Wittgenstein’s Three Living Principles

More of the fruits of cleaning–an old essay I forgot that I wrote.  I gave it at a Pacific APA, I think; anyway, I likely forgot it because it got anaphora’d (carried up) into my Concept ‘Horse’ Book.  But it now strikes me as usefully revealing the topography of that book.


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”)

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.

Teaching The Blue Book

I’ve been teaching The Blue Book in my Intro to Philosophy class.  Not an easy sell.  I’ve been trying to get the students to orient on the inceptive question:  “What is the meaning of a word?”  And I am trying to get them to see that when Wittgenstein says he is going to attack that question, that is what he means–attack it.  Not answer it.  Wittgenstein takes the question to be suspect.  Part of his attempt to show that is his attack on what he takes to be the favored answer to the question:  the meaning of a word is a mental image.

Although it required sailing our little skiff onto still deeper water, I worked to get the students to see that the opening sections of the book, from the inceptive question through the red flower example and to the commentary on it, are structured by Frege’s Three Principles (in Foundations).  Frege’s second principle, The Context Principle (Never ask for the meaning of a word in isolation but only in the context of a proposition), is openly transgressed by the inceptive question of The Blue Book.  The favored answer to that question is itself the answer Frege forecasts being given by anyone who violates The Context Principle.  (It is itself an answer that violates Frege’s first principle, Always sharply to separate the logical from the psychological, the objective from the subjective.)  The details of the red flower example capitalize on Frege’s observation that the fact that we cannot form any idea of its content is no reason for denying all meaning to a word.  And so on.

Recognizing the Fregean structure of the opening makes tracking the sometimes nearly trackless discussions of book easier, since the structure extends past the opening deep into the rest of the book.  But that is a topic for another post.

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.

Topsy-Turvy Frege

Davidson’s Truth and Predication–at least parts of it–have been in front of me this weekend.  Good stuff, although I am out of sympathy with many of the details of the stories he tells, both about the history of the problem of predication and about the solution of the problem.

But I guess my fundamental disagreement with Davidson centers on the reality of the problematic he investigates.  For Davidson, the unity of the proposition must be explained; explaining it requires solving the problem of predication.  Seeing things this way, when Davidson turns to Frege he understands objects and concepts as constituents of propositions, constituents fashioned, as it were, so as to constitute a propositional unity.  Predictably, Davidson is most fascinated with concepts, since they are–even more than objects–fearfully and wonderfully made:  they are incomplete.   Objects of course are complete–as are propositions (although in a different sense (Frege got confused about this, unfortunately)).  The beginning of wisdom in reading Frege is recognizing the varieties of incompleteness and completeness he thematizes in his thinking–but that is a topic for another post.  What I want to consider here is the way that Davidson turns Frege upside-down.  I believe Frege understands objects and concepts as abstractions from propositions, not constituents of propositions.  Objects and concepts are, shifting descriptions, made from propositions, not made for them.  The proposition, the propositional unity, is prior to objects and concepts.  There is no explaining the unity; and there is no problem of predication to solve.  Davidson’s problematic is unreal.

Of course there is a problematic looming here, but it is more metaphilosophical than metaphysical.  Namely, how do we philosophize without this problem?  What would it be to philosophize constrained by the unity of propositions, recognizing that ultimately our only grip on anything as an object of thought is as what we are thinking instead of as what we are thinking about?  Or, to put this in a more Fregean way, what would it be to philosophize constrained by The Context Principle–and its two companion Principles from Foundations?  Frege’s Principles, as I believe (and have argued elsewhere), are the methodological counterpart to the unity of the proposition.  Taken seriously–kept is Frege’s word–the Principles reorient philosophy itself.  Wittgenstein’s work, both in TLP and in PI, strives to keep Frege’s Principles.  Arguably, Davidson senses this.  Although he shies away from Wittgenstein (saying a bit about why in a long footnote) he does at one point talk of a “deep truth” in a “Wittgensteinian thought”–but he seems unable to see how really to entertain the thought.  That is unsurprising, since the thought impugns the problematic that provides the very structure of Davidson’s thinking.

Kant and Frege and Objectivity and Objects

I’ve been thinking actively again about Frege. I was puzzling through his apparent Platonism, wondering about Tom Ricketts’ way of responding to that (in his masterful paper, “Objectivity and Objecthood”), and I recalled this passage of Karl Jaspers. It strikes me as useful on Kant (as it was intended to be) but also as useful about Frege–and as marking a deep similarity in the problematic each faces.

The fundamental difficulty is that Kant, in striving to disclose the conditions of all objectivity, is compelled to operate within objective thinking itself, hence in a realm of objects which must not be treated as objects. He tries to understand the subject-object relationship in which we live as though it were possible to be outside it. He strives toward the limits of the existence of all being for us; standing at the limit, he endeavors to perceive the origin of the whole, but he must always remain within the limit. With the transcendental method he strives to transcend while remaining within the world. He thinks about thought. Yet he cannot do so from outside thought, but only by thinking.

Frege does not use Kant’s transcendental method. But his symbolism can be understood as striving to transcend thought while remaining within it, to disclose the conditions of all objectivity while operating within objective thinking itself.

Quotable and Unquotable Signs (Peter Long)

As Frege was perhaps the first clearly to recognise, the sign for a property or relation…is not a quotable sign:  it is not an isolable piece of language. Of course, it is not incorrect to call ‘(is) white’ a predicative expression or ‘north of’ a relational expression, but what is here being called a predicative or relational expression is logically peripheral to what we should call the sign proper for a property or relation. For the sign that is proper to a property must, of course, have a different form from that which is proper to a relation. We give expression to this difference when we say ‘It is of the essence of a property to be of something’ and ‘It is of the essence of a (dyadic) relation to be between one thing and another’. What these propositions convey could be expressed at the level of language by saying ‘The sign for a property contains the form of a sign for a possible subject of the property’ and ‘The sign for a relation contains the form of signs for possible terms of the relation’. These formulations are not Frege’s, but they express what he meant by calling such signs ‘incomplete’, as opposed to those signs whose form is such that they do not contain the form of other signs, which he calls ‘complete’.  –Peter Long, “Universals:  Logic and Metaphor”, p. 97

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