Fixing Frege

Frege ("Logic in Mathematics"):

Definitions proper must be distinguished from elucidations [Erläuterungen]. In the first stages of any discipline we cannot avoid the use of ordinary words. But these words are, for the most part, not really appropriate for scientific purposes, because they are not precise enough and fluctuate in their use. Science needs technical terms that have precise and fixed Bedeutungen, and in order to come to an understanding about these Bedeutungen and exclude possible misunderstandings, we provide elucidations. Of course in so doing we have again to use ordinary words, and these may display defects similar to those which the elucidations are intended to remove. So it seems that we shall then have to provide further elucidations. Theoretically one will never really achieve one’s goal in this way. In practice, however, we do manage to come to an understanding about the Bedeutungen of words. Of course we have to be able to count on a meeting of minds, on others’ guessing what we have in mind. 

Also Frege (The Foundations of Arithmetic):

At first, indeed, [Mill] seems to mean to base the science, like Leibniz, on definitions, since he defines the individual numbers in the same way as Leibniz; but this spark of sound sense is no sooner lit than it is extinguished, thanks to his preconception that all knowledge is empirical. He informs us, in fact, that these definitions are not definitions in the logical sense; not only do they fix the meaning of a term, but they also assert along with it an observed matter of fact. But what in the world can be the observed fact, or the physical fact (to use another of Mill’s expressions), which is asserted in the definition of the number 777,864? Of all the whole wealth of physical facts in his apocalypse, Mill names for us only a solitary one, the one which he holds is asserted in the definition of the number 3. It consists, according to him, in this, that collections of objects exist, which while they impress upon the senses thus, \, may be separated into two parts, thus, (.. .). What a mercy, then, that not everything in the world is nailed down; for if it were, we should not be able to bring off this separation, and 2+1 would not be 3! What a pity that Mill did not also illustrate the physical facts underlying the numbers 0 and 1!

I'm no philosopher of mathematics, but Frege's criticism of Mill does seem on target. Mill goes wrong by imagining too limited a set of examples and by thinking of the one example he does consider as if it were fixed. But that is not the real world, and somehow we do manage to get by even though not everything is nailed down. But then Frege seems to want to pin down the meanings of words, despite conceding that in practice this is not really necessary and that in theory it is impossible.

Mill makes what, after reading Frege's criticism of it, seems like a stupid mistake. Frege's problem is of a different kind. There is something wrong with what he wants. He sees the problems himself, but still, apparently, goes on wanting the same thing. So pointing out the problems won't help at all. We might say he needs a kind of therapy, although this won't be regular psycho-therapy. Nor does it at all follow that therapy is what Mill needs.

The unacknowledged legislators of the world

The only person I have ever heard of to have the name Bysshe is Percy Bysshe Shelley. His "A Defence of Poetry" (you have to scroll down) is something that I have now finally read, and is clearly important for the Romantic view that Rorty describes. What follows are some quotes and some of my initial reactions to them.

Poetry, in a general sense, may be defined to be 'the expression of the imagination': and poetry is connate with the origin of man.

In this sense poetry is certainly relevant to any understanding of the expressive arts. It might just be the same thing as them.

The savage (for the savage is to ages what the child is to years) expresses the emotions produced in him by surrounding objects in a similar manner; and language and gesture, together with plastic or pictorial imitation, become the image of the combined effect of those objects, and of his apprehension of them. Man in society, with all his passions and his pleasures, next becomes the object of the passions and pleasures of man; an additional class of emotions produces an augmented treasure of expressions; and language, gesture, and the imitative arts, become at once the representation and the medium, the pencil and the picture, the chisel and the statue, the chord and the harmony.

We feel, and we express our feelings, and then we react to these expressions in turn. Somehow what results is not just noise but a kind of harmony and mutual adjustment.

In the youth of the world, men dance and sing and imitate natural objects, observing in these actions, as in all others, a certain rhythm or order. And, although all men observe a similar, they observe not the same order, in the motions of the dance, in the melody of the song, in the combinations of language, in the series of their imitations of natural objects. For there is a certain order or rhythm belonging to each of these classes of mimetic representation, from which the hearer and the spectator receive an intenser and purer pleasure than from any other: the sense of an approximation to this order has been called taste by modern writers. Every man in the infancy of art observes an order which approximates more or less closely to that from which this highest delight results: but the diversity is not sufficiently marked, as that its gradations should be sensible, except in those instances where the predominance of this faculty of approximation to the beautiful (for so we may be permitted to name the relation between this highest pleasure and its cause) is very great. Those in whom it exists in excess are poets, in the most universal sense of the word; and the pleasure resulting from the manner in which they express the influence of society or nature upon their own minds, communicates itself to others, and gathers a sort or reduplication from that community. Their language is vitally metaphorical; that is, it marks the before unapprehended relations of things and perpetuates their apprehension, until the words which represent them become, through time, signs for portions or classes of thoughts instead of pictures of integral thoughts; and then if no new poets should arise to create afresh the associations which have been thus disorganized, language will be dead to all the nobler purposes of human intercourse. [my emphasis]

This idea of metaphor and marking and perpetuating relations that had till then gone unapprehended is very important to me (although it hardly seems to apply to all the expressive arts, music most obviously).

Every original language near to its source is in itself the chaos of a cyclic poem: the copiousness of lexicography and the distinctions of grammar are the works of a later age, and are merely the catalogue and the form of the creations of poetry.

This sounds right, especially the bit about distinctions of grammar, etc. coming only after the 'poetic' creation of language.

Hence all original religions are allegorical, or susceptible of allegory, and, like Janus, have a double face of false and true.

I quote this just because it struck me, not because it directly bears on my project of trying to understand, or say something about, philosophy's relation to the expressive arts. It reminds me of Wittgenstein, around the time of the Lecture on Ethics, on religion, although Shelley isn't just saying the same thing as Wittgenstein.

[E]very great poet must inevitably innovate upon the example of his predecessors in the exact structure of his peculiar versification. The distinction between poets and prose writers is a vulgar error. The distinction between philosophers and poets has been anticipated. Plato was essentially a poet—the truth and splendour of his imagery, and the melody of his language, are the most intense that it is possible to conceive.

I tend to read Plato this way, probably because I've been influenced by people influenced by Shelley (Nietzsche who got his Shelley from Emerson, perhaps). The line between poetry and prose is blurry, I suppose.

All the authors of revolutions in opinion are not only necessarily poets as they are inventors, nor even as their words unveil the permanent analogy of things by images which participate in the life of truth

Rorty echoes this view of intellectual innovators as strong poets.

[P]oetry is a mirror which makes beautiful that which is distorted

I like this. It reminds me of all Schopenhauer's references to mirrors, and of Larkin's idea that one kind of poetry is beautiful but not quite true. Mirrors don't distort all that much, though. Or they only distort what is there to be distorted. Though perhaps that's enough.

But poetry acts in another and diviner manner. It awakens and enlarges the mind itself by rendering it the receptacle of a thousand unapprehended combinations of thought. Poetry lifts the veil from the hidden beauty of the world, and makes familiar objects be as if they were not familiar

This is reminiscent of Cora Diamond's idea of literature enlarging the moral imagination, and of Wittgenstein's idea that we need to wake up from the kind of sleep to which science puts us and see the world with wonder or astonishment.

[E]ven crime is disarmed of half its horror and all its contagion by being represented as the fatal consequence of the unfathomable agencies of nature

Also reminiscent of Wittgenstein. This time I'm thinking of (was it?) Rush Rhees's report that Wittgenstein said you could see German bombers as not evil but tragic if the right music were played when the newsreel was shown.

[Poetry] creates anew the universe, after it has been annihilated in our minds by the recurrence of impressions blunted by reiteration.

There probably isn't, but I wonder whether there's any link between impressions blunted by reiteration and the fact that words start to sound nonsensical when reiterated. Thoughtlessness is involved in both, and poetry (Shelley is claiming, at least) is a cure for this. Poetry might be called thinking then.

Poetry, as has been said, differs in this respect from logic, that it is not subject to the control of the active powers of the mind, and that its birth and recurrence have no necessary connexion with the consciousness or will.

Poetry would be involved in something like the creation of games or systems of meaning. Logic would apply within them. (Or am I straying too far from the text here? I've got thoughts of Frege and Heidegger dancing around together.)

Poets are the unacknowledged legislators of the world.

The last line of Shelley's essay, which reminds me of Derrida on law and, as I recall, rule-following. All good stuff.

Wittgenstein on clarity

In the Tractatus Wittgenstein says the following things about clarity and elucidation:

One could put the whole sense of the book perhaps in these words: What can be said at all, can be said clearly and whereof one cannot speak, thereof one must be silent.

3.251 A proposition expresses what it expresses in a definite, clearly specifiable way: a proposition is articulated.

3.263 The meanings of primitive signs can be explained through elucidations.  Elucidations [Erläuterungen] are propositions which contain primitive signs.  They can thus only be understood if one is already acquainted with the meanings of these signs.

4.112 The end of philosophy is the logical clarification of thoughts.

Philosophy is not a subject but an activity.

A philosophical work consists essentially of elucidations.

The result of philosophy is not "philosophical propositions" but the clarification of propositions.

Philosophy should make clear and distinct thoughts that, without it, are, as it were, unclear and indistinct.

 4.115 It [i.e. philosophy] will refer to the unsayable in that it presents clearly the sayable.

4.116 Everything that can be thought at all can be thought clearly. Everything that can be said can be said clearly

5.45 If there are primitive signs of logic then a correct logic must make clear their position with regard to one another and justify their being.  The construction of logic out of its primitive signs must be made clear.

5.452 The introduction of a new device in the symbolism of logic must always be an important event.  No new device may be introduced into logic – with, so to speak, a wholly innocent face – in brackets or in a footnote.

(Thus in the Principia Mathematica of Russell and Whitehead there appear definitions and basic laws in words. Why suddenly words here?  This would need a justification. This is missing and must be missing, since the procedure is actually forbidden.)

If, however, the introduction of a new device has proved necessary in one place, then one must ask oneself straightaway: Where must this device now always be used?  Its place in logic must now be made clear.

6.54 My propositions elucidate by whoever understands me perceiving them in the end as nonsensical, when through them – upon them – over them, he has climbed out.  (He must, so to speak, throw away the ladder after he has climbed out upon it.)

He must overcome these propositions, then he sees the world rightly. 

The words "It is clear" and "it is clearly" occur often in the book, about 18 or 19 times in my translation (which aims to be very literal). At first these are references to what is clear in logic, as in 3.251 and 4.115 quoted above, having to do with the clear specification or presentation of what can be said. But later we get into ethics and some strange claims about what is clear, e.g. "6.421 It is clear, that ethics cannot be articulated." To whom is that clear? It isn't clear just on its own but, if at all, then to someone. And not just anyone, but an ethical being.

The inescapability of our humanity, both our physical being, which is affected by sounds when we hear others speak, and our subjective being (is that the word?), which can guess and pick up hints, is made clear enough by Frege (especially by Beaney's Frege Reader and its helpful index). It also comes up in Schopenhauer when he writes that, "The aim of realism is just the object without subject; but it is impossible even to conceive such an object clearly" (The World as Will and Representation, Volume II, p. 12). There is no escaping subjectivity, no as it were absolutely objective communication, no understanding a speaker's sentences without understanding the speaker (although presumably Wittgenstein thinks we can understand an author without understanding his sentences, as indeed does seem to be the case).

Frege and Russell 'cheat' (see, e.g. 5.452 above) because they have to. It is not possible to do what they are trying to do without 'cheating', as Frege, at least, recognizes. And that means there is something wrong with what they are trying to do. It involves a false view of clarity. There is not the clearly sayable and the having-to-be-guessed-at. Or rather, since, after all, some things are clearly sayable and others do have to be guessed at, the distinction between the sayable and the un-sayable can be overstated.

Does this really matter? Wittgenstein seems to think it makes a huge difference to philosophy, to how we conceive of and do philosophy. "Philosophy is not a subject but an activity. A philosophical work consists essentially of elucidations." I take this to mean that philosophy should consist of elucidations, and that these elucidations are acts, not clarificatory statements. The clarification of propositions is not the production of clear propositions. Every proposition that means something, i,.e. every proposition that actually is a proposition, has a clear meaning. It just might not be clear to this or that person. Philosophy, Wittgenstein appears to be saying, is the activity of helping people understand this meaning. Clarity and the lack thereof are psychological matters.

But what about 3.263? It says that: "The meanings of primitive signs can be explained through elucidations.  Elucidations are propositions which contain primitive signs.  They can thus only be understood if one is already acquainted with the meanings of these signs." So elucidations are propositions, after all, not acts of elucidation. But this proposition is sheer nonsense, isn't it? It reads like a joke. The meaning of primitive signs can be explained through elucidations, and these elucidations can only be understood if one already is acquainted with the meanings of these primitive signs. So the point of an elucidation is to explain something in a way that can only be understood by people already acquainted with what is to be explained.

Elsewhere I commented as follows on this passage:

What the…?! This sounds circular and pointless. Don’t know the meaning of a primitive sign? An “elucidation” will help. But you will only understand it if you already know the meaning of the relevant primitive sign! So either knowledge of meaning is not the same thing as understanding when it comes to signs, which seems unlikely (but who knows?). Or explanation of meaning is quite impossible (in the terms presented by the Tractatus up to now). See p. 44 and pp. 49-50 of Joan Weiner’s essay in Future Pasts.

Anscombe (p. 26) suggests that this passage, along with 3.261, provides the best evidence for thinking that the elementary propositions of the Tractatus are simple observation statements, such as “This is a red patch.” Names and only names are primitive signs. Logical signs, as he indicates elsewhere, are not primitive signs. But (see p. 27) what elucidates a name need not be an elementary proposition. And from 6.3751 it follows directly that “This is a red patch” cannot be an elementary proposition.Anscombe concludes that elementary propositions are not simple observation statements, and that this explains why Wittgenstein did not refer to observation in connection with them. What they are he cannot say, but they must exist. See, for instance, 5.5562, 3.23, 2.021, 2.0211, and 4.221.

See also 5.526.

(I had forgotten that I had read Joan Weiner's essay before.) N.N. commented:

Hacker argues (persuasively, it seems to me) that elucidations are ostensive definitions 'seen through a glass darkly.' That is, they are ostensive definitions misconstrued as bipolar propositions (see 'Frege and Wittgenstein on Elucidations,' Mind, Oct., 1975).

The 'smoking gun' in favor of his interpretation is a remark that Wittgenstein made to Waismann in 1932: 'In the Tractatus logical analysis and ostensive definition were unclear to me.' That is, according to Wittgenstein, ostensive definition is addressed in the Tractatus. And even Kenny, who denies that elucidations are ostensive definitions, concedes that the only passage Wittgenstein could be referring to is 3.263 (see Anthony Kenny, 'The Ghost of the Tractatus,' in Legacy of Wittgenstein).  

It isn't clear to me that Wittgenstein means in this remark that the Tractatus says something about ostensive definitions. Perhaps he meant that he had overlooked them. And we only have Waismann's report that Wittgenstein said this, so it's secondhand evidence. I wouldn't put too much weight on the smoking gun therefore.

Nevertheless, Hacker's interpretation has at least a certain plausibility. If we read 3.263 as saying that the meanings of primitive signs can be explained by means of sentences that use those signs to refer to objects with which one is familiar, then it sounds about right. But Anscombe's argument seems good. If a primitive sign is the name of an object and we cannot give any examples of objects then surely an elucidation containing primitive signs is not an ostensive definition. We can give lots of examples of them.

Whatever we make of 3.263, it seems clear to me that the elucidations mentioned in 6.54 and 4.112 are different in kind than those described in 3.263. The latter sound much more like the kind of thing Frege struggles with. The "elucidations" of 3.263 would be philosophical propositions, wouldn't they? But these are rejected in 4.112.

It's still a little hard to see how this is supposed to help anyone see the world rightly. To see Frege's work rightly perhaps, and to see philosophy rightly perhaps also. But the world? For that I think we would have to look more at the remarks on ethics towards the end of the Tractatus. 

What can be said at all can be said clearly

In the foreword to his Tractatus Wittgenstein writes that:

One could put the whole sense of the book perhaps in these words: What can be said at all, can be said clearly; and whereof one cannot speak, thereof one must be silent. 

But what is it to say something clearly? In Joan Weiner's paper "Theory and Elucidation" there is a nice quotation from Frege:

When a straight line intersects one of two parallel lines, does it always intersect the other? This question, strictly speaking, is one that each person can only answer for himself. I can only say: so long as I understand the words ‘straight line’, ‘parallel’, and ‘intersect’ as I do, I cannot but accept the parallels axiom. If someone else does not accept it, I can only assume that he understands these words differently. Their sense is indissolubly bound up with the axiom of parallels. [Weiner, p. 20]

What could be clearer than the axioms of Euclidean geometry? Or that a straight line intersecting one of two parallel lines must also intersect the other? And yet, as Weiner points out, that doesn't mean we can all understand these axioms without elucidation. There is nothing to guarantee that everyone will accept or understand any given such axiom. Recall Frege on "Logic in Mathematics":

Of course we have to be able to count on a meeting of minds, on others’ guessing what we have in mind. But all this precedes the construction of a system and does not belong within a system. In constructing a system it must be assumed that the words have precise Bedeutungen and that we know what they are.   

Without checking the context of this quotation, I would say that it suggests a three-part distinction: what precedes the construction of a system, the construction of a system, and what is done within a system. As distinct as these three are, they might not always be completely distinct. Wittgenstein's remarks about the riverbed in On Certainty suggest this, but it is quite evident in Frege's work too (as, again, Weiner makes clear). In his work to construct a system he ends up dropping hints and counting on others' guessing what he has in mind. The precise sciences are born of the 'poetic' humanities, most obviously philosophy (most obviously, that is, if we accept the common story that philosophy is the mother discipline from which other disciplines are off-shoots). If we think in terms of a system, game, or calculus, then I'm inclined to say that the expressive arts, works of color and shade, the land of hints and guesses, belong to something like a foundational level or outer sphere, on top of or within which is the level or sphere of construction of the system or rules of the game, and then inside or above that is the working of the system or playing of the game itself. So the expressive arts or poetry or whatever we want to call it provides, or perhaps merely shapes, something like the context needed for the construction of games, systems, etc. This construction in turn is necessary for the use of the system, the playing of the game, etc. And hence mathematicians, logicians, scientists, need poetry.

And there's more. Problems can arise within the game that call for interpretation of the rules, or the introduction of new rules. And in constructing a system or game we can find that we have to resort to the undefined, to communication by non-scientific means. So the levels or spheres are not completely distinct. So science is continuous with poetry, not merely dependent on it but involved in a somewhat fluid relationship with it.

But: a) I need to check the context of the quotation from Frege, b) I need to think about whether he is really right, c) I especially need to be careful to distinguish the expressive arts' belonging to a sphere of communication or human relations on which technical work depends and the more dramatic claim that technical work depends on the expressive arts themselves (if Frege has to do the work of a poet it does not follow that without Goethe there could be no Frege, or anything like that), d) what about Wittgenstein on saying things clearly? I might get to that in my next post.

Different colours, different shades

Or "Frege on color and shading." This is a footnote in Frege's "On Concept and Object":

Nowadays people seem inclined to exaggerate the scope of the statement that different linguistic expressions are never completely equivalent, that a word can never be exactly translated into another language. One might perhaps go even further, and say that the same word is never taken in quite the same way even by men who share a language. I will not enquire as to the measure of truth in these statements; I would only emphasize that nevertheless different expressions quite often have something in common, which I call the sense, or in the special case of sentences, the thought. In other words, we must not fail to recognize that the same sense, the same thought, may be variously expressed; thus the difference does not here concern the sense, but only the apprehension [Auffassung], shading [Beleuchtung], or colouring [Färbung] of the thought, and is irrelevant for logic. It is possible for one sentence to give no more and no less information than another; and, for all the multiplicity of languages, mankind has a common stock of thoughts. If all transformations of the expression were forbidden on the plea that this would alter the content as well, logic would simply be crippled; for the task of logic can hardly be performed without trying to recognize the thought in its manifold guises. Moreover, all definitions would then have to be rejected as false. [Beaney, pp. 184-185]

I think it is quite right that the same thought may be variously expressed. Some translations are perfectly accurate, and it is possible to say the very same thing in two (or more) different ways. That is, sometimes differences in shading don't matter. It could be argued that they are always there nonetheless, but I don't know what the point of making this argument would be.

In "Logic" Frege writes:

In many cases a sentence is meant to have an effect on the ideas and feelings of the hearer as well; and the more closely it approximates to the language of poetry, the greater the effect is meant to be. [Beaney, p. 239]

He goes on to discuss a case of onomatopoeia from Homer, in which sails are said to be torn apart by the wind in a sentence that combines windy whistling sounds with violent, snapping-sail sounds. This is a pretty clear case of word-choice mattering in a way that is not wholly dependent on word-meaning, but there is surely more to the color and shade of language than this. Frege says that:

it cannot be denied that the spoken word affects the ideas we have just because it enters consciousness as a complex of auditory sensations. Right from the start we experience the series of sounds themselves, the tone of the voice, the intonation and rhythm with feelings of pleasure or displeasure. These sensations of sound are linked to auditory ideas that resemble them and these latter are linked in turn with further ideas reactivated by them. This is the domain of onomatopoeia. [Beaney, pp. 239-240]

The physical nature of speech is essential here. It belongs to the world of cause and effect, of stimulus and response, in a way that, seemingly, cannot but affect our feelings one way or another. The same need not be true of words read silently, or of thoughts. But it surely depends how one reads or thinks. To understand Homer in this case one should read as if aloud, attending to the sound of each word, and not quickly scanning the line for its sense. (I only ever read as if aloud. My lips move when I read or think, so I don't know what it's like to read in the more efficient way. Must there be some trace of the sound of the spoken words even in this case? And what about thinking?) Everything is surely written in some tone of voice, even if this is often the impersonal or instructive tone, the deadly language of the textbook or legal document. (Although, in fact, legal documents have their own tone, with notes of bureaucracy, minute deliberation, and just a hint of electric chair or prison cell. Textbooks, vetted by committees, are more psychotic, with a blank where the personality ought to be, like the personae suggested by the name Ghostface Killah or the Ruthless Rap Assassins' claim that "ice cold water races through my veins".) In short, Frege seems to be suggesting, rightly, that there is always some tone, but that it is not always relevant.

 More from "Logic":

In human beings it is natural for thinking to be intermingled with having images and feeling. Logic has the task of isolating what is logical, not, to be sure, so that we should think without having images, which is no doubt impossible, but that we should consciously distinguish the logical from what is attached to it in the way of ideas and feelings. There is a difficulty here in that we think in some language or other and that grammar, which has a significance for language analogous to that which logic has for judgement, is a mixture of the logical and the psychological. If this were not so, all languages would necessarily have the same grammar. [Beaney, p. 243]

There is a sort of mind-body problem here. Language combines or intermingles the psychological, the sensory, the personal, the physical, with the strictly logical, the impersonal. So logic is in a sense pitted against language--it must struggle to disentangle itself. Over the page Frege goes on:

Instead of following grammar blindly, the logician ought rather to see his task as that of freeing us from the fetters of language. For however true it is that thinking, at least in its higher forms, was only made possible by means of language, we have nevertheless to take great care not to become dependent on language; for very many of the mistakes that occur in reasoning have their source in the logical imperfections of language. [Beaney, p. 244]

Plenty to chew on there if we want to think about Wittgenstein's emphasis on grammar. Translation is a key issue for Frege, because different languages do not have the same grammar, and logic deals with what sentences in different languages that mean the same thing have in common, i.e. the same thing that they mean. I don't think Wittgenstein would necessarily reject this idea, but there is something about his talking about grammar rather than logic that suggests doubt about the feasibility of the Fregean task of freeing ourselves from the fetters of language. Language is, after all, not a cage, and we cannot understand one another without language.

In "Thought" Frege points out that:

It is just as important to ignore distinctions that do not touch the heart of the matter, as to make distinctions which concern essentials. But what is essential depends on one's purpose. To a mind concerned with the beauties of language, what is trivial to the logician may seem to be just what is important. [Beaney, p. 331]

So questions of value, of what matters, are always relevant, at least as a background to what one is doing.

And human activities are not always as distinct as we might think. There is often an element of the dry in the wet, and vice versa:

What are called the humanities are closer to poetry, and are therefore less scientific, than the exact sciences, which are drier in proportion to being more exact; for exact science is directed toward truth and truth alone. Therefore all constituents of sentences not covered by the assertoric force do not belong to scientific exposition; but they are sometimes hard to avoid, even for one who sees the danger connected with them. [Beaney, p. 330]

Only relative purity is attainable.

Finally, back to translation and the question of psychology or personality:

The more rigorously scientific an exposition is, the less the nationality of its author will be discernible and the easier it will be to translate. On the other hand, the constituents of language to which I here want to call attention make the translation of poetry very difficult, indeed make perfect translation almost always impossible, for it is just in what largely makes the poetic value that languages most differ. [Beaney, p. 331]

Apart form the Lecture on Ethics, Wittgenstein always wrote his philosophical work in German, as far as I know, which might show something about how far he thought his work was scientific. I plan to turn to Wittgenstein in the next post in this series. Meanwhile, here's Ian Curtis taking the blame for mistakes made over different colours, different shades.

Philosophy and the expressive arts: Frege

One of my goals between now and the end of October is to write an essay on philosophy and the expressive arts. I have about two weeks before my kids get out of school for the summer, and hope to have a (probably very) rough draft by then that I can return to about once a month until it's done or my time is up. What I think I would most like to do is to offer a reading of Coetzee's In the Heart of the Country as philosophy, but I doubt that's really what the organizers of the competition are looking for. Maybe I can incorporate elements of such a reading in the essay, but for the most part I think it ought to be about Frege and Wittgenstein (and possibly Davidson and maybe Rorty) and what we can learn from them. What follows is preliminary notes (really just a series of quotations) on Frege on hinting. Perhaps I should have called this post "Wink, wink, nudge, nudge," but I won't.

Here's the relevant part of the explanation of the competition:

From Plato on, philosophy has had an uneasy relationship with expressive arts such as narrative, poetry, drama, music, painting, and now film. If philosophy today can learn from science, can it learn from the arts as well—or even instead? If so, what can it learn?

Does expressive art access truths, particularly ethical truths, that cannot be expressed any other way? If it does, what can ethicists and other philosophers say about these truths? If it does not, what differentiates expressive from merely decorative art?

Some philosophers insist with Wittgenstein that “whatever can be said at all can be said clearly”. In that case, are artistic uses of language such as metaphor and imagery just "colour", as Frege called it - just ways of dressing up thoughts that philosophers, by contrast, should consider in their plainest possible form?

We welcome submissions of 8,000 words or fewer addressing these or other questions about philosophy and the expressive arts.  

The penultimate paragraph seems like a good starting point. In "On Sinn and Bedeutung," Frege distinguishes between Vorstellung (idea), Sinn (sense), and Bedeutung (reference), all three being kinds or aspects of meaning.

The idea is subjective: one man's idea is not that of another. There result, as a matter of course, a variety of differences in the ideas associated with the same sense. A painter, a horseman, and a zoologist will probably connect different ideas with the name 'Bucephalus'. This constitutes an essential distinction between the idea and the sign's sense, which may be the common property of many people, and so is not a part or a mode of the individual mind. [Beaney, p. 154]

Frege is not very interested in ideas (understood as here), but they surely are important to the expressive arts. He identifies three "levels of difference" that can exist between "words, expressions, or whole sentences" (Beaney, p. 155). These are differences in ideas only, in (ideas and?) sense but not reference, or in reference as well (in which case, presumably, there will be differences in sense and ideas too).

The difference between a translation and the original text should properly not overstep the first level. To the possible differences here belong also the colouring and shading which poetic eloquence seeks to give to the sense. Such colouring and shading are not objective, and must be evoked by each hearer or reader according to the hints of the poet [nach den Winken des Dichters] or the speaker. Without some affinity in human ideas art would certainly be impossible; but it can never be exactly determined how far the intentions of the poet are realized.

In what follows there will be no further discussion of ideas and intuitions... [Beaney, p. 155]

Hints are fundamental in Frege's work, though. In "Function and Concept" he writes that he cannot give a regular definition of what he is calling an object:

I regard a regular definition as impossible, since we have here something too simple to admit of logical analysis. It is only possible to indicate that is meant [gemeint]. [Beaney, p. 140]

Gemeint could also be translated as 'intended', I believe. Reluctantly, Frege is seemingly doing (what he regards as) the work of a poet here, hinting at his intentions in uncertain hope that the reader will share enough affinity with him to receive what he is trying to evoke. He resorts to similar hinting in "On Concept and Object":

Now something logically simple is no more given us at the outset than most of the chemical elements are; it is reached only by means of scientific work. If something has been discovered that is simple, or at least must count as simple for the time being, we shall have to coin a term for it, since language will not originally contain an expression that exactly answers. On the introduction of a name for something logically simple, a definition is not possible. There is nothing for it but to lead the reader or hearer, by means of hints, to understand the words as is intended. [Beaney, p. 182]

He goes on over the page:

...we cannot understand one another without language, and so in the end we must always rely on other people's understanding words, inflexions, and sentence-construction in essentially the same way as ourselves. As I said before, I was not trying to give a definition, but only hints, and to this end I appealed to the general feeling for the German language. [Beaney, p. 184]

The essay concludes:

'Complete' and 'unsaturated' are of course only figures of speech; but all that I wish or am able to do here is to give hints.

It may make it easier to come to an understanding if the reader compares my work 'Function and Concept'. For over the question what it is that is called a function in Analysis, we come up against the same obstacle; and on thorough investigation it will be found that the obstacle is essential, and founded on the nature of our language; that we cannot avoid a certain inappropriateness of linguistic expression; and that there is nothing for it but to realize this and always take it into account. [Beaney, p. 193]

Two more quotations to fill in the picture of Frege on the necessity of 'poetic' hinting:

We come to definitions. Definitions proper must be distinguished from elucidations [Erläuterungen]. In the first stages of any discipline we cannot avoid the use of ordinary words. But these words are, for the most part, not really appropriate for scientific purposes, because they are not precise enough and fluctuate in their use. Science needs technical terms that have precise and fixed Bedeutungen, and in order to come to an understanding about these Bedeutungen and exclude possible misunderstandings, we provide elucidations. Of course in so doing we have again to use ordinary words, and these may display defects similar to those which the elucidations are intended to remove. So it seems that we shall then have to provide further elucidations. Theoretically one will never really achieve one’s goal in this way. In practice, however, we do manage to come to an understanding about the Bedeutungen of words. Of course we have to be able to count on a meeting of minds, on others’ guessing what we have in mind. But all this precedes the construction of a system and does not belong within a system. In constructing a system it must be assumed that the words have precise Bedeutungen and that we know what they are. ["Logic in Mathematics" in Beaney, p. 313, quotation cut and pasted from the Stanford Encyclopedia of Philosophy] 

Finally, from a footnote in "Thought":

I am not here in the happy position of a mineralogist who shows his audience a rock-crystal: I cannot put a thought in the hands of my readers with the request that they should examine it from all sides. Something in itself not perceptible by sense, the thought is presented to the reader – and I must be content with that – wrapped up in a perceptible linguistic form. The pictorial aspect of language presents difficulties. The sensible always breaks in and makes expressions pictorial and so improper. So one fights against language, and I am compelled to occupy myself with language although it is not my proper concern here. I hope I have succeeded in making clear to my readers what I want to call ‘thought’. [Beaney, pp. 333-334, quotation cut and pasted from the Internet Encyclopedia of Philosophy] 

This last quotation rings a bell, I think because either Kelly Dean Jolley or James Conant quotes it in something I read not too long ago. I'll have to investigate. But throughout there are Wittgensteinian themes here: battling with language, philosophy needing to be written on the model of poetry, and the essentialness to a certain (attempted) task of an obstacle or impossibility, for instance. Not all that glisters is gold, but these apparent foreshadowings are surely worth investigating (which will involve, of course, looking at what others have written about this--I know it's not uncharted territory).

Recent work has suggested...

The Stone is my go-to site when I want to criticize something so as to have something to post on my blog. I have realized that this is neither noble nor really worthwhile, but I'm not sure I can resist this time. Peter Ludlow writes:

Recent work in philosophy, psychology and artificial intelligence has suggested a [...] picture that rejects the idea that languages are stable abstract objects that we learn and then use.  According to the alternative “dynamic” picture, human languages are one-off things that we build “on the fly” on a conversation-by-conversation basis; we can call these one-off fleeting languages microlanguages.  

Well, yes, we can I suppose. But how do we learn these microlanguages? It surely helps to know some other microlanguage already, to have had other conversations before. More specifically, here is Ludlow's example:

suppose I am thinking of applying for academic jobs and I tell my friend that I don’t care where I teach so long as the school is in a city.  My friend suggests that I apply to the University of Michigan and I reply “Ann Arbor is not a city.”  In doing this, I am not making a claim about the world so much as instructing my friend (for the purposes of our conversation) to adjust the meaning of “city” from official definitions to one in which places like Ann Arbor do not count as cities.  

This reminds me of p. 234 of this essay by James Conant, in which he discusses Frege's sentence "Trieste is no Vienna." It isn't news that we can do things like this with language. Nor that we can break language into parts and call them something, be it microlanguages or language-games.

I don't mean to reject what Ludlow is saying though. Apart from this invitation to invent counterexamples:

If word meanings can change dramatically during the course of a single conversation how could they not change over the course of centuries?  

(Compare: "If whether I'm alive or not can change dramatically during the course of a single conversation how could it not change over the course of several decades?") For the most part I think I agree very much with Ludlow. And as ever with articles in The Stone the main problem might just be with the task he has taken on of explaining complicated issues and ideas in simple terms. But I hate the thought that an idea is only valuable when recent work in some kind of science has suggested that it is true. If people insist on thinking like that then maybe they deserve to come late to what has long since been pointed out.