Nietzsche, Frege and Plato.pdf

Howard Lidsky Final Paper-December 2016 Semantics Univ. of Florida Translation key: to know, knowledge, to believe, belief, to ignore, ignorance, real world, to be, not to be, to exist, to not exist, existence, idea, form= as defined by Plato.1 Idea = form Propositional logic p = to know, ~p = ignorance Predicate logic P=property of knowledge, ~P=property of ignorance, a= Bessie, B= being a dog, M=being a cow Q= beauty All other English words used are to have their meaning in colloquial American English. Three given sentences: 1. Bessie is a dog. 2. Bessie is a cow. 3. Bessie is beautiful. This paper is an attempt to ignore the three sentences given above. All three concern the same proper name. 1 Fine, Gail, Plato on Knowledge and Forms, Oxford University Press (2003). The interpretation of Plato in this paper is hers. To accomplish this task, I begin an intellectual historical examination of ce 1888 within German culture. At that time, Friedrich Nietzsche and Gottlob Frege2 had reached the same intellectual conclusion concerning Platonic epistemology; there is nothing useful about it. It had been totally refuted. Frege’s conclusion I will extract from his semantic systems of notation: propositional logic and predicate logic. Nietzsche makes this observation in Twilight of the Idols in a short chapter entitled “How the ‘Real World’ at last Became a Myth.” Nietzsche provides a highspirited intellectual history in six stages of Plato’s erroneous belief that there exists the world of the form, the real world. Nietzsche’s stage one is “The real world, attainable to the wise, the pious, the virtuous man-he dwells in it, he is it. (Oldest form of the idea, relatively sensible, simple, convincing. Transcription of the proposition ‘I, Plato, am the truth.’)” 3 and skipping to stage five, “The real world-an idea grown useless, superfluous, consequently a refuted idea: let us abolish it! Broad daylight; breakfast; return of cheerfulness and bon sens; Plato blushes for shame; all free spirits run riot.)4 2 Notations in propositional and predicate logic are Frege’s method of representing the truth- conditions of natural language. Nietzsche, Friedrich, Twilight of the Idols, p. 40, trans. R.J. Hollingdale, Penguin Books (1988), first published 1889, translation copyrighted 1968. 3 4Twilight of the Idols, p.40. Nietzsche hates Socrates. 5 Here, Nietzsche reduces Platonic epistemology to selfapotheosis6; Plato’s ‘real world’ has the same truth value and meaning as the simple proposition “I, Plato, am the truth.” Nietzsche is not as much disproving Plato as reducing him to ridicule. To critic the insightfulness of Nietzsche’s accusation will require first a description of Plato’s real world. For Plato, the real world is not the world that we inhabit every day, that world Plato calls the apparent world or the world of the senses. For Plato, people only have indirect contact with the real world. The real world contains knowledge, truth, existence. It is unchanging. Idea or forms exist in the real world. For Plato, the real world is a necessity to solve many difficult Semantic problems. I will use the three given sentences to describe Plato’s concern and depict how elegantly he solves these difficult problems. The elegance of Plato’s solution accounts for its longevity. The first given sentence informs the hearer that the thing named Bessie is a dog. In predicate logic, the first given sentence is notated: B(a) The issue to be addressed is the meaning of B, being a dog, as it regards Bessie, a. Dog is the predicate of the argument, Bessie. 5 “It was an altogether new-born demon. And it was called Socrates. Thus we have a new antithesis-the Dionysian and the Socratic; and on that antithesis the art of Greek tragedy was wrecked.” Nietzsche, Fredrich, The Birth of Tragedy, p. 42. trans. Clifton Fadiman, Dover Publications (1995), first published 1872, translation copyrighted 1927. 6 Nietzsche refers to Plato sarcastically as believing himself divine when he writes, “Similarly the divine Plato for the most part speaks but ironically of the creative faculty of the poet…” The Birth of Tragedy, p. 45. In this paper, I imprecisely refer to Socrates and Plato interchangeably. Before commencing the inquiry, Plato resolves Meno’s paradox: how is it possible to inquire about the meaning of dog if one does not know anything about what a dog is? How would one know if one found a dog? Meno, 71b, “And I myself, Meno, am in the same case; I share my townsmen's poverty in this matter: I have to reproach myself with an utter ignorance about virtue; and if I do not know what a thing is, how can I know what its nature may be? Or do you imagine it possible, if one has no cognizance at all of Meno, that one could know whether he is handsome or rich or noble, or the reverse of these?” For Plato, to have knowledge of a thing one must first know what it is 7. Knowledge must precede knowledge. The knowledge of what a thing is may come from knowledge of the definition of the thing. For Plato, dog-ness is that characteristic or quality that all dogs share. In the Meno, Plato uses the example of a bee to make this point, “I should ask you what is the real nature of the bee, and you replied that there are many different kinds of bees, and I rejoined: Do you say it is by being bees that they are of many and various kinds and differ from each other, or does their difference lie not in that, but in something else-for example, in their beauty or size or some other quality…what do you call the quality by which they do not differ, but are all alike?”8 Zoologically, a bee is defined by studying its parts. All bees share the same body parts. The definition is thus provided with reference only to the world of the senses. In set theory, bees are that set of all bees or a set comprising all individuals that share exactly the same collection of 7 Meno 71b and Fine, Plato on Knowledge and Forms, p. 2. 8 Plato, Meno, section 72b and 72c. body parts that is called “bees”. Bee-ness is the least common denominator so to speak of every member of the set of bees. Please note, that to explain the semantic meaning of the first given sentence, Plato did not refer to his theory of a real world. The knowledge of what is a bee is in the examination by the senses of a thing to determine if it shares the description of a bee. The description is found in a close zoological examination. The knowledge of the definition of bee provides the knowledge. Knowledge proceeds knowledge. The close zoological examination necessary is the logos9. Bessie with perfect truth can be a bee or a dog. Plato points to a more difficult problem in the quoted passage from the Meno, “Does their difference lie not in that, but in something else-for example, in their beauty or size or some other quality?” The third given sentence is such an example, Bessie is beautiful. Q(a) What is the meaning of the lexical beautiful, but even more importantly, how can the speaker know that Bessie is beautiful? Plato distinguished beauty and size from bee-ness. He solved bee-ness by reference to the sensible world, however for Plato the knowledge of beauty or size is not found in the world of the senses, but in the eternal world of the form. The idea of beauty is eternal, unchanging, and not reliant on subjectivity. At Cratylus 402a, Socrates says, “ Heracleitus says, you know, that all things move and nothing remains still, and he likens the universe to the current of a river, saying that you cannot step twice into the same stream.” For Plato, beauty can never be moving and changing. It is eternal. Plato’s real world answers Heracleitus. If beauty changes as Heracleitus says or relies 9 For Plato, knowledge requires logos as well as proceeding knowledge. The Republic 534(b). only on the senses, then beauty does not truthfully exist. Can words have meanings that continually change? Plato takes up this task in earnest in The Republic continuing an observation made in Meno 9710 that knowledge and a true belief are not synonymous although their material implications are the same. If one has either knowledge or true belief, then one gets to the right answer. However, a belief can be true or untrue. A belief may exist or not exist. In the Republic 476e, 477, Plato defines knowledge as something that is completely knowable and something that exists. Ignorance is the complementary, ungradable antonym to knowledge. The relation between knowledge and ignorance notated in propositional logic: p v ~p “Then knowledge is set over that which is, and ignorance of necessity over that which is not; and over this that is between, must we not now seek for something between ignorance and knowledge, if there is such a thing?11” Plato will continue his proof to show that belief is such a thing that lies between knowledge and ignorance. Since knowledge is always true and a belief can be either true or untrue, knowledge and belief are separate and distinct. A thing that is known always exists, but a 10 Plato observes that both the seasoned guide and the complete moron when giving the same directions will correctly get the inquisitor to Larissa. 11 Plato, The Republic, trans. p. 166. belief may exist or not. Likewise, ignorance and belief are separate and distinct as ignorance is always untrue and a belief may or may not be untrue. 12 Plato then further defines knowledge as a power. The Republic 477c, d. Any distinct thing that knowledge might have power over is either completely knowable or completely unknowable. This is noted in predicate logic, P(x) v ~P(x) Plato’s extension of knowledge to be a power permits him to not only draw a complete distinction between knowledge and true belief but additionally, the subjects of their respective influence. P(x) v ~P(x) is a tautology. For any variable argument x, the notation P(x) v ~P(x) is always true. Since a belief defies this tautology, a belief and the things over which it has power can never be x. The subject of a belief is notated ~x With this distinction fixed, Plato is prepared to solve the semantic issues raised in the third given sentence. The third given sentence is notated in predicate logic: Q(a) Before yielding again to Plato, I note that Frege has already left Plato’s bus. The given notations cause concern for Plato’s theory regardless of where he is about to proceed. Plato’s theory that the power of knowledge is either completely knowable or completely unknowable notated as P(x) v ~P(x) is not only a tautology but is also the notation for any complimentary pair of antonyms. In essence, Plato has identified a semantic category and not the secret of the universe. 12 Thus for Plato, ignorance and a false belief are distinct although they both result in nothingness. Complimentary antonyms are pairs of words in which one word completely negates the possibility of the other: open/shut, alive/dead, knowledge/ignorance. For example, the door can be either open or shut. There is no third possibility, and the existence of one negates the possibility of the other. If the door is open, it is not shut. The completeness of description entailed in complimentary antonyms is applicable only to the types of things subject to what the pair predicates. For instance, a window can be open or shut as can be a store or a drawer, but to say that a stone is open is absurd as is saying that it is closed. Plato observes that knowledge and ignorance are complimentary antonyms. He differentiates knowledge and belief partially through simply defining complimentary antonyms. Not surprisingly, Frege wants to conduct “an unceasing struggle against psychology and in part against language and grammar as they do not express only what is logical.” (NS, 7/PW, 6-7). Frege sees that Plato has fallen into a trap and does not wish to do the same. Plato writes in The Republic 479(d)-(e) of Socrates stating, “We shall affirm, then, that those who view many beautiful things but do not see the beautiful itself and are unable to follow another's guidance to it, and many just things, but not justice itself, and so in all cases—we shall say that such men have opinions about all things, but know nothing of the things they opine.” After the affirmative reply, Socrates continues, “And, on the other hand, what of those who contemplate the very things themselves in each case, ever remaining the same and unchanged —shall we not say that they know and do not merely opine?” Plato is in essence disproving Heracleitus. Plato writes in The Republic 507(b) of Socrates stating, “We predicate ‘to be’ of many beautiful things and many good things, saying of them severally that they are, and so define them in our speech.” “We do.” “And again, we speak of a self-beautiful and of a good that is only and merely good, and so, in the case of all the things that we then posited as many, we turn about and posit each as a single idea or aspect, assuming it to be a unity and call it that which each really is. “It is so.” “And the one class of things we say can be seen but not thought, while the ideas can be thought but not seen.” Within the two cited passages above, Plato provides his answer to what it means to express “Bessie is beautiful”. First, it is important to note that Plato does not define beauty as existing within or as a part of Bessie. This places beauty in a different category of attributes than bee-ness or dog-ness. To express that Bessie is a dog is to express that Bessie fits the definition of a dog. The individual Bessie like all other individuals that are dogs has within their individual selves dog-ness because they each fit the definition of dog. 13 Bessie does not and cannot have beauty within herself. If every individual to which beauty applies had their own beauty within themselves, that is to opine that there are many beauties. That opinion leads to the further conclusion that beauty is subject to change, in fact continuous change. For truth-conditional semantics to operate, words must have a fixed meaning. If words have only a pragmatic meaning, the sentences that the words form can never act as a measuring stick. We can see that Plato’s real world is a necessity to know a definition for words like beauty, good or big. These are words that require a judgment. 13 I will address given sentence two only in this footnote as it is not necessary to comprehend Nietzsche’s critic but is necessary to give a fuller recognition of the elegance of Plato’s accomplishment. The second given sentence “Bessie is a cow” informs the hearer that the individual named Bessie fits the definition of a cow. In predicate logic: M(a) It is necessary to distinguish cow from dog because the definition of a cow includes more and a different type of information than the definition of a dog. A cow is a female bovine that has had a calf. The definition of a cow includes not just a zoological examination of body parts but additionally a history of the individual’s past. With this distinction noted, the semantic solution to M(a) is very similar to the B(a). The definition of a cow gives the knowledge necessary to state that Bessie is a cow. The application of that definition to a given individual or argument is the truth value of the sentence. The semantic value of the predicate “cow” is in its definition which is determinable by the application of the senses. The knowledge of the definition precedes the knowledge of the application to the individual. Plato provides a definition does not always change and that is more than pragmatic. To solve this very real problem, we will see that Plato provides a very elegant answer. So is Nietzsche’s rather harsh judgment of Plato overdone? Plato defines beauty as existing in the idea of beauty which exists in the real world which is outside of and apart from our senses. To state that Bessie is beautiful is to state that Bessie is participating in the idea of the beautiful or that she is correctly representing the form of beauty. The form is in existence, true, unchanging, eternal. The assertion that Bessie is participating in the idea of beauty is making a proposition that is measurable because it is fixed to something unchanging. Please keep in mind that although Plato is making a measurable beauty possible, he is not making it very available. “Those who view many beautiful things but do not see the beautiful itself and are unable to follow another's guidance to it” and his poor townspeople14 likely comprise the vast majority 15 of the population. Nietzsche’s critic now comes into closer focus, “The real world, attainable to the wise, the pious, the virtuous man-he dwells in it, he is it.” Nietzsche is not attempting to refute Plato in a philosophical engagement. Nietzsche is attempting much more than that. Nietzsche is attempting to ridicule Plato. So far at least, Plato has not claimed to be the truth. 14 Meno 71b 15 “Then we have apparently discovered that the multitude’s multitudinous formulae concerning the beautiful and so on tumble about somewhere between what is not and what absolutely is?” The Republic, Book Five 479d. And then we read, “This reality, then, that gives their truth to the objects of knowledge and the power of knowing to the knower, you must say is the idea of good, and you must conceive it as being the cause of knowledge, and of truth in so far as known.” The Republic Book, six, 508(e). In the above passage, Plato relates that the idea of the good gives its truth to the objects of knowledge. Knowledge, truth, and good are all inherent in the idea as found in the real world. Plato has no proof for this assertion. He is demanding that “you must conceive it” but he provides no proof. Plato is reduced to insisting ‘I, Plato, am the truth.’ Although Frege and Nietzsche have correctly surmised that Plato has oversold the real world, the issue remains as to whether Nietzsche also is overselling his conclusions. The answer is found in the differing reactions that Frege and Nietzsche have to their similar assessment of Plato. Frege like Plato refuses to concede to Heracleitus that nothing is fixed. Frege is always concerned to discover a logical notation that will permit an examination of ideas for their truth value and the knowledge contained. For Frege, the reference of a sentence is an object. This results in his theory remaining unable to account for the semantic value of beauty. Frege is honest enough to recognize that his notations are unable to account for nearly the scope of Plato’s epistemology, and he never resorts to claims to the unknown or unknowable to resolve the short arms of his logic. Frege always goes back to work. Nietzsche’s reaction to his determination that the Platonic real world is refuted is found in stage six of his six stage history of an error. “We have abolished the real world: what world is left? the apparent world perhaps?…But no! with the real world we have also abolished the apparent world!” 16 When Nietzsche asserts that the apparent world has been abolished along with the real world, he is making an observation that without Plato’s real world it is not possible to make judgments about the apparent world. In essence, Nietzsche is agreeing with Plato that if Heracleitus is correct, then words like beauty, truth, big cannot have a meaning. Nietzsche has the complete opposite reaction of Plato and Frege to this peer into the chasm. For Nietzsche, the unfixing of knowledge from language is a cause for rejoicing. The cause for Nietzsche’s joy is obscure and is only hinted at in this essay. In stage five of the history of the error of the real world, after Nietzsche declares the real world a refuted idea to be abolished, he anticipates a “return to cheerfulness.” The reference to cheerfulness hints at Nietzsche’s real concern. The cheerfulness is Greek cheerfulness, and this indicates that Nietzsche’s engagement with Plato is still 17 concerning aesthetics. The Birth of Tragedy is Nietzsche first major publication in 1872. His central thesis is that early Greek tragedy is the perfect expression of the Dionysian artistic force fused with the Apollonian artistic force. Nietzsche blames Socrates and Plato for ruining Greek tragedy. The influence of the Socratic practical man in Greek culture destroys Greek tragedy, the pinnacle of Greek artistic achievement, and the character of the noble Greek cheerfulness. The bold central prediction of The Birth of Tragedy is that there is about to be a radical change in German culture and the return of the true artistic aims of the Dionysian and Apollonian. The last paragraph of chapter twenty-four, the next to last chapter, is as follows: 16 Twilight of the Idols, p.41 17 Nietzsche published Twilight of the Idols in 1888, at the end of his creative life before his mental decline beginning in 1889. “My friends, ye who believe in Dionysian music, ye also know what tragedy means to us. There we have tragic myth reborn from music-and in this birth we can hope for everything and forget what is most afflicting. What is most afflicting to all of us, however, is-the prolonged degradation in which German genius has lived estranged from house and home in service of malignant dwarfs.18 You who understand my words-as you will also, in conclusion, understand my hopes.” Nietzsche needs to destroy the reputation of Plato to accomplish an aesthetic goal. If he can discredit Plato, he can remove Platonic influence in German culture and remove an impediment to the return of the true art. Amazingly, this concern is still animating his writing at the end of his literary career as much as it was at the beginning. In short, Nietzsche is unfair to Plato. Plato may not have achieved Socrates’ stated goal in epistemology, but he 19 devises an elegant solution to a very difficult semantic challenge. Nietzsche, himself, wrote, “that we have our highest dignity in our significance as works of artfor it is only as an esthetic phenomenon that existence and the world are eternally justified…”20 18 I read the dwarfs to be Socrates and Plato. 19 The Republic is a pseudepigrapha. Nietzsche forgets this. 20 The Birth of Tragedy, p. 17.