Follow-up On Color Exclusion and Metaphysical Necessity

This is a follow up to the previous post.

At 6.3751 Wittgenstein mentions this issue. (6.3 is about logic as the investigation of regularity, while 6.37 and 6.375 deal with all necessity being logical.) “For two colors, e.g., to be at one place in the visual field, is impossible, logically impossible, for it is excluded by the logical structure of color.” He then compares this with a physical particle’s only having one velocity, and then says parenthetically that “It is clear that the logical product of two elementary propositions can neither be a tautology or a contradiction.  The assertion that a point in the visual field has two different colors at the same time, is a contradiction.”

Thinking out loud: while there might be such things as spacetime points, there are no such things as points in the visual field. Furthermore, if there were, they would not have any color, since only extended things have color. (“Ort” was better than “punkt.”)

If we accept the claim that only extended things (be they in the visual field or elsewhere) have color, and the claim that extended things are divisible, then it seems to follow that any arbitrary patch or place (ort) in the visual field can have one color or many. In which case, if we call the patch a, a is red can be true, a is green can be true, a is completely red can be true, a is completely green can be true, (a is red and a is green) can be true, and so on. As in the post this comment is responding to, then, the conflict between “a is completely red” and “a is completely green” is in fact purely logical along the lines I laid out. An arbitrary color patch can have one color or many and to say that it has only one is to say that it has no others: you can’t therefore say it is completely green and red for the usual reasons, not for any special metaphysical ones.

I wonder, what with the parentheses and the word shift, whether Wittgenstein might have been thinking something similar here?

At 4.0031 Wittgenstein wrote: “Russell’s merit is to have shown that the apparent logical form of the proposition need not be its real form.” This is often taken to be a reference to Russell’s theory of Definite Descriptions. “Walter Scott is the author of Waverly” according to Russell encodes three separate claims, two of which are numerical – there is at least and at most one author of Waverly. This, in turn, would tell us that “Charles Dickens is the author of Waverly” is false – not because of anything empirical, but in essence because in having attributed unique authorship to Scott we can’t then attribute it to Dickens as well.

Following this out according to the parenthetical conclusion of 6.3751, we see at once that “Charles Dickens is the author of Waverly” and “Walter Scott is the author of Waverly” can’t both be elementary propositions, because if they were, they could not contradict one another. This is no big deal though, because Russell has shown us one way to analyze these out. Leaving aside worries about authorship and which propositions are ultimate, “Walter Scott is author of Waverly” and “Charles Dickens is author of Waverly” could in this respect at least both be elementary propositions, since novels can in principle have two authors.

Likewise, “color patch a is green” and “color patch a is red” can both be true, since extended regions can have parts of different colors. But if there were such things as points (punkte) in the visual field, “point a is green” and “point a is red” could not both be true. So – on this line of thinking anyway – we should conclude that the possession of colors by points is an amusing bit of word salad, something that sounds meaningful but isn’t.

One problem with this approach – as a solution to the problem at least – comes from Wittgenstein’s paper “Some Remarks on Logical Form,” which in effect treats this problem as a real one, rather than conjuring it away in the way I am attempting to. He in fact explicitly disavows the claim of 6.3751 on page 168, and the general thrust of that paper seems to suggest that there is a new sort of necessity in the offing, much as contemporary philosophers wish to indicate under the head of metaphysical necessity. Wittgenstein himself became quickly dissatisfied with that paper; but even if we accept the analysis here given for color, might not his other examples, e.g. of brightness, velocity, and so forth still present us with the problem under discussion?

It’s not clear to me that it would. Why can’t a single light source have two different degrees of brightness at the same time? Well, that’s not how we use the word ‘brightness.’ But why doesn’t that just show that when we attribute a degree of brightness, we are also claiming that there is no other degree of brightness it possesses? Certainly a large enough source of light could have different brightnesses at different points.

Taking this approach would allow us to treat “the kite is moving westward at 10 mph” and “the kite is moving westward at 20 mph” as independent elementary propositions, and the English language claim that “the kite is moving westward at 10 mph” as really disguising “the kite is moving westward at 10 mph” and “there is no velocity other than 10 mph that the kite is moving westward at” – in other words, as a simultaneous affirmation of one of the (infinite) number of propositions attributing velocity to the kite and denial of all the others. This preserves logical necessity as the only form of necessity at the expense of attributing hidden meaning to our speech – but we have already allowed that in this framework, and we do in fact deny all the other velocities when we attribute the one, on whatever grounds we do so.

If we suppose, with some but not a lot of evidence, that Wittgenstein in the Tractatus was thinking along the lines of this post, it is tempting to wonder whether when confronted with “Some Remarks on Logical Form” the Tractatus-era Wittgenstein might have responded somewhat as Kripke did to Putnam’s “Is Logic Empirical?” and suggest that the whole question about the logical forms of elementary propositions must be misguided, perhaps as requiring a standpoint outside of sense-making and logic themselves to even formulate. The facts that Wittgenstein wrote that paper fresh after returning to philosophy, quickly disavowed it, and largely did not pursue that line of reasoning (though he did pursue some similar ones) in work following it up might even, with even less evidence, support the idea that Wittgenstein himself had this reaction upon some reflection. This is all speculative of course.

One might think that because of Wittgenstein’s desire to eliminate both the equals sign and number-terms from properly formulated Tractarian sentences this kind of analysis would be hard to give in that framework. In fact it wouldn’t be: take all the propositions of the form ‘x is author of Waverly’ you like and declare them elementary. To say that Scott is the author of Waverly is just to say that ‘Scott is author of Waverly’ is true and that all the other propositions of this form are false – not in that way, but by denying each of them individually (‘Dickens is author of Waverly’, ‘Shakespeare is author of Waverly’, ‘Bacon is author of Waverly’, etc.).

Whatever Wittgenstein’s views on the question there are some interesting things to consider here. We do seem to have a general framework for translating at least one type of supposed metaphysical necessity into a logical one, simply by adding additional propositions which take up the extra structure we’re missing. (So we don’t say that ‘l has brightness 1’ and ‘l has brightness 2’ are contradictory, but rather that ‘l has brightness 1 and there are not any other brightnesses such that l has them’ and ‘l has brightness 2’ are contradictory, and that it is really the latter and not the former to which we are committed in our ordinary attributions of brightness.)

What do we then gain by positing this additional type of necessity?

To sharpen things a bit more: we say that a particle can only have one velocity, and that this is not a logical truth, but a metaphysical one, or a conceptual one.

If we call it a conceptual one, we are presumably saying something like: the concept ‘velocity’ is such that a body can only have one.

What does that amount to other than saying if we assert that O is moving at V1 we also deny that there is any other Vi such that O is moving at it?

I suppose the thought would be that you get the denial ‘for free’ with the assertion, that if you understand ‘velocity’ you will also understand that there can be only one. Why does that represent a grasp of the concept of velocity, or a metaphysical truth about velocity, rather than just our determination to only use the word ‘velocity’ in one way?

When we learn to add velocities of particles in 3-dimensional space we learn to add their three component velocities. In a sense this is three velocities for one particle after all. Perhaps this is just a fiction for calculational purposes, but it is nonetheless a meaningful way to in a sense attribute multiple velocities to the same particle.

But there is also this: perhaps we try to attribute multiple velocities to the same particle and see that it doesn’t work out. If it were merely empirical that it didn’t work out, this claim would have the status of a scientific generalization – ‘maybe someday someone will observe a particle with two velocities at once’. (Quantum indeterminacy?) But that’s not ever what we do; we just lay it down that there can be only one.

What is the positing of this other form of necessity supposed to be helping us with? Any necessity we can specify at the predicate level we can also specify at the propositional level, so why insist that in some cases it’s really in the predicates, in others in the propositions?


The So-Called Color Exclusion Problem

People, by which I mean philosophers, often say that there is a difference between logical possibility and metaphysical possibility. Maybe there is, but I want to poke at one commonly given example of so-called non-logical metaphysical possibility a bit.

This example runs as follows: a thing can’t be both completely red and completely green, but this is not a matter of logic, because CR(x) and CG(x) are different predicates, and so in terms of ‘sheer consistency’ or whatever there’s no contradiction in holding (CR(x) & CG(x)), but nonetheless ‘if you know what they mean’ you’ll see that this is impossible. (This is sometimes referred to as ‘the color-exclusion problem’.)

Not sure I’m buying the setup today. Here’s another argument for comparison: a thing can’t be both a unicorn and a bicorn, but this isn’t a matter of logic, because U(x) and B(x) are different predicates, and so in terms of ‘sheer consistency’ or whatever there’s no contradiction in holding (U(x) & B(x)), but nonetheless ‘if you know what they mean’ you’ll see that this is impossible.

We would object to that argument presumably because we can explicate one-hornedness and two-hornedness in more exact terms, and once we do we see that it’s in fact sheerly inconsistent to hold that the same entity has exactly one horn and exactly two horns – this is a contradiction and hence ‘logically impossible’. What was happening in the original argument is that we were ignoring what the predicates meant – underinterpreting the signs, if you like.

This morning I am somewhat of the opinion that exactly the same thing is going on in the color-exclusion problem.

Can something be red and green at the same time? Of course; the Italian flag will do as an example, with white thrown in for good measure. Can it be completely red and completely green at the same time? No – but what are we saying when we say this?

It strikes me that to say that x is completely red is to say that x is red and that there is not a color other than red such that x has that color, or something like that. In which case the assertion that x is completely red and that x is completely green, or for that matter even completely red and also green, contradict one another – but in entirely the ordinary way. It’s inconsistent to say that a thing has no color but red, and also that it has the color green, in just the way that it’s inconsistent to say that a thing has exactly one horn and exactly two horns, or that an object has both exactly zero vertices and exactly four.

So on this way of thinking there’s no special ‘metaphysical necessity’ in the so-called ‘color exclusion problem.’ To say that something is completely such-and-such a color just is to say that it doesn’t have any other colors alongside the color it completely is. If it’s red all over there’s no space left into which to tuck another color; but we said that already when we said “all over.”

As a counter-argument: imagine a four-predicate universe, where the four predicates are round, square, entirely-green, entirely-red. We can’t have (round & not round) by logic, but we can have (round & entirely green) or (square and entirely red). Why can’t we have (round & square) or (entirely-green & entirely-red)? We can’t, but it’s not a logical contradiction, so this isn’t a matter of logic, but something else.

If you insist on representing it like this, there’s a sense in which you’re right, but it’s peculiar to insist on representing it like this. For example, here is an argument that all inferences (except perhaps “a, therefore a”) are invalid.  The premises and the conclusion are different propositions. Therefore, the premises should be symbolized with different letters – p, q, r, and so on – and the conclusion with c. But inferring from one or an arbitrarily large set of propositions to another proposition is invalid. So all propositional inferences are invalid.

You might object to this that the inference from “George W. Bush was a U. S. President and Barack H. Obama is a U. S. President” to “Barack H. Obama is a U. S. President” is not an inference from some arbitary p to some arbitrary q, but rather from a compound proposition (p & q) to p alone, which inference would be valid. And you would be right; but you would only be right because you understand the words you are speaking and represent them in accordance with that understanding. Qua uninterpreted signs, there is no reason to think that representing this as inferring q from p&q is any better than representing this as inferring q from p. (That’s just what ‘uninterpreted’ means.)

Similarly if we understand round and square as descriptors of shapes in the plane, we can understand them as, say, ‘uniformly symmetrical 0-vertex figure’ and ‘uniformly symmetrical 4-vertex figure,’ and likewise ‘entirely red’ and ‘entirely green’ as ‘red and no other color’ and ‘green and no other color’, and then we’re just dealing with good old fashioned contradiction here. A thing can’t have green and no other color and also have red, and it can’t have exactly four vertices and exactly zero. That’s just the usual stuff.

I feel that I must be missing something obvious here, since so many gifted thinkers accept this distinction, but just now I am not sure I understand it, even though I’ve given presentations on it in the classroom – “and very good ones they were, as I thought” – from time to time.

What is it?

What Would A Tractarian Calculus Look Like?

This is another post I wrote while not finishing up my post about the notion of sense. The use Wittgenstein makes of the notions of the sense of a proposition and the form of representation of a picture is to undercut what might be called ‘the problem of mental representation’: how does this thought here in my head represent that thing out there in the world?  This is a core problem in the history of philosophy and W rejects the setup that leads to it. I think seeing that and how he does that is critical to understanding his philosophy of logic and with it the questions we started out with about how to understand the book as a whole.

But I’m not going to talk about that today. Instead I want to reflect on how we would set up a system of formal logic Tractatus-style.

Wittgenstein does make recommendations, for instance at 4.1273: since “the concept symbolized by ‘term of this formal series’ is a formal concept,” “the general term of a formal series can only be expressed by a variable,” and thus the way “Frege and Russell…express general propositions like [a stands in some ancestral of the successor relation to b] is false; it contains a vicious circle.” In this passage we see Wittgenstein’s belief that logical statements are meaningless applied: a general abstract description (or ‘description at the meta-level’) of the ancestral of the successor relation, according to him, asserts nothing at all, because its objects are not objects at all, but variables, formal concepts.

Wittgenstein’s solution to this is to suggest that what are called ‘inductive definitions’ in mathematics are a better approach to the general term of a formal series: we give “its first term and the general form of the operation, which generates the following term out of the preceding proposition.” And then when he comes to the general form of propositions in 6, he does just this, giving a rule for generating whatever propositions you like by repeated applications of the Sheffer stroke to the elementary propositions. But you don’t say that any of those propositions ‘exist’, or quantify over them; you just give a rule for generating them which can be applied as many times as you need. This means that you never have to talk about them; you just provide a procedure for iterating as many as you need.

We wouldn’t quantify over propositions at the meta-level in a Tractarian calculus, it seems.

I think it’s also an interesting question how we would deal with what are called, in ordinary logic, predicates and relation-terms. It seems likely to me that e.g. “that ball is red” would be most perspicuously symbolized not, as we normally learn, “Rb,” but as something like f(location, ball, red). Remember that “the elementary proposition consists of names” (4.22, 5.55) – and so “The elementary proposition I write as function of the names, in the form “fx”, “f(x,y)”, etc. Or I indicate it by the letters p, q, r.” (4.24)

Consider by contrast “the cat is on the mat.” One can debate here whether “being-on” is the relation that the cat stands in to the mat, or whether the sentence as a whole asserts that a particular cat, being-on, and a particular mat are organized in a certain way. I have some inclination, though, to think that f(particular cat, being-on, particular mat) is more perspicuous, in the sense that logic is supposed to abstract from all structure, even spatial structure, and that being-on is a matter of a particular kind of spatial structure (perhaps spatial-gravitational or spatial-perceptual as well, but leave that aside). Furthermore, it is something that we verify by looking – we see whether a thing is on something else or not – so in that sense “being on” is just as much something that we can project on to reality as part of a sensible proposition as being Mitten the Kitten is.

So too with “redness” – it is something manifest, there along with the ball so to speak. Is it therefore an ‘object’? Why not? All this word signifies in the Tractatus, remember, is a formal concept – a variable for names. (So now – go back to 1-2 and consider the fact as consisting of objects – two plums in the icebox. To say that “facts consist of objects” is really to say nothing at all – it is a senseless – but on the other hand, there are two plums in the icebox, and if you understand it, you know which plums and icebox are meant.)

We could put arbitary physical entities in the same spatial arrangement, but we could also put the same physical entities in arbitary spatial arrangements. Since we can make any part of a proposition into a variable, and the parts of propositions are objects, it seems to me to follow from this that any as it were ‘abstractable feature’ ought to be an object in the technical sense of the Tractatus. So that if we are going to think of f(a,b,c…) as a proposition, where f is what it asserts about its constituents, then there is a sense in which all the significant stuff, which is to say anything that we can ‘abstract over’ and thus ‘turn into a variable’, needs to be among the ‘names’, and the f should be only be their logical structure, so to speak.

The difficulty with that suggestion, however, is that logical structure is in a way just a shadow of spatial, temporal, social, etc. structure – there isn’t any ‘logical structure’ – ‘logical structure’ is a formal concept in which e.g. spatial structure is turned into a variable. (Another reason why this stuff I’m saying right here in this post is meaningless.)

So it’s just a list of names? “The cat is on the mat” analyzed as the cat, being-on, the mat?

Well, no – there’s a connection between these names – that’s the sense of “the cat is on the mat” and it shows itself if you understand what someone who says “the cat is on the mat” is saying. But you can’t represent that sense. The sense is what you understand when you understand what the proposition says. On the other hand, you can represent spatial relatedness, by exhibiting the same relations with different entities standing in them to one another. So plausibly, a spatial relation is something named in a proposition, an object if you like, and not the ineffable structure of the proposition which ‘fact-izes’ those objects together.

I realize that I am here picking up a thread of thought that came out of long-ago discussions with Lynette. In a paper of hers you can check out here:’s%20Ladder.pdf

she is reflecting on, upon other things, the notion of a ‘category clash’ and says (pp. 122-3):

“One of the anti-metaphysical stands of the Tractatus is that logic cannot judge in advance what the internal articulation of fully analyzed propositions will be: contrary to Frege and Russell, who think it essential to the nature of representation that a proposition segment into subject and predicate of some sort, the Tractatus denies that there is any point in discussing in advance whether elementary propositions will consist of names and concept-expressions, or n-termed relation-expressions, or anything else. The only interest logic takes in the internal composition of propositions is that they contribute to what we ask of the world in determining whether propositions are true or false; logic only interests itself in this because this is how they contrast with logical constants, and confusing the two is the primary error that gives birth to metaphysics.”

This is on the right track, but I wonder if we shouldn’t maybe say something even more severe: that in effect any system of categories is just going to produce what is in effect a list of names from a logical point of view. (So you might say something like: the details of structure never matter to logic, only the fact that things are structured.)

Or to go back to Frege for a minute – it’s not that we have object-terms and concept-terms with holes for them; rather we have object terms, and the proposition itself is ‘the system of holes’ into which those object-terms are dropped.

(Also, going back to the original question: does anyone know of old dissertations floating around out there which make plausible stabs at ‘the logical system of the Tractatus’)?

The Generality of Logic

At 2.182, Wittgenstein says: “Every picture is also a logical picture. (On the other hand, for example, not every picture is spatial.)”

I can imagine someone worrying that this might be an oversimplification of some kind. For example, people have sometimes debated whether ‘quantum logic’, which is a sort of probability logic, should be the ‘true logic’, since physics tells us that there are some systems in which ‘particle P is at (x,y,z)’ (all of this is itself grossly oversimplified, but never mind) is ‘neither true nor false’ but only probable to such-and-such a degree.

“The cat is on the mat” asserts a spatial relationship between two extended things. If Wittgenstein is right it also asserts a ‘logical’ relationship between them. But in what does that ‘logical’ relationship consist?

The right answer here, surely, is that all it consists in is the cat’s being on the mat. “The proposition is a picture of reality, for I know the state of affairs presented by it, if I understand the proposition.” (4.021)

The geometry, physics, biochemistry, evolution, embedded cognition, etc. of cats on mats might be enormously complicated. Perhaps there are lots of interesting things to study here. But those details don’t really matter to the proposition’s being a logical picture.  

“The proposition shows its sense. The proposition shows how things stand, if it is true. And it says, that they do so stand.” (4.022) Sense, or ‘how things stand if it is true’, is not something which itself has any representation for Wittgenstein in the Tractatus. Likewise the picture’s form of representation: it is not itself represented. There’s nothing ‘in virtue of which’ a proposition is a logical picture of the facts. It is a logical picture of the facts – even, in a way, by virtue of representing them – but there is no ‘representation-relation’, or even a nontrivial second-order fact that such-and-such is a representation, picture, etc.

The key to understanding how this can be so for Wittgenstein is in the way he thinks about sense (Sinn), about which I am preparing a post. Because of the tight link between propositions, thoughts, pictures, and facts they don’t come apart for Wittgenstein in the way that they do for most philosophers. It’s in a way a result of this that there’s nothing to be represented here. But more on that anon.

In any case, it’s a logical picture just because it’s a picture, and the way in which it pictures isn’t relevant to its logical picturing. Logic leaves the facts and our means of representing them off to one side. What matters to logic is just that the picture could apply to reality or fail to do so.

This is connected to something he said later, in 1931:

“When I ‘have done with the world’ I shall have created an amorphous (transparent) mass and the world in all its variety will be left on one side like an uninteresting lumber room. Or perhaps more precisely: the whole outcome of this entire work is for the world to be set on one side. (A throwing-into-the-lumber-room of the whole world.)” (Culture and Value, 9e)

This is quite a striking remark, and in a way cuts against my bit about ‘turning off the TV and going outside’ in the “True but Nonsensical” post from August 31, 2013. The assumption made there is that showing that the terms in which we philosophize are inevitably nonsensical would serve to render the pursuit of philosophy valueless. But this is a bad assumption, privileging product over process. If “the logical clarification of thoughts” (4.112) is what is wanted, then kites and chemical reactions aren’t so much of interest after all.

But let’s get back to quantum logic. We might, as many physicists seem to think, have to employ a notion of ‘chance’ as fundamental in our physical representations of the universe. But even if so this would not make much of a difference for logic as Wittgenstein understood it. We might for example move the probabilities into the propositions, so that “there is a q% chance that particle P is at (x,y,z)” is either true or false, that being the sort of proposition that we can confidently apply to the world on the basis of current theory.

The question which gave rise to this post, though, is – how do we know that’s always something we can do? Can we always reduce the things we say about the world to pictures which either apply or do not apply to reality?

The answer that Wittgenstein gives, roughly, is something like this: if a proposition isn’t a picture, it’s without sense, and we don’t need to worry about it. If it is a picture, it’s also a logical picture, and then it either applies or it doesn’t. No matter how fantastically complex the picture is, this will be the case.

This seems like a plausible claim to me. But do we have to accept it? Are there other options?

When I first started writing this post I was wondering if there were very complicated sorts of facts that were on the one hand so interconnected that you couldn’t break them out cleanly from one another, but on the other hand individually expressible independent of those interconnections. But now that I’ve finished writing the post the sentence I just wrote really reads like nonsense to me. It seems to be asserting that a fact could be atomic and compound at the same time, or that we could have big pictures which both could and couldn’t be broken into smaller pictures. Which, um.

Have I achieved clarity? Or just drunk the kool-aid? Inquiring minds want to know.

Names and Propositions

Lynette and I have been carrying on a discussion under the “Tractatus One” post that has been nicely wide-ranging. I wanted to pull out a few different themes for separate treatment:

1. The general question I’ve focused on, possibly too quickly, is – how do we understand the propositions of the Tractatus, and indeed the Tractatus as a whole, as – for lack of a better term – a ‘speech act’? What is Wittgenstein up to here and what is he trying to do philosophically?

2. What, if anything, is the Tractatus’ doctrine of ordinary assertion/the propositions of natural science? This is where the saying/showing distinction comes in, which needs more discussion, and probably what will be taken up in the next series of posts (although I still have four planned to get on here). 

(1) and (2) are both more central than an issue which has come up in my conversation with Lynette, which is

3. Is Wittgenstein’s view of the relation between names and propositions, and the corresponding relation between objects and facts, coherent? 

That’s what I want to discuss here, touching on (2) and (1) only where necessary.

Wittgenstein says that atomic facts are composed of objects (2.01) and that elementary propositions are composed of names (4.22). He also says that knowing an object is knowing the possibilities of its occurrence in atomic facts (2.0123), and that names only have meaning in the context of a proposition (3.3). There are many other passages that restate these points in slightly different ways.

The question I have about this runs like this. If we held to a kind of ‘Platonism’ about the world, so that as it were all facts are just laid out there, corresponding to a Book of Life which contains all true propositions I suppose, then we would, by reading this book, be able to have a complete grasp of all the names by way of our understanding of all the propositions in which they occur; and likewise we would know all the objects completely by knowing all the facts in which they were involved.

Lacking that, however, it might seem that our ability to use old names in new propositions and to ask new kinds of question about the objects they name (e.g. questions about chemical composition) suggests some kind of grasp of the name which is quasi-independent of the _actual_  propositions one understands antecedent to the new use.

I have a sense that this is the wrong kind of question to be asking relative to the Tractatus, but this is what I was trying to get at in the exchange with Lynette in the comment thread. The formal issue is that given a complete specification of a ‘language’ as a set of propositions constructed out of names, one can indeed ‘reduce’ the names to classes of propositions that contain them. But our language is not completely specified in this way, which leaves the question of how names and propositions relate to each other, whether they can really be perfectly interdependent in the way that Wittgenstein wants to say, a little bit unsettled in my mind.

I think that talking about saying and showing in significant propositions (e.g. Miriam is watching a movie on the couch) may help bring out whether there is a serious issue here or not. But the work that Wittgenstein uses our grasp of names to do e.g. in ruling out the significance of the equals sign makes me wonder a bit. Do ‘evening star’ and ‘morning star’ name the same object or not? I am not sure I want to give a univocal answer to that question. 

The First Rule of Wittgenstein Club?

I’d like in this post to consider a doctrine I will call Semantic Pyrrhonism.

Classical Pyrrhonism (as defended by Sextus Empiricus, e.g.) is most naturally understood as an epistemic doctrine. This doctrine contains the following components: first, that propositions may be divided into two types, roughly, the propositions of ordinary life (whichever those are – usually they are thought of as being grounded in some kind of more-or-less unproblematic types of perception, desire, and/or social life) and the propositions of, let us say, ‘theory’: science, philosophy, religion, and so on. Second, that the theoretical propositions are one and all unknowable, so that one should neither believe nor disbelieve them, but rather maintain neutrality with respect to them – to be skeptical of them in one sense of that word.

One problem with Epistemic Pyrrhonism is that of delimiting the boundary between the ordinary and the theoretical. It is simply not clear where that boundary lies, as anyone familiar with realist-empiricist debates in philosophy of science over the last half-century can attest to. (An unfertilized egg is a single cell; are cells theoretical posits or objects of ordinary observation?) But the deeper issue is that of specifying the boundary. It seems that any specification of a boundary between the ordinary and the theoretical would have to be a theoretical specification, since we don’t seem to be provided with clear criteria here by nature or some simple form of perception. But as such, the boundary thus specified would have to remain unknowable, since it would fall on the theoretical side of the division.

I leave it as an exercise for the interested reader to determine whether this aspect of Epistemic Pyrrhonism should be a matter of concern to a serious adherent of that view.

Having adumbrated this doctrine, however, let us move on to its stronger analogue, Semantic Pyrrhonism. Semantic Pyrrhonism accepts some similar sort of distinction between types of propositions, say those belonging to ‘ordinary language’ and/or ‘natural science’ on one side and those belonging to philosophy, metaphysics, etc. on the other.  But its claim about the propositions of the far side is not that they are unknowable; rather, they are simply meaningless. It’s not that we can’t know whether, say, being is intrinsically determinate (that is, whether being is always being-such-and-such); rather, the propositions ‘being is intrinsically determinate’ and ‘being is not intrinsically determinate’ are alike nonsensical, saying nothing at all.

Let us say that, for whatever reason, a person was attracted to Semantic Pyrrhonism. It seems to me that such a person might well pass through several stages of understanding of her own doctrine.

The first stage might run like this: “We now have a clear demarcation of sense from nonsense. Being in possession of this, we can now sort out the sciences, humanities, and other forms of human discourse, and in general let people know which utterances of theirs are meaningful and which are not.” To argue this position, you would need to state more precisely what constituted the boundary between meaningful and meaningless propositions. If you were a thoughtful person, or if other philosophers pestered you about it enough, you would eventually come to realize that your proposed demarcation was itself on the ‘philosophical’ or ‘metaphysical’ side of the boundary, and thus that your actual pronouncements about your own position were meaningless.

(A special case of the above: the verification theory of meaning is not itself verifiable.)

At this point a mild bewilderment might set in. You tried to demarcate the meaningful from the meaningless, but your demarcation failed to meet its own standard. And yet! You were so sure that you had exposed various propositions as nonsense, and likewise gotten a grasp of how sensible propositions were constructed. And it can’t after all be doubted that reasoning has its structures, and arguing in language as well.

So what to make of all this? You might think: well, we can’t state what separates significant propositions from nonsense, but we recognize sense where we find it, and recognize too what constitutes good reasoning from propositions with sense and what doesn’t. There is some confusing thing here, perhaps analogous to the paradoxes of self-reference, that prevents us from completely articulating what the bounds of sense might be, but nonetheless we can think those bounds by way of this kind of sustained conceptual investigation. By investigating that which has sense we can develop a sense for its boundaries and recognize what lies without and what lies within, even if the precise bounds are unstatable.

But this position winds up being unstable too. What is this thought that compasses all sensible utterance and yet which cannot be stated? A strange sort of meta-seeing, this: not watching the sunrise or drinking cool water, but rather a mental appreciation that what we say about sunrises and glasses of water and things of that sort can be true or false, while what we say about the freedom of the will and the intrinsic determinacy of being and non-things of that sort can’t

This is quite a lot of structure to pack into a non-linguistic perception, even assuming such things are possible.

But what else can you do? Well, there is a third way, after all. Like the Epistemic Pyrrhonean, we appear to have a problem here with our proposed demarcation of sense from nonsense. We can’t coherently state what this demarcation is, since it rules itself out, and we can’t think it either.

But what we can do is simply stick to saying things that make sense. When someone else talks to us in a way that doesn’t make any obvious sense, we can quiz her to see what she is talking about; perhaps she knows something we don’t and we can learn from her. If this doesn’t work out there may eventually come a point where we try to shake her out of her complacent acquiescence to talking nonsense by trying to expose that nonsense for what it is, deriving contradictions, exposing lacunae, asking for the meaning of terms, and so on. And likewise, when we find ourselves driven to talk in similar ways, we can try to chase down what makes us want to talk that way in the first place.

From this point of view we take our existing forms of sense-making as a given and resist the urge to include things that don’t make sense, or cut off things that do, on the basis of various generalizations we might be inclined to make about what makes sense and what doesn’t.

So has the Semantic Pyrrhonist undermined her own doctrine at this third phase or not? On the one hand, the answer is in some sense yes, in that there is no particular doctrine here to be expressed any more; any attempt to express it must end in meaningless utterance. On the other hand – the Semantic Pyrrhonist seems now to relate to language and communication in a different way. Propositions having a clear sense in context are de-problematized, regardless of odd inferences one might draw from them – the odd inferences are the problem, not the propositions. And generalizations are now no longer any better than their application.

If someone accuses the Semantic Pyrrhonist of being conservative, or perverse, she has a simple recourse: she’s just trying to figure out what people are saying, and whether or not it is true, the same as the rest of us.

6.53 The right method of philosophy would be this. To say nothing except what can be said, i.e. the propositions of natural science, i.e. something that has nothing to do with philosophy: and then always, when someone else wished to say something metaphysical, to demonstrate to him that he had given no meaning to certain signs in his propositions. This method would be unsatisfying to the other—he would not have the feeling that we were teaching him philosophy—but it would be the only strictly correct method.

7 Whereof one cannot speak, thereof one must be silent.