Leonard Linsky:
Wittgenstein’s ladder is Frege’s grain of salt.
(H/T to Chad Kidd)
Category Archives: logic
Frege Betraying Frege
“We speak not only of the relation of a city to a country of which it is the capital or of a man to a child of which he is the father, but of the relation of an object to a function of which it is the argument. But whereas the first relation finds expression in sentences that have in common the expression ‘capital of’ and the second have in common the expression ‘father of’, the function-argument relation finds expression in complex designations such as ‘the capital of Holland’ and ‘Rembrant’s father’, which have no expression in common. For this relation is not one that can be put into words at all. We might say, echoing Tractatus 4.121, that it is not something we can express by means of language, but something which expresses itself in language…
“Frege’s thesis that a concept is a particular case of a function embodies the fundamental insight that the sense in which we speak of the relation of an object to a concept it falls under is the same as that in which we speak of the relation of an object to a function of which it is an argument. As there is no expression for the latter, so there is none for the former. If therefore we use the locution ‘a falls under the concept F‘ and write ‘Gold falls under the concept malleable‘ in place of ‘Gold is malleable’, we do not express in words a relation that is expressed in the shorter sentence without words. Frege thus betrays his own insight when we allows himself to be persuaded that because ‘falls under’ is a transitive verb, it stands for a relation…
“Since ‘falls under’ is not a relational expression, it follows that phrases of the form ‘the concept F‘ are not singular terms. Unlike ‘the city of Leeds’, which designates a certain city, ‘the concept malleable‘ does not designate a certain concept. Hence we cannot regard the verb and accusative of ‘Gold falls under the concept malleable‘ as signs in their own right. In combination they form an expression for a concept, but in themselves are not expressions for anything. Frege of course recognized that phrases of the form ‘the concept F’ are not concept-words, but if you take ‘falls under’ to be a genuine Beziehungswort, as Frege did in “On Concept and Object”, you have in consistency to construe such phrases as singular terms. Frege was thus forced to equivocate: as a singular term a phrase of this form must stand for an object, so by parity with ‘the city of Leeds’ it should stand for an object that (somehow) represents a concept. –And yet how easy it is to go astray here! For in our sentence there is expressed a relation between gold and the concept malleable. So what is more natural than to assume that ‘falls under’ is an expression for that relation? And yet the right conception is so close at hand! For if ‘the concept malleable‘ is not an expression for a concept, it cannot stand for the second term of the relation of an object’s falling under a concept. And so ‘falls under’ cannot itself be an expression for that relation. We thus reach the conclusion that the relation expressed in our sentence is not expressed by it.” (Peter Long, “Formal Relations”)
Philosophical Questions 1
I’ve been thinking lately about questions, philosophical questions. It seems to me–although I admit to being unable to take this thought very far yet–that one useful way of gaining insight into a philosopher’s work is by working delicately to typify the relationship between the philosopher’s questions and her answers to them. Perhaps, so stated, that seems obvious. But what I mean is typifying the relationship as such (if that can be done), independent of the particular erototetic content or declarative content of the question and answer, respectively. There are, I submit, a vast number of different typifying relationships to be discovered. Part of the reason I began to think about this was re-reading a comment of mine on G. E. Moore:
Moore insists that we often ask a philosophical question without knowing quite what question our interrogatory words express. But Moore does not ever seriously doubt that there is a philosophical question that the words express. We can rightly say that Moore doubted the clarity of the questions that philosophers asked, and we can rightly say that he often doubted whether philosophers really believed the answers they gave to the questions; but we cannot rightly say that he doubted whether there were philosophical questions to be asked and answers to be given to them. That Moore took this view of philosophical questions is shown by his deep unease with his own answers to them. Moore, I think, believed his answers; but he also did not believe his answers. (“I believe; help thou my unbelief.”) His deep unease was the result of the mismatch between his understanding of the questions and the believability of his answers to them: given his view of the questions, the very believability of his answers to them made the answers hard to believe.
Socrates’ questions and answers bear one sort of relationship to each other. Augustine’s another. Aquinas’ another. Kant’s another–and so on. Consider Heidegger, at least late: he so absolutizes the question over the answer that it is no longer clear that there is, that there could be, even that there should be any answer to the question or even an attempt at an answer. Such an attempt would violate the absoluteness of the question, allow us at least the hope of being able to end, at least for a moment, enduring the interrogative rack, to stop bearing the question mark, to finish the forever-rising inflection–to scramble off the heath and into shelter, no longer exposed as mad Lear. But Heidegger would have us stay.
(Ok, so I got a little carried away there. Apologies. But I plan to return–soberly–to this line of thought in coming days.)
Ordinary Language Philosophy
A few years ago I wrote the chapter on Ordinary Language Philosophy in The Edinburgh (Columbia) Encyclopedia of Twentieth-Century Philosophies. The chapter got cut in certain ways that I thought diminished its value. Here is a .pdf of a draft of the original chapter.
Merleau-Ponty on Ideal Language
We all secretly venerate the ideal of a language which in the last analysis would deliver us from language by delivering us to things.
Distinctions Among Distinctions
I posted the G. A. Cohen impersonation of Ryle (below) both because I thought it was funny and because it seemed to me to satirize moments in my own work. Now of course I am not worthy to lace Ryle’s boxing gloves, but I have on occasion distinguished distinctions from distinctions–or tried to. Here’s a short section from late in my book on the Concept ‘Horse’ Paradox.
At this juncture someone might object that the respondents whose responses I’ve been typifying end up looking quite a lot like Frege (as Wittgenstein read him) and Anscombe and Wittgenstein (early and late)—a lot like the philosophers I think we should follow here. I comment on this as Cavell does on a similar fact: The work of these philosophers forms a sustained and radical criticism of such respondents—so of course it is “like” them. It is “like” them in the way that any criticism is “like” what it criticizes. But ultimately, the work of these philosophers and of the respondents is radically unlike: to use an example of Anscombe’s, as radically unlike as soap and washing.
Why is that? Why this radical unlikeness? Well, I’ve done my best throughout the chapter to provide answers to that question. There is a gulf fixed between the work of these philosophers and the respondents, a gulf that closely resembles the gulf between constative language and ladder-language because it is that gulf. The gulf is another of these distinctions without a genus. The philosophers I think we should follow do not take themselves to be trying to bargain the absoluteness of the distinction between concepts and objects away—although I admit they occasionally slip from the strait and narrow onto the broad way. But, no, they are trying to make clear that we can come to see the CHP as no paradox at all only by letting the distinction between concepts and objects be the distinction it is. It is not a distinction with a genus. It is not a distinction of which we need to be informed; we need rather to be reminded of it. It is not a distinction which we recognize and then, having recognized it, impose on thoughts that were thinkable before the imposition. Again, it is know-how, not know-that.
The distinction is of philosophical importance not because it can be given as an answer, in some bit of constative language, to a deep philosophical question. The distinction is of philosophical importance because it is implicated as deeply in thoughts as any distinction could be. No matter how far into thinking nature we retreat, when we turn to think we find such distinctions retreating and turning with us. They are a part of what we are. They are elements in that tawny grammar, that mother-wit, that know-how, that we are initiated into when we are initiated into what Cavell calls “human speech and activity, sanity and community.” They are what we do. They are what thinkers do.
There are distinctions and distinctions—and so of course the details make a difference. One of the things that reflecting on the CHP’s respondents reveals is how very hard it is to keep straight distinctions among distinctions. After we have distinguished quantitative distinctions from qualitative distinctions, we think we’ve finished distinguishing distinctions. But there are more distinctions to make yet. Is the distinction between soap and washing quantitative or qualitative? It seems to me to be neither. But it’s still a distinction, for all that.
The Sublimity of Logic
PI 89: A nodal point in PI–a point where numerous intimate connections can be traced. I am not going to trace them now, not all of them. But one is that the problem of the sublimity of logic is, at least partially, the result of our subliming of logic, of our relationship to the problem. We are not wholly confused in subliming logic–logic is sublime. But its sublimity must square with its not supplying us with new facts, with its investigation of the hardly memorable and easily forgettable. –Can we so square the sublimity of logic without feeling that Wittgenstein has changed the subject?
These considerations bring us up to the problem: In what sense is logic something sublime?
For there seemed to pertain to logic a peculiar depth–a universal significance. Logic lay, it seemed, at the bottom of all the sciences.–For logical investigation explores the nature of all things. It seeks to see to the bottom of things and is not meant to concern itself whether what actually happens is this or that.—-It takes its rise, not from an interest in the facts of nature, nor from a need to grasp causal connexions: but from an urge to understand the basis, or essence, of everything empirical. Not, however, as if to this end we had to hunt out new facts; it is, rather, of the essence of our investigation that we do not seek to learn anything new by it. We want to understand something that is already in plain view. For this is what we seem in some sense not to understand.
Augustine says in the Confessions “quid est ergo tempus? si nemo ex me quaerat scio; si quaerenti explicare velim, nescio”.–This could not be said about a question of natural science (“What is the specific gravity of hydrogen?” for instance). Something that we know when no one asks us, but no longer know when we are supposed to give an account of it, is something that we need to remind ourselves of. (And it is obviously something of which for some reason it is difficult to remind oneself.)
William Temple on the Frege Channel
Because Psychology studies mental processes, it is very liable to behave as if Logic…were one of its subdivisions. But in fact Psychology, like every other science, must presuppose the autonomy of Logic; otherwise the writings of psychologists could be no more than their own autobiographies–not nearly so interesting or important as the autobiographies of statesmen, soldiers or artists. The interest which a psychologist claims for his theory is not that he happens to hold it, but that it is a true account of your experience and mine as well as of his own. But in this case he must have something to say in support of his theory over and above its psychological history. For every theory ever held has a psychological history.
Say Show Elucidate
(Another class handout. Last one for a while, I promise.)
Let’s think more about saying and showing—and about elucidating. To do so, I want to use an example of Edmund Dain’s but to situate it in a little more detail.
Imagine that you have been thinking about metaphysics. After a long, brow-knit silence, you intone: “There are objects.” I have been sitting next to you, drinking coffee and losing to myself at tic-tac-toe. I close my notebook full of x’s and o’s and look at you, puzzled. “Huh?”
Again you intone, with increased metaphysical drama: “There are objects.”
I can tell that you regard what you are saying as urgent, so I try to understand: “Huh?”
You sigh, shaking your head at the hardness of mine, and you explain: “Descartes, you know doubt recall, quested heartily for something that was clear and distinct, indubitable. He hit upon ‘I think, therefore I am’. But I have hit upon something at least as good, likely better: ‘There are objects.’ That, my good man, is a true metaphysical principle. It survives even the furies of the evil genius. After all, if the evil genius fools me, then HE fools ME. There are objects, you see, him and me. I cannot be mistaken if I believe that there are objects. And notice how cleverly I have escaped Cartesian subjectivity. No need to talk of thinking at all. No need to find a path from in here to out there. I start out there. Me, the good genius, and him, the evil genius. Just objects, only objects; there are objects. There are objects.”
I say that I do not understand. “What do you mean, ‘objects’? I don’t get it. If you tell me that ‘There are objects that fell’ in answer to my question, ‘What made that noise?’ I would understand. I would know how to symbolize it even, after taking my logic class: ‘(Vx) (Fx)’. Or if you said, pointing to the fruit on the table here, ‘There are apples’, I would understand that, too: ‘(Vx) (Gx)’. But you don’t seem to be telling me anything about objects—like, they fell—or telling me that there are certain sorts of objects—like, apples—you are telling me what?”
You look disappointed. As usual, I have failed to match the seriousness of your thinking.
“I wish you had never taken that logic class. It has ruined you for thinking. You now just monger symbols. –Anyway, when I say ‘There are objects’, I mean that there are objects. And if I must resort to symbols to explain this to you, then I symbolize my indubitable thus: ‘(Vx) (Ox)’.”
“Huh. So you mean ‘There are objects’ to be like ‘There are apples’. But then what is the variable in your symbolization doing? In the Tractatus, Wittgenstein says something about how ‘object’ talk, when used rightly, is expressed symbolically by variable names. So, if I want to say ‘There are two objects which…’ I say it by ‘(Vx, y)…’ I can thus predicate something of the ‘objects’. For example, when I symbolize ‘There are apples’ as ‘(Vx) (Gx)’ I can elucidate that by saying ‘There’s an x such that x is an apple’. So your symbolizing of your indubitable could be elucidated in a parallel way: ‘There is an x such that x is an object.’ But notice that your use of ‘object’ there is predicative, as my use of ‘apple’ is. Is that what you want, to predicate ‘( ) is an object’ of some x?’
You look puzzled. “Well, I am not quite sure. That seems like what I want and it does not seem like what I want. I am unsure that I want a predicative use of ‘object’. That seems to make the objects I am talking about too robust, too spatio-temporal, too ordinary. When I say that there are objects, although I am glad to be right because there are apples or because there are alligators, I take it that such objects as apples and alligators are not the best examples of my objects. I want objects that are less robust, less spatio-temporal, less ordinary. The more I think about it, I am not sure that I really mean to be using ‘object’ predicatively. I am using ‘object’, not to predicate, but rather to indicate that which is the subject of predications. I want to symbolize it in a way that resembles the symbolization of ‘There are objects that fell’, ‘(Vx) (Fx)’.”
“Oh. Huh. But what do you want to predicate of your ‘objects’? The sentence you mean to be analogous to your indubitable predicates ‘fell’ of the ‘object’. But your indubitable lacks any such predicate. I don’t understand what you want.”
“Well,” you say, now becoming exasperated, “this is what happens when you mix logic and metaphysics. Philosophy consists of two parts, metaphysics and logic—and the metaphysics is the basis of philosophy. How do I want to symbolize my indubitable? Like this: ‘(Vx) ([ ]x)’. There. That. Says. It.”
“It does?” I ask. “I don’t think that says it. I don’t think that says anything at all. I understand that you want it to say something, in fact, to somehow say your indubitable. But, as it stands, with the ‘[ ]’, it is a propositional variable, not a proposition. We need a predicate. I also understand that, as it stands, it seems indubitable, but that is because, since it fails to be a proposition, no one can take a propositional attitude toward it. Cheap indubitability, as it were.”
“Ok. I suppose I concede that. I must want something else: maybe ‘(Vx)’, just that. But that looks weird.”
“Yeah. Frege would’ve regarded that as a monstrosity. But I see, in a way, what is happening to you. But there isn’t really anything you are saying when you say ‘There are objects’. You are drawn both to what Wittgenstein calls the ‘pseudo-concept’ use of ‘object’—the one replaced by the variable—and to some other use of ‘object’, a use on which it means something like ‘anything that can be carried’. But the problem is that neither of those is really what you want. The first won’t let you say anything, and so won’t let you say enough; the second lets you say something, but it says too much. An isolated quantifier is a monstrosity; it says nothing. A propositional variable says nothing; but it at least provides a kind of stencil for saying something. But the predicative use of ‘object’ seems wrong too. I wonder if part of the reason why your indubitable seems indubitable to you is that is not only seems to say something, it seems to say more than one something and, oddly enough, more than one nothing, all at once. Depth, indeed.”
You meet this with a profound frown. “Huh!”
Comment: I do not take the argumentative movements in this little conversation to be obligatory. The point is not to establish anything seriously about ‘There are objects’ but rather to provide an incarnated example of elucidation.
Much that is said in the conversation is what I call “ladder-language” (borrowing a term from Sellars). It is language that is meant to help to show (transitively) what shows (intransitively) or does not show (intransitively) in some sentence or sentence-like structure. Thus the language is didactically useful, but is not meant to stand—constatively—on its own. The language is unformalizable but nonetheless tied to formalization, tied to (intransitive) showing or its failure. (Remember, in nonsense, nothing (intransitively) shows.) When someone comes to see clearly the symbols in a genuine sentence or when someone comes to see that there is nothing that he means by some sentence-like structure, then what was said to get him to see that has no further role to play. All that matters is the person’s clear recognition of the sense or the nonsense.
Chump Change: a Thought on TLP 1
(Handout.)
What should we say of TLP 1, what should we do with it? We could note, I guess, that it plays an interesting role in a song by New Pornographers, Chump Change. But that’s scarce help.
One odd feature of 1 is its Eliotic dual-aspect as Bang-Whimper (of course this at the beginning, not, as Eliot’s was, at the end).
Bang: The world is everything that is the case! Whoa! Who woulda thunk it? Everything, everydamnthing! The world, man, the whole frickin’ world! This must be the near end of a gargantuan Metaphysical Buffet! Upcoming dishes: God, The Soul, …Who Knows? I can’t stand the suspense. What next?
Whimper: The world is everything that is the case… Well, yeah. What else would it be? “Everything that is the case.” Less exciting even than the Times’ “All the news that is fit to print”. The world is–the world. Whoopee… Wake me at 1.1.
Why begin with a proposition that is somehow both thunderclap and cricket’s chirp, new news and old hat?
It is incredibly tempting to read TLP as follows: The 1′s tell us What There Is. The 2′s and 3′s tell us How Language Hooks onto What There Is. The Bang aspect rules on this reading. But is there another reading, one that perhaps allows the Whimper aspect to rule? And if there is, what would we make of it, and of the 1′s, 2′s and 3′s?
