Thursday, 5 April 2012

Meaning is Use Part 2: the Caveat and Ostensive Definition

As you may recall, while considering Wittgenstein’s linking of meaning to use I’ve been fretting about the caveat he introduces in §43:

For a large class of cases of the employment of the word “meaning” – though not for all – this word can be explained in this way: the meaning of a word is its use in the language.

This seems to suggest that for some words their meaning is not their use. But which types of word does Wittgenstein have in mind, and what actually is their meaning if it isn’t their use?

One possibility (which I’ve certainly found tempting) runs as follows: for abstract nouns, adjectives, verbs, etc, the meaning is their use. For concrete nouns, however, meaning is more straightforwardly connected to the objects named. The meaning, in other words, is the object. Why is this distinction tempting? Because when asked for the meaning of a word like “love” we can’t point to the thing itself and so fall back on descriptions of use, synonyms, etc. But with a concrete noun such as “apple” we can simply point to an example and say “This q b”. This method (known as “ostensive definition”) seems clear and exact, and yet doesn’t involve an explanation of use. After all, “This q b” would be a perfectly good answer to “What does the word ‘apple’ mean?” but not to “How is the word ‘apple’ used?”

At this point the clarity and exactness of ostensive definition might tempt us to go further and claim it provides a foundation for meaning. Descriptive definition looks vague by comparison and always seems open to misinterpretation. True, we might clarify it with a further description, but won’t that also be vague? So our clarification itself requires a clarification, and now we’re in danger of falling into a regress. As the interlocutor puts it in §87: “how does an explanation help me to understand, if, after all, it is not the final one? In that case the explanation is never completed; so I still don’t understand what he means, and never shall!” The very possibility of meaning seems to require an escape from this regress, and ostensive definition looks like a promising solution.

If it is to play this role then we can identify three connected conditions that ostensive definition must satisfy:

i.                    It must be fundamental. Descriptions of meaning might be analysed into a series of ostensive definitions, but such definitions can themselves neither have nor need any further analysis. After all, if an ostensive definition requires further explanation presumably this will take the form of a description and we’re back with the problem of a regress. Ostensive definition must be the end of the line.

ii.                  It must be complete. If ostensive definition doesn’t provide the whole meaning of a word then it leaves some aspects undecided and therefore meaning is not clear. In that case the definition would not be fundamental. To put it another way, if the object is the meaning and ostensive definition picks out the object then it must also pick out the meaning. All of it.

iii.                It must be unambiguous. If the connection established between word and object isn’t completely clear then doubt as to meaning is still possible. Once again, further support is needed and so a foundation has not been provided.

At this point we have arrived at what might be called a mythology of ostensive definition. Puzzlement over certain aspects of meaning has led us, step by step, to a theory about what must be the case – in other words, a metaphysical theory. (It is also worth noting how this theory threatens to pull the whole of language into its gravitational field. It was introduced to explain the meaning of concrete nouns, but surely other types of word need a definite meaning too? And if definite meaning cannot be provided by description then an alternative is just as necessary for “love” as for “apple”). Not surprisingly, Wittgenstein is critical of this mythology and (characteristically) he attacks it on two fronts: from the inside, by demonstrating that – on its own terms – it cannot provide an unassailable foundation for meaning; and, from the outside, by contrasting the mythology with a description of the diverse but more modest role ostensive definition actually plays in our lives.

At §28 Wittgenstein imagines ostensively defining “two” by pointing at two nuts. The interlocutor objects that such a definition is inadequate because it is open to misinterpretation: “he will suppose that ‘two’ is the name given to this group of nuts!” Wittgenstein’s reply turns the tables: “he might equally well take a person’s name, which I explain ostensively, as that of a colour, of a race, or even of a point of the compass. That is to say, an ostensive definition can be variously interpreted in any case.” The potential pitfalls that accompany the ostensive definition of abstract terms are – from a logical standpoint – equally pressing in the case of concrete nouns. This simple observation threatens to unravel the whole mythology at a stroke: if a mistake is always possible then ostensive definition is never unambiguous. And if that’s true then it isn’t complete either, for something else is needed to ensure that the correct meaning is grasped on each occasion. And if it’s neither unambiguous nor complete then it can hardly be called fundamental. What seemed so clear and secure is in danger of falling to pieces before our eyes.

At §33 the interlocutor attempts to patch up the damage: “one need only – obviously – know (or guess) what the person giving the explanation is pointing at.” The idea is that the gesture’s intended target (colour, shape, etc) is contained within the act itself – perhaps via a mental state reflected in a characteristic form of behaviour (eg, pointing or gazing in a particular way). By observing the behaviour we can infer the mental state and, therefore, grasp the meaning. In this way everything is kept “in-house” and, needing no external support, ostensive definition retains its fundamental status. This picture of “inner” meaning inferred from “outer” behaviour is one Wittgenstein confronts on numerous occasions in the Investigations. For the moment, however, he restricts himself to some brief, but significant, observations: “… neither the expression ‘to mean the explanation in such-and-such a way’ nor the expression ‘to interpret the explanation in such-and-such a way’ signifies a process which accompanies the giving and hearing of an explanation” (PI §34). Why not? Because “even if something of the sort [ie, a characteristic experience of pointing] did recur in all cases, it would still depend on the circumstances – that is, on what happened before and after the pointing – whether we would say ‘He pointed at the shape and not at the colour’.” (PI §35).

It is important to note here that Wittgenstein is not denying the existence of mental experiences accompanying instances of meaning or understanding. Nor, indeed, is he denying that such experiences play an important role in allowing us to use language the way we do. What he is pointing out is that the rules governing the correct application of concepts like “meaning” and “understanding” do not hinge upon the identification of mental experiences (or states or processes). If I point at various red objects saying “red” each time and you then consistently pick out red objects when asked to do so, you have correctly understood my meaning. That is how “correct understanding” is defined in such cases. This is not a claim about brain functions or psychological processes (which would be empirical claims requiring scientific investigation). It is a fact about the grammar of the concepts “meaning”, “understanding” and “correct”. From this point of view, your opinion about what was going through my mind when I gave the definition “Red q nis neither here nor there. And, likewise, my opinion about your mental state when you correctly followed the order “pick out the red object” is irrelevant. Furthermore, my mental state when saying “Red q nis not the criterion for correctly defining “red”. And your mental state when picking out red objects is not the criterion for understanding the order “pick out the red object”.

Ostensive definition fails to operate in its assumed role as the unmistakable, stand-alone foundation for meaning. And yet it does operate – we use it all the time. Clearly, then, it has merit outside of any metaphysical function we may assign it. This brings us to Wittgenstein’s description of the role ostensive definition plays in our lives. It is a relatively brief passage, stretching from §§27-32 (though §6 and §10 should also be borne in mind), but several points emerge.

First (§27), requesting and receiving ostensive definitions is a language-game we learn along with the rest of our linguistic activity. We do not simply drum the names of objects into children’s heads and leave them to it (“As if what we did next were given with the mere act of naming”); we also use the words in situ, even before a child is in any position to understand what we are saying. So rather than being the fundamental building-block of language, ostensive definition is just one element among many and only functions as a definition within this wider context.

Secondly, it is more varied in subject-matter than the mythology might suggest. At §28 Wittgenstein lists some examples and, far from being confined to concrete nouns, they include colour-words, number-words and points of the compass. This is the upside of the fact that all definitions are open to misinterpretation; once the myth of unambiguousness is removed the key question changes from "can I point to something?" to "will he apply the definition correctly?" It’s then possible to ostensibly define even subtle, abstract words like "otiose" by (eg) showing a series of texts and underlining the redundant clauses: "The batchelor was unmarried", "He played patience by himself", "√25=5+0.0r", etc. Maybe the pupil will understand, maybe she won’t; the general success-rate defines the method’s usefulness.

Here (thirdly) we start to see how not just the subject-matter but also the form of ostensive definitions may be varied, and how there is not always a clear distinction between ostensive and descriptive methods. The “otiose” example is itself close to being an idiosyncratic type of description; it is certainly a long way away from “Apple q b”, and could easily be recast into descriptive form. A similar point applies to written lists with the form "[x] signifies [y]". These are a variation of ostensive definition yet Wittgenstein calls them an abbreviated description of use (§10). Why abbreviated? Because they take for granted the wider context in which the defined word operates. In effect, “Apple q b” is (usually) a shorthand for something like “Use the word ‘apple’ to refer to the type of fruit of which this q b is a typical example”. We don’t often give such long-winded explanations because the context of asking generally renders them unnecessary. Forgetting this can make it seem as if everything was done by the ostensive act itself whereas, in fact, even what is defined depends on the context. Consider the following cases:

  1. I have deduced the rules of chess by watching the game but without hearing any talk about it (I need not even know that it’s called chess). Now I start playing and during the game my opponent says “Your king is exposed.” I ask, “What do you mean by ‘king’?” And he replies “This qè.”

  1. I have learnt chess on a computer using a 2-D board where the symbol for the king is the letter “K” in a circle (I know that this is called the king). Now I’m introduced to a standard wooden chess set and I ask “Which is the king?” My opponent replies: “This qè.”

  1. I know nothing at all about chess. My friend is setting up the boards for a chess club meeting and notices one set has a piece missing. He tells me to fetch a spare king from the cupboard. I ask “What do you mean by king?” And he replies: “This qè.”

In each case the meaning explained is different. In (i) it could be expressed as: “The piece that looks like this qè and moves in such-and-such a way is called the king.” In (ii) as: “The piece called the king, which moves in such-and-such a way, looks like this qè.” And in (iii) as: “The object that looks like this qè is called a king.” But now suppose you give the definition “King qè“ to someone who not only knows nothing about chess, but has never even encountered board games or any activity involving pieces. What, exactly, have you achieved with your definition? At most (it seems to me) you have alerted the pupil to the fact that there is some sort of connection between something about the object and the word “king”. That hardly seems to count as a definition at all.

Of course “the king in chess” is a relatively sophisticated concept, but even at the level of apples or pebbles similar considerations apply. The ostensive definition “Apple q bqua definition presupposes some level of linguistic competence: (eg) a familiarity with the language-game of asking for, and being given, the names of physical objects, and the way in which such names are subsequently used. This competence is so basic it is easy to overlook it entirely and assume the function of the definition is somehow built into the act itself. It will then appear as if the mere performance of an ostensive definition was enough to guarantee its success.

It seemed we had two entirely separate types of definition: ostensive and descriptive. Of these two, ostensive definition appeared fundamental, unambiguous and complete. Description, on the other hand, was distinctly second-best; it was what we made do with when we couldn't define a word ostensively. But this assessment turned out to be founded on an inability to look clearly at how ostensive definition functioned in practice. Once we had done this, a quite different picture emerged. Ostensive definition was neither complete, unambiguous nor fundamental. It was not even entirely distinct from description. Instead, it was simply one technique amongst many, extremely useful in some contexts, less so in others. Its privileged status was a chimera, because language is not founded in unambiguous definitions, but in application - that is to say, in human behavior.

Obviously this spells trouble for my initial suggestion that ostensive definition might be an example of a “use-free” explanation of meaning suggested by §43. Ostensive definition only appeared use-free when considered in isolation – as a fundamental, stand-alone performance requiring no context or outside factors to give it meaning. Viewed in that light, it may well not involve use, but it doesn’t function as a definition either. As soon as context is reintroduced, the question of use inevitably follows in its wake. Take, for example, my earlier point that “This q b” would be a strange reply to the question “How is the world ‘apple’ used?” It isn’t actually difficult to imagine a context in which that reply would be more or less helpful. For example, I use the word “apple” in a sentence but my friend is unsure whether I mean the fruit or the increasingly evil technology company. He asks “How were you using ‘apple’ just then?” His question alerts me to the ambiguity of my statement (ie, I understand his confusion), and I clarify matters by saying “This q b”. True, this is still idiosyncratic, but it gets the job done and only requires a little tweaking to provide it with a more conventional form: “I was using it to mean the fruit. This q b for example”. Once again, it becomes apparent that the ostensive act is a context-dependent distillation of description. There is no getting away from it: ostensive definition is up to its neck in use.

But in that case what about the caveat? Are there any remaining candidates for words whose meaning is not their use? At this point I must confess that I think I've made a grade-A, bone-headed blunder. Allow me to explain.

One of my difficulties with §43 is that I find the Hacker/Schulte translation rather torturously phrased. Its meaning keeps slipping away from me as I read it over and over. With this in mind, I recently checked it against Anscombe's original version. This is what I found:

For a large class of cases - though not for all - in which we employ the word "meaning" it can be defined thus: the meaning of a word is its use in the language.
PI §43, Third Edition

I can’t say whether the third or fourth edition best captures Wittgenstein’s style, but the third edition’s rendering of §43 seems admirably clear. More importantly, it at once suggested an obvious point which I had previously ignored: the cases in which we employ the word “meaning” include numerous ones that are not about the use of words for the simple reason that they are not about words at all. A few examples:

“What was the meaning of that look you gave me?”
“What is the meaning of that tattoo on your arm?”
“What does the opening of Beethoven’s 5th symphony mean?”
“What is the meaning of all this noise?!”
“What is the meaning of life?”

I had been treating meaning as a kind of mechanism that only worked in one particular way and was exclusively related to the phenomenon of language. But it now seems to me that at least one reason for the caveat is to warn us against such a narrowly restricted focus. “Meaning” is a diffuse concept, connected to use, synonymy and definition, but also to significance and aptness. Keeping this diversity in mind is, for Wittgenstein, a way of avoiding being trapped by a particular picture – for example, “The object is the meaning of the word”.

Can we now therefore sum up §43 along the following lines: “insofar as meaning is concerned with words, it is concerned with their use”? Even this, I think, would be going too far. Consider the following exchange:

“I have called my new shop ‘Tesco’.”
“What does that mean?”
“It’s a combination of ‘T.E. Stockwell’ and my name, ‘Cohen’.”

Or how about this:

Kummerspeck is the German word for weight-gain due to emotional overeating. It literally means ‘grief bacon’.”

Words, just as much as looks or musical phrases, can have a meaning over and above their use. The complexity of the concept “meaning” defies reduction to a simple formula, and so we’re thrown back upon broad generalisations such as “much of the time meaning is about use”. And that, of course, is simply a paraphrase of §43.

Are these examples the sort of thing Wittgenstein has in mind when he introduces the caveat into §43? Are there not perhaps other, more pertinent, cases that I’ve overlooked? In a way these questions miss the point. The key thing is to recognise the complexity of the phenomenon at hand and to describe it accurately despite the urge to boil things down to a satisfying but misrepresentative formula. Or, as Wittgenstein puts it, “Say what you please, so long as it does not prevent you from seeing how things are. (And when you see that, there will be some things that you won’t say.)” PI §79.

Meaning is Use Part 3


  1. Hi Phil,

    So my reading of this is that Wittgenstein is anticipating an objection concerning words like logical connectives: "and", "or" and so forth. With words like this, which do not function to pick objects out, W.'s characteristic worries about metaphysics will not arise by admitting that their definitions are (relatively?) fixed. But this was purely speculative on my part... does it make sense to you?

    1. Hi Nick.

      I vaguely recall Wittgenstein having a fair amount to say about connectives in the Tractatus [A little help, please, TLP gurus!]. By the time of the Investigations, however, they don't get much of a look in, although I suppose they're lurking in the background when he states that language doesn't function like a logico-mathematical calculus. Basically, however, these words fall squarely under the "meaning is use" rubric. Are they rigidly defined? I'm not sure. Compare: "The square root of 25 is either 5 or -5". "It's either him or me". "Dr Strangelove, or How I Learned to Stop Worrying and Love the Bomb". Does "or" play the same role in each case?

      The only one that really features is the logical solecism concerning "is" (or "="). Interestingly, this point is also in the Tractatus and plays an important part (albeit in a rather different context) at various points in the PI. It's also linked to issues regarding "the same", which (I think) is a hugely significant term in the Investigations.

    2. "My fundamental thought is that the logical constants do not represent," he says, in TLP 4.0312. That seems relevant. (But I'm no TLP guru, so I can't provide much help.)

  2. Hi Phil. Welcome back! And it has surely been worth the wait. Great post with a nice and convincing punch in the tail. I wonder if there is a link here with the idea that words are not just tools we use but also gestures we make. When we are in danger of getting metaphysical, it is useful to focus on use so we do not tie ourselves up in confused knots, but as you suggest, we shouldn't forget that some aspects of meaning are not primarily about getting things done. [Frank aka paul!]

    1. Hi Frank (or Paul!)

      Thanks for your kind words, I appreciate it. I hope my point about the diverse nature of "meaning" is pertinent, though I was also using it to save face after not spotting the bleeding obvious! :)

  3. Ah! Good to be reading you again. Thanks for this.

  4. Philip -

    Yet another "welcome back!"

    During much of your absence I've been struggling with meaning et al and will have several things to say about your post after digesting it a bit more. For the moment I'll just note that re §43, your lucid distinction between the "meaning" of words and other uses of "meaning" is what I was trying to capture here with "linguistic" and "non-linguistic". Ie, I second your speculation about "but not for all".

    1. Hi Charles.

      I look forward to your comments on §43. I have one more post on meaning, and then (thank heavens) I'll be through with it (for now).

  5. I have a horrible feeling that my rather nifty symbols for "pointing", "apple" and "king" don't show up on other people's browsers (though I can see them on mine). It's a shame, because I enjoyed hunting them out and incorporating them, but I'll substitute something more basic idc.

  6. Re §28:

    Sellars argues that awareness of a presented X as an X is not a Given. Assuming he's correct, perhaps one teaching a child by ostensive definition should use simples rather than objects. Presenting, say, a uniform red surface (eg, a large sheet of red construction paper) while uttering "red" should remove the ambiguity. Only later should different red shapes be presented (again against a uniform background), thereby emphasizing what feature is to be associated with uttered "red". Similarly, one might want initially to present a large uniform white surface on which is drawn a black circle (or disc) while uttering "circle". But to start with, say, a red ball while uttering "red" obviously results in ambiguity as addressed in §28. Is "red" to be associated with the color, the 2-D outline, the 3-D shape, the whole integrated object, other? This seems like something that Liz Spelke-type researchers might have addressed.

    If I point at various red objects saying “red” each time and you then consistently pick out red objects when asked to do so, you have correctly understood my meaning.

    This highlights an important point that may obscured by summarizing W's message as "meaning is use". The more cumbersome "the meaning of a word is its role in a language game" (this general idea also appears in Part VII of Sellars' EPM) seems better but still possibly incomplete, depending on how one interprets "role". The quote from Philip's post makes it explicit that "use" or "role" should be interpreted as including a speaker's objective, namely either to cause the hearer to act or to change the hearer's dispositions to act. As indicated in the quote, "meaning" in that expanded sense is understood if the hearer responds as intended by the speaker. Various aspects of this interpretation of "meaning" appear in the early sections of PI (discussed here under the sections labeled "ostension").

    This raises a question about Davidson's position that "only sentences have meaning". I started to write that I'm inclined to agree because even when the builder simply shouts "Slab!", that utterance functions as a command, ie, a sentence. But my vague impression is that Davidson's position is based on the truth bearing feature of propositions, and a command presumably doesn't have such a feature. Thinking of meaning in terms of intended responsive action seems to evaporate distinctions like sentence vs command vs proposition. Which I'm inclined to say is just fine since I have come to think of all "mental" issues in terms of generic action-response pairs (although with due consideration of possibly relevant aspects of underlying neural issues). Any opinions on this re Davidson?

    1. Hi Charles - thanks for your comments. I'll respond bit by bit as I'm rather pushed for time at the moment.

      RE: your first paragraph, two points.

      First, if you're talking about the most effective way to teach language then that is outside Wittgenstein's philosophical concerns - it is a matter for empirical study and experimentation. The point is that we DO learn language (including the names of objects) despite there being - from a logical point of view - ambiguity in our methods. As a form of life we "get" ostensive definition. Why or how we get it is not a question the philosopher can answer. From a philosophical point of view the abilities of the form of life represent a terminus - the given (PPF 345). I think you can sum up Wittgenstein's point as follows: a logically unambiguous foundation for language is neither possible nor necessary.

      Secondly, your suggestion of a uniform red surface is not logically unambiguous. It still has a particular shape, a particular number, it's made of a particular material, it lies in a particular direction etc. All of these qualities are potential candidates for the object of the definition and so the opportunity for misunderstanding remains. Don't forget, we're trying to find a LOGICALLY unambiguous foundation for Ostensive Definition - not one that, as it happens, the vast majority of people understand the vast majority of the time.

      More to follow....

  7. Re the examples of meanings of "king", I don't see that word as necessary in any of the three either as having "meaning" (in some sense) or even as a name.

    Implicit in example i) is the assumption that the player knows what it means for a piece to be "exposed", ie, how to react to the warning. So, associating the name "king" with the appropriate piece suffices for the player to be able to demonstrate "understanding" of the warning. But even that association isn't necessary since just saying "That piece (pointing at the king) is exposed" would achieve the desired result while "eliminating the middle man".

    In example ii), there are in essence two representations of the pieces and the board (I don't see one being 2-D and the other 3-D as significant, although I will use those as convenient labels). The player knows how to proceed using the 2-D representations. Naming the 3-D pieces requires only a mapping from the 2-D piece representations to the corresponding 3-D piece representations, and the starting positions of the pieces provide that. But as in example i), the names don't seem necessary, except perhaps as mnemonics for the unfamiliar objects.

    Example iii) seems another case of unnecessary naming - the result could be achieved by saying "Please get one of these (pointing) from the cupboard." In any event, "king" is no better than "Fred" since the name is irrelevant to the task.

    Or perhaps I'm missing something.

  8. Well, I think we need to review the bidding.

    There's nothing wrong in general with ostensive teaching - it's obviously the way infants are taught. The problem with Augustinian methodology (at least as represented in the famous quote) is not that it employs ostensive teaching (actually, learning) but that it's incoherent. It assumes a child with multiple sophisticated capabilities - eg, awareness of objects, and of "elders" and their subtle expressive miens; creation of recallable memories; inference - who is nonetheless still ostensively learning primitive associations of words and objects, and also how to utter basic sounds. Assuming such abilities while one is still in the early stages of learning is a major aspect of the Given, the subject of the first half of EPM. To coherently address the foundational potential of ostensive teaching, it is necessary to think in terms of teaching an infant that has none of those capabilities.

    In that vein, I was addressing the narrow issue of ambiguity in ostensive teaching that is raised in §28 (and §35, et al) and how such ambiguity might be reduced or, ideally, eliminated. Starting ostensive teaching with composites seems an obvious mistake both practically and logically. And I see no obvious reason why - at least in principle - teaching aids that amount to simples can't be created. Eg, if ostensive teaching begins with a surface that fills the FOV and is illuminated by controlled light, there is neither visible shape nor number (ie, distinguishable features), and the ability to tailor the spectral composition of light incident on the retina makes surface characteristics irrelevant. Strictly speaking, there is no need for a surface at all since in principle, appropriately tailored light shown directly into the eye will do the job. In such an idealized environment, the learner "sees pure disembodied color". (Quoted since each of those words is problematic.) Ie, ambiguity has been eliminated in such an idealized environment. This general idea could be extended to basic shapes, etc. Multi-featured objects would arrive late to the party.

    Of course, I'm not arguing for ostensive learning as foundational for meaning, just suggesting that some of the more difficult problems arise at advanced stages. At the early stages, ostensive teaching is, in a sense, foundational since it's how infants learn the abilities that Sellars argues aren't "given".

  9. I take your point, but I still think you're conflating the empirical question of the most effective way of ostensively teaching names with the philosophical requirement for a logical foundation. The former does not approach the latter as its techniques improve because the possibility of doubt always remains. Even with your example of disembodied light, it is possible a person might think (eg) "Red" referred to that particular way of experiencing that colour. This may strike us as unlikely, but that's not the point.

    1. I recently had much this same practical-vs-logical exchange (at the new Sellars blog), and at that time had to retreat since I didn't really get the distinction. However, in the interim I've been reading Hylton's "Quine" in which Quine's views on precisely these early aspects of learning language are discussed in detail. So although I still don't get why any aspect of it is properly called "logical", I know I'm in good company in "conflating" the practical aspect with whatever other aspect of the process that term is intended to capture.

      OTOH, I'm happy to drop the issue since my interest was only in reducing (not eliminating - my slip) ambiguity in support of building a foundation, "logical" or not.

    2. It's interesting you should mention Quine, because in my last reply I was going to say we were straying into the argument between Quinian Naturalism and the analytic/synthetic distinction. As you suggest, that's probably something to discuss at another time, but it is important.

      For now, I'll merely say that Wittgenstein would not have agreed with Quine's view on this. On the other hand, I doubt he'd have been happy with his inclusion in the Strawson/Carnap analytic/synthetic camp either. Wittgenstein wanted to debunk the sublimated approach of Fregean/Russellian logic. But he didn't want to replace it with anything like Quine's Naturalism (he most certainly did not see philosophy and science as continuous). His distinction was between grammatical propositions and empirical ones.

      Like I say, it's an important issue, and one that has profoundly shaped the development of American philosophy over the last 60 years. But for now we'd probably best put it to one side.

    3. Your posts always drive me back to previously read (and multiply reread) sections of PI in which I invariably find ideas missed before (perhaps part of why after over a year I'm still stuck in the early 200s!). §32 is the latest victim of such a reread, and my current take on it may help bridge our practical-vs-logical disconnect. It was quickly thrown together for this purpose, so critical assessment will be appreciated.

  10. Neologisms provide examples of words whose meanings (at least initially) are not supplied by use but rather by their creators.

  11. Hi Karl - but surely what the creator provides are rules for the use of the neologism?