottom level of the universe." This is really a thesis about dualism rather than a definition of the supernatural. But I think Reppert is right to focus on minds in talking about the supernatural.
Imagine that large boulders spontaneously levitated at random times. Such a phenomenon would be inexplicable according to current science, but I don't think it would be considered supernatural. It would just be another kind of natural phenomenon to be described. On the other hand, suppose they only levitated when a car was about to crash into them. Then we would suspect a purpose behind the levitations, and a mind behind that purpose. Since the phenomenon is beyond the ability of any human, we would have to suspect a supernatural being. (Or, I suppose, a powerful extra-terrestrial who can know about these events in advance and who has the ability to move rocks from a distance. In effect, such a being would be supernatural from our point of view.)
This all ties in to the discussion about the fine tuning argument for naturalism, and what sort of observations would be considered evidence of supernatural intervention - but I'm still thinking about how.
The first is a paper by Fishman and Boudry that makes the point that methodological naturalism is not an a priori commitment of the scientific enterprise; rather, it is a conclusion arrived at in the same way as other scientific results, namely, by applying the usual criteria of economical explanation of phenomena. They argue that "supernatural," as it is commonly used, is too loose a term to be useful. Instead, they say, we should talk about the "overnatural" - beings or powers that are similar to natural ones, but beyond what is normally possible (like Superman or walking on water) - and the "transnatural" - things that are "categorically different from ‘natural’ ones, so much so that their properties are essentially mysterious, ineffable, and incomprehensible."
The overnatural can be investigated the way we investigate any scientific hypothesis. The transnatural, on the other hand, cannot be scientifically investigated, since it (by definition) is incomprehensible and inexplicable. However, they argue, the transnatural is an empty concept. They quote Martin Mahner:
There neither is an ontological theory proper of the transnatural nor could there be, because there can be no theory of the unintelligible.Scientists thus reject a transnatural explanation, not because of any a priori commitment, but for the same reason they reject any other unintelligible or ill-formed hypothesis.
The second bit is a blog post by Victor Reppert, who argues that the supernatural is a claim that minds are not composed of non-mental things - they are part of the "rock bottom level of the universe." This is really a thesis about dualism rather than a definition of the supernatural. But I think Reppert is right to focus on minds in talking about the supernatural.
Imagine that large boulders spontaneously levitated at random times. Such a phenomenon would be inexplicable according to current science, but I don't think it would be considered supernatural. It would just be another kind of natural phenomenon to be described. On the other hand, suppose they only levitated when a car was about to crash into them. Then we would suspect a purpose behind the levitations, and a mind behind that purpose. Since the phenomenon is beyond the ability of any human, we would have to suspect a supernatural being. (Or, I suppose, a powerful extra-terrestrial who can know about these events in advance and who has the ability to move rocks from a distance. In effect, such a being would be supernatural from our point of view.)
This all ties in to the discussion about the fine tuning argument for naturalism, and what sort of observations would be considered evidence of supernatural intervention - but I'm still thinking about how.
Thursday, February 7, 2013
Contingency
Tyler has brought up the cosmological argument from contingency and linked to a Philosophy of Religion (POR) article and a paper by Alexander Pruss. The latter is a long article and will take me a while to read and digest. So I'm just going to post some comments on the first article by way of starting (I hope) a discussion.
The argument runs like this:
I have two immediate objections to the argument, which I'll call the Nature of Necessity objection and the Quantum Mechanics objection. I've already discussed QM and reasons in my debate with Prof. Feser (see here and here), so in this post I'll just address the Nature of Necessity objection.
Cosmological arguments always begin by implicitly carving out a "God exception."
Properly speaking, "necessity" and "contingency" are terms that apply to propositions. Necessary truths are those that cannot fail to be true: the usual examples are mathematical and logical truths. Contingent truths could fail to be true. "It is raining right now" might be true, but it could have been the case that it didn't rain today.
The argument from contingency rips these terms out of their proper context and attempts to apply them to things. It asserts that there are contingent things - those that could possibly have not existed - and necessary things - those that could not have not existed. The problem is, no one ever seems to be able to point to something that exists necessarily - except God.
"Exists necessarily" is supposed to mean "exists in all possible worlds." But what is a possible world? Philosophers distinguish different types of possibility. Physical possibility means that which, according to the laws of nature, could happen. Logical possibility means anything that is not logically incoherent. (There are other types of possibility, but these are enough for discussion.) In making a modal argument - one based on what might happen in other "possible worlds" - it makes a big difference whether we are talking about physically possible worlds or logically possible worlds. So, it might be logically possible for the universe not to have existed, while at the same time it is physically impossible for the universe not to have existed. (That would be the case if the laws of physics somehow guaranteed that a universe spring into existence. I'm not claiming that they do guarantee this - only saying that some set of laws might do so.)
The POR article considers logically possible worlds and suggests that it seems logically possible that the universe not exist. This is, of course, true. Among the logically possible worlds is the empty world, in which nothing exists. So, no universe.
But also, no God. Because when necessary existence is construed according to logical possibility, it is an empty concept. Nothing exists in the empty world. So there is nothing that exists in all possible worlds. So there is nothing that exists necessarily.
The Nature of Necessity objection was articulated by Bertrand Russell a long time ago, so I'm sure someone has thought up a response to it. If you know of one, let me know!
The argument runs like this:
(1) Everything that exists contingently has a reason for its existence.
(2) The universe exists contingently.
Therefore:
(3) The universe has a reason for its existence.
(4) If the universe has a reason for its existence then that reason is God.
Therefore:
(5) God exists.
I have two immediate objections to the argument, which I'll call the Nature of Necessity objection and the Quantum Mechanics objection. I've already discussed QM and reasons in my debate with Prof. Feser (see here and here), so in this post I'll just address the Nature of Necessity objection.
Cosmological arguments always begin by implicitly carving out a "God exception."
- - "Nothing can be beginningless - except God."
- - "Nothing can exist without a cause - except God."
- - "Nothing can be undesigned - except God."
Properly speaking, "necessity" and "contingency" are terms that apply to propositions. Necessary truths are those that cannot fail to be true: the usual examples are mathematical and logical truths. Contingent truths could fail to be true. "It is raining right now" might be true, but it could have been the case that it didn't rain today.
The argument from contingency rips these terms out of their proper context and attempts to apply them to things. It asserts that there are contingent things - those that could possibly have not existed - and necessary things - those that could not have not existed. The problem is, no one ever seems to be able to point to something that exists necessarily - except God.
"Exists necessarily" is supposed to mean "exists in all possible worlds." But what is a possible world? Philosophers distinguish different types of possibility. Physical possibility means that which, according to the laws of nature, could happen. Logical possibility means anything that is not logically incoherent. (There are other types of possibility, but these are enough for discussion.) In making a modal argument - one based on what might happen in other "possible worlds" - it makes a big difference whether we are talking about physically possible worlds or logically possible worlds. So, it might be logically possible for the universe not to have existed, while at the same time it is physically impossible for the universe not to have existed. (That would be the case if the laws of physics somehow guaranteed that a universe spring into existence. I'm not claiming that they do guarantee this - only saying that some set of laws might do so.)
The POR article considers logically possible worlds and suggests that it seems logically possible that the universe not exist. This is, of course, true. Among the logically possible worlds is the empty world, in which nothing exists. So, no universe.
But also, no God. Because when necessary existence is construed according to logical possibility, it is an empty concept. Nothing exists in the empty world. So there is nothing that exists in all possible worlds. So there is nothing that exists necessarily.
The Nature of Necessity objection was articulated by Bertrand Russell a long time ago, so I'm sure someone has thought up a response to it. If you know of one, let me know!
Monday, January 7, 2013
... We Have Heard On High
Ed Feser has a new paper out explaining why Newton's First Law of Motion is not incompatible with Aquinas's principle that "whatever is in motion is moved by another." In it he expands on some comments he made in response to my criticism of his book, The Last Superstition.
Newton's law states that anything that is in motion will remain in motion unless acted on by an outside force, so the two principles seem to be directly contradictory, at least at first glance. Newton says that an object that is completely isolated, so that it has no external influences on it, will continue to move. Aquinas denies this.
So how does Feser resolve the conflict? Easy! The object in uniform motion is moved along by....
(wait for it)
ANGELS!
Yes, angels are necessary to keep a moving object moving. I'm not making this up, he really says it:
Here Feser is considering inertial motion as "real change." He also considers what happens if you consider inertial motion as a "state" that doesn't involve any real change: no actualization of a potential. Feser seems to be getting confused by the way physicists use the term "state": the "state" of a (classical) object refers to its location and its rate of change (velocity), so by definition it involves change. Ultimately, though, the question of whether inertial motion is or is not "real change" is not a physical question but a metaphysical one. One would think that Feser's Aristotelian-Thomian metaphysics would tell us which it is. That it cannot just shows how useless that metaphysics is.
The idea that angels are responsible for inertial motion raises a whole (heavenly) host of questions. Presumably, an object at rest doesn't need any angelic mover. However, in Newtonian physics, any uniformly moving reference frame can be considered to be at rest (Galilean relativity). If we have two objects in uniform motion relative to each other, which one does the angel need to guide? If we consider object A at rest, then the angel must move B. But if we consider object B at rest, then the angel must move A. What's a poor angel to do?
And how many angels are needed for this heavenly guidance? If an asteroid is being guided by an angel, and suffers an impact that splits it in two, does the angel recruit another angel to guide the second piece? Or can the first angel handle both pieces? What if the asteroid gets shattered into smaller and smaller fragments? Maybe each elementary particle has its own angel? How many angels are needed to guide a fragment the size of a pin? (And do they dance?)
Once again we see the Sophisticated Theologian in action. When the world doesn't work the way you want it to, just invent some invisible, undetectable beings to fill the gap.
I have to thank Prof. Feser for this paper; it shows more clearly than anything I could write what absurdities result when you try to force the world into a pre-conceived metaphysics.
Newton's law states that anything that is in motion will remain in motion unless acted on by an outside force, so the two principles seem to be directly contradictory, at least at first glance. Newton says that an object that is completely isolated, so that it has no external influences on it, will continue to move. Aquinas denies this.
So how does Feser resolve the conflict? Easy! The object in uniform motion is moved along by....
(wait for it)
ANGELS!
Yes, angels are necessary to keep a moving object moving. I'm not making this up, he really says it:
So, it is difficult to see how inertial motion, when interpreted as involving real change, could have a physical cause. But as we implied above, even if its lacks a physical cause, there is nothing in the principle of inertia that rules out a metaphysical cause. Indeed, if inertial motion involves real change, then given the principle of motion together with the absence of a physical cause, such a metaphysical cause is necessary.
Of course, that raises the question of what exactly this metaphysical cause is....
If inertial motion involves real change, then, only a metaphysical cause external to the moving object could be the ultimate source. And we already have a model for such a cause in the Aristotelian tradition. For the motions of celestial bodies were in that tradition regarded as unending, just as inertial motion is (barring interference from outside forces) unending; and while this view was associated with a mistaken astronomy, a metaphysical kernel can be extracted from the obsolete scientific husk. Now the causes of celestial motion in this earlier Aristotelian tradition were, of course, intelligent or angelic substances....
Hence the only possible cause of inertial motion—again, at least if it is considered to involve real change—would seem to be a necessarily existing intelligent substance or substances, of the sort the earlier Aristotelian tradition thought moved celestial objects. (Unless it is simply God Himself causing it directly as Unmoved Mover.)
Here Feser is considering inertial motion as "real change." He also considers what happens if you consider inertial motion as a "state" that doesn't involve any real change: no actualization of a potential. Feser seems to be getting confused by the way physicists use the term "state": the "state" of a (classical) object refers to its location and its rate of change (velocity), so by definition it involves change. Ultimately, though, the question of whether inertial motion is or is not "real change" is not a physical question but a metaphysical one. One would think that Feser's Aristotelian-Thomian metaphysics would tell us which it is. That it cannot just shows how useless that metaphysics is.
The idea that angels are responsible for inertial motion raises a whole (heavenly) host of questions. Presumably, an object at rest doesn't need any angelic mover. However, in Newtonian physics, any uniformly moving reference frame can be considered to be at rest (Galilean relativity). If we have two objects in uniform motion relative to each other, which one does the angel need to guide? If we consider object A at rest, then the angel must move B. But if we consider object B at rest, then the angel must move A. What's a poor angel to do?
And how many angels are needed for this heavenly guidance? If an asteroid is being guided by an angel, and suffers an impact that splits it in two, does the angel recruit another angel to guide the second piece? Or can the first angel handle both pieces? What if the asteroid gets shattered into smaller and smaller fragments? Maybe each elementary particle has its own angel? How many angels are needed to guide a fragment the size of a pin? (And do they dance?)
Once again we see the Sophisticated Theologian in action. When the world doesn't work the way you want it to, just invent some invisible, undetectable beings to fill the gap.
I have to thank Prof. Feser for this paper; it shows more clearly than anything I could write what absurdities result when you try to force the world into a pre-conceived metaphysics.
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