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.

8 comments:

  1. "At the core of Ross's argument is his insistence that our logical thinking must involve 'pure forms'."

    The problem with Ross and his supporters is not so much the "pure forms" part as their fatal slipperiness on the "involve" part.

    Surely our thoughts about 900-pound purple gorillas "involve" the color purple, and "involve" being very heavy. But why should anyone expect our thoughts (however they are instantiated) to be purple, or to be 900 pounds?

    This is just super-basic vehicle/content stuff.

    Surely, our thoughts about formal logic and mathematics "involve" determinate forms. But why should anyone (again, irrespective of how they believe mind is instantiated) agree that our thoughts themselves be determinate forms?

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    1. Hi Staircaseghost,

      I hope I made it clear that I was referring to Ross's concept of "pure forms". There might be some other ways of using the words "pure forms" or "determinate forms" that make more sense than Ross's, though I think those words are probably best avoided altogether. Whatever is true can probably be expressed more clearly in other words.

      What I would say is that purely abstract facts like "2+2=4" are true in some absolutely precise sense. I would also say that we can have such verbal thoughts as "2+2=4", and we can engage in the sort of thinking that we call "adding two and two". But we must avoid conflating real-world thoughts/thinking with abstract facts. This is similar to your distinction between our thoughts and what we're thinking about.

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    2. "I would also say that we can have such verbal thoughts as '2+2=4', and we can engage in the sort of thinking that we call "adding two and two". But we must avoid conflating real-world thoughts/thinking with abstract facts."

      I also agree with you that we don't "really" add, for sufficiently unclear and extreme definitions of "really".

      We can add this to the long list of hopelessly equivocal terms in the argument: "form", "really", "pure", "involve", "determinate", "material process"...

      Just when you think you've blasted a chunk of Thomistic jello with enough dry ice to nail it to the wall, a dozen more blobs start flying through the air.

      Of what observational consequence is the conclusion that we don't "Ross-really" add? If it is not the same as that we don't plain-English-add, then what is it? If it doesnt entail me throwing up my hands in despair when I'm told we'll be adding two guests for Thanksgiving, so please prepare that many extra chairs, what does it entail?

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    3. Hi again, Staircaseghost. I've been thinking about how to put this more clearly.

      Facts of pure (abstract) logic are a very different sort of thing from facts about the real-world. The former are absolute (or determinate) in a way that the latter or not. Ross has jumped from the absolute determinacy of abstract logical facts to the assumption that our logical thinking must be determinate in the same sense. This is both a non sequitur and a category error.

      In fact, Ross has committed a double category error. He hasn't just applied a property of abstract logical facts to real-world facts; he's gone further and applied it to real-world processes. He persistently applies the words "determinate" and "indeterminate" to processes, rather than to facts about those processes. This leads him into all sorts of confusion.

      Ross's paper is an ill-considered mess from start to finish. He throws words around with very little thought as to whether they are applicable in the given context, or whether he is using them consistently. This sort of thing gives philosophy a bad name.

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    4. "Ross has jumped from the absolute determinacy of abstract logical facts to the assumption that our logical thinking must be determinate in the same sense."

      Indeed, this is some weird superstitious kind of sympathetic-magic type thinking. It's what I was getting at with the vehicle/content distinction; on some level these people literally think that thoughts must have all the properties as the things they're about.

      Walnuts look like brains, so eating walnuts must be good for your brain...

      He throws words around with very little thought as to whether they are applicable in the given context, or whether he is using them consistently. This sort of thing gives philosophy a bad name.

      In my experience modern Aristotelians operate on the level of Truthyness, not the level of truth. They construct these grand philosophical edifices that simply glorify the deliverances of common sense and gut intuition and folk physics and folk psychology. Since truth is simple and intuitive, why, anything which is complex or counterintuitive must by definition be false!

      So they are prevented from seeing the problems in their position not (primarily) because they are dogmatists, but because consistency and attention to details of empirical fact and clarity borne of close attention to distinctions are literally invisible to their epistemic radar. These things are by definition indicators of falsehood.

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    5. "It's what I was getting at with the vehicle/content distinction; on some level these people literally think that thoughts must have all the properties as the things they're about."

      Yes, I should have been clearer that I basically agreed with you on that. I was just reluctant to use the words "content" and "about". Those are tricky words that often lead philosophers into confusion. Misguided interpretation of that sort of language can lead to the Platonistic idea that there must be a "realm" of mathematical "objects" for statements like "2+2=4" to be about. Plantinga (in his EAAN) gets very confused talking about the "content" of beliefs, as if a belief was a kind of receptacle, separable from its content.

      "They construct these grand philosophical edifices that simply glorify the deliverances of common sense and gut intuition and folk physics and folk psychology."

      I'm not familiar with Aristotelians in particular, but I'd say that's true of theistic philosophers generally. Of course it's also true to some degree of many non-theist philosophers (can I say "The Chinese Room argument"?), but it's particularly true of theist philosophers. If you're not going to take a skeptical look at your intuitive belief in God, then why take a skeptical look at other intuitions, especially those which are strongly related to God-belief, like mind-body dualism and moral realism?

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  2. I hope this doesn't seem too pedantic, but I'd like to say that the title of this post ("Purity of Form and Function") was added by Robert, not me. I feel it's slightly misleading. The issue I'm addressing is not purity as such. In rejecting Ross's concept of "pure forms", I'm not saying that logical thinking has an impure form. I don't know what that would mean. I'm saying that Ross is employing a misguided concept of "form". I've referred to his "forms" as "pure forms", not with the emphasis on "pure", but because this seemed a convenient way of identifying that I was talking about Ross's own concept of a "form". I can see how my post left this unclear, so Robert's choice of title has at least had the virtue of motivating me to clarify this point now.

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  3. My short, Devil's Advocate, response is that Ross seems to think that pure functions are indispensable to mental apprehension because otherwise knowledge systems would quickly spin out of control into incoherence. He doesn't make a very firm argument to support this, but that's what I think he means. To be honest, I half-agree with him, except I don't think either the definitions that he provides, or the ramifications he asserts are justified. There I think we agree. I do believe that in order for things like math (or for that matter, language) to be possible, we do need to capture what operations like addition (or components, like words) really mean, not just instantiate ("simulate") enumerations, but this is where I turn to describing our understanding as being at a meta-level. We understand what the operation of addition is "about," therefore we mentally encapsulate the operation as a rule. This allows us to think about it in totality, "all at once" or however else you might want to describe it. This eliminates the ambiguity, determines the function (or whatever else) exactly and explicitly, at least to the extent of our cognition. How exactly our brains accomplish this is not yet understood, which is why Ross's argument has some plausibility. It's still an argument from ignorance though.

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