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Aristotle · On Sophistical Refutations §22#2

The Third Man Argument and Category Errors

Passage 22 of 29 · Greek

Summary

Taking up specific examples of fallacies based on category confusion—such as questions about what one does not possess, the truth-value of statements, the manner of learning or walking, and the "Third Man" argument—Aristotle criticizes the error of treating a common term as a particular substance ("a this").

§22#2Ὅμοιοι δὲ καὶ οἱ τοιοίδε πάντες.
All arguments of the following kind are also similar.
Ἆρ᾿ ᾗ μὴ ἔχει χειρὶ τύπτοι ἄν;
'Would a man strike with a hand which he does not have?
ἢ ᾧ μὴ ἔχει ὀφθαλμῷ ἴδοι ἄν; Οὐ γὰρ ἔχει ἕνα μόνον.
Or would he see with an eye which he does not have?' For he does not have only one.
Λύουσι μὲν οὖν τινὲς λέγοντες καὶ ὡς ἔχει ἕνα μόνον καὶ ὀφθαλμὸν καὶ ἄλλ᾿ ὁτιοῦν ὁ πλείω ἔχων.
Some people, then, solve this by saying that the person who has more than one has also only one eye, or only one of any other thing.
Οἱ δὲ καὶ ὡς ὃ ἔχει ἔλαβεν· ἐδίδου γὰρ μίαν μόνον οὗτος ψῆφον· καὶ οὗτός γ᾿ ἔχει, φασί, μίαν μόνην παρὰ τούτου ψῆφον.
Others solve it by saying that he received what he has; for this man was giving only one vote, and the other, they say, has only one vote received from this man.
Οἱ δ᾿ εὐθὺς τὴν ἐρώτησιν ἀναιροῦντες, ὅτι ἐνδέχεται ὃ μὴ ἔλαβεν ἔχειν, οἷον οἶνον λαβόντα ἡδύν, διαφθαρέντος ἐν τῇ λήψει, ἔχειν ὀξύν.
Others, immediately destroying the question, say that it is possible to have what one did not receive; for instance, having received sweet wine, but it having spoiled during the receiving, to have sour wine.
Ἀλλ᾿ ὅπερ ἐλέχθη καὶ πρότερον, οὗτοι πάντες οὐ πρὸς τὸν λόγον ἀλλὰ πρὸς τὸν ἄνθρωπον λύουσιν.
But, as was also said before, all these people solve not against the argument but against the man.
Εἰ γὰρ ἦν αὕτη λύσις, δόντα τὸ ἀντικείμενον οὐχ οἷόν τε λύειν, καθάπερ ἐπὶ τῶν ἄλλων· οἷον εἰ ἔστι μὲν ὃ ἔστι δ᾿ ὃ οὔ, ἡ λύσις, ἂν ἁπλῶς δῷ λέγεσθαι, συμπεραίνεται· ἐὰν δὲ μὴ συμπεραίνηται, οὐκ ἂν εἴη λύσις·
For if this were a solution, it would not be possible to solve it by granting the opposite, just as in other cases; for example, if the solution is 'this is so, but that is not', if one grants simply that it is spoken of, the conclusion is reached; but if it is not reached, it would not be a solution.
ἐν δὲ τοῖς προειρημένοις πάντων διδομένων οὐδέ φαμεν γίνεσθαι συλλογισμόν.
But in the aforementioned cases, we say that even if everything is granted, no deduction takes place.
Ἔτι δὲ καὶ οἵδ᾿ εἰσὶ τούτων τῶν λόγων.
Further, there are also the following among these arguments.
Ἆρ᾿ ὃ γέγραπται, ἔγραφέ τις;
'Did someone write what is written?
Γέγραπται δὲ νῦν ὅτι σὺ κάθησαι, ψευδὴς λόγος· ἦν δ᾿ ἀληθής, ὅτ᾿ ἐγράφετο· ἅμα ἄρα ἐγράφετο ψευδὴς καὶ ἀληθής. Τὸ γὰρ ψευδῆ ἢ ἀληθῆ λόγον ἢ δόξαν εἶναι οὐ τόδε ἀλλὰ τοιόνδε σημαίνει· ὁ γὰρ αὐτὸς λόγος καὶ ἐπὶ τῆς δόξης.
But it is written now that "you are sitting", which is a false statement; yet it was true when it was being written; therefore, at the same time, what was being written was false and true.' For a statement or opinion being false or true does not signify a 'this' but a quality; for the same argument applies also to opinion.
Καὶ ἆρ᾿ ὃ μανθάνει ὁ μανθάνων, τοῦτ᾿ ἐστὶν ὃ μανθάνει;
And 'is what the learner learns, that which he learns?
Μανθάνει δέ τις τὸ βραδὺ ταχύ. Οὐ τοίνυν ὃ μανθάνει ἀλλ᾿ ὡς μανθάνει εἴρηκεν.
But someone learns slow fast.' He has spoken, then, not of what one learns, but of how one learns.
Καὶ ἆρ᾿ ὃ βαδίζει τις πατεῖ;
And 'does someone trample what he walks?
Βαδίζει δὲ τὴν ἡμέραν ὅλην. Ἢ οὐχ ὃ βαδίζει ἀλλ᾿ ὅτε βαδίζει εἴρηκεν· οὐδ᾿ ὅταν τὴν κύλικα πίνειν, ὃ πίνει ἀλλ᾿ ἐξ οὗ.
But he walks the whole day.' Or rather, he has spoken not of what he walks but of when he walks; nor when they say 'to drink the cup' do they mean what one drinks but from what.
Καὶ ἆρ᾿ ὅ τις οἶδεν ἢ μαθὼν ἢ εὑρὼν οἶδεν;
And 'does someone know what he knows either by having learned it or by having found it?
Ὦν δὲ τὸ μὲν εὗρε τὸ δ᾿ ἔμαθε, τὰ ἄμφω οὐδέτέρον. Ἢ ὃ μὲν ἅπαν, τὸ δ᾿ ἅπαντα.
But of those things, of which he found one and learned the other, he knows both, which is neither.' Or rather, the one is the whole (each), and the other is all of them.
Καὶ ὅτι ἔστι τις τρίτος ἄνθρωπος παρ᾿ αὐτὸν καὶ τοὺς καθ᾿ ἕκαστον.
And that there is a 'third man' besides the man itself and the individual men.
Τὸ γὰρ ἄνθρωπος καὶ ἅπαν τὸ κοινὸν οὐ τόδε τι, ἀλλὰ τοιόνδε τι ἢ πρός τι ἢ πῶς ἢ τῶν τοιούτων τι σημαίνει.
For 'man' and every common term do not signify a 'this' (a particular substance), but a 'such' (quality), or a relation, or a manner, or something of this sort.
Ὁμοίως δὲ καὶ ἐπὶ τοῦ Κορίσκος καὶ Κορίσκος μουσικός, πότερον ταὐτὸν ἢ ἕτερον;
Similarly also in the case of 'Coriscus' and 'Coriscus the musical', whether they are the same or different.
Τὸ μὲν γὰρ τόδε τι τὸ δὲ τοιόνδε σημαίνει, ὥστ᾿ οὐκ ἔστιν αὐτὸ ἐκθέσθαι· οὐ τὸ ἐκτίθεσθαι δὲ ποιεῖ τὸν τρίτον ἄνθρωπον, ἀλλὰ τὸ ὅπερ τόδε τι εἶναι συγχωρεῖν.
For the one signifies a 'this' and the other a 'such', so that it is not possible to set it out; and it is not the setting out that makes the 'third man', but the granting that it is what a 'this' is.
Οὐ γὰρ ἔσται τόδε τι εἶναι, ὅπερ Καλλίας καὶ ὅπερ ἄνθρωπός ἐστιν.
For it will not be possible for what Callias is and what 'man' is to be a 'this'.
Οὐδ᾿ εἴ τις τὸ ἐκτιθέμενον μὴ ὅπερ τόδε τι εἶναι λέγοι ἀλλ᾿ ὅπερ ποιόν, οὐδὲν διοίσει· ἔσται γὰρ τὸ παρὰ τοὺς πολλοὺς ἕν τι, οἷον ὁ ἄνθρωπος.
Nor will it make any difference even if someone should say that what is set out is not what a 'this' is, but what a quality is; for there will still be a certain one thing besides the many, for instance, 'man'.
Φανερὸν οὖν ὅτι οὐ δοτέον τόδε τι εἶναι τὸ κοινῇ κατηγορούμενον ἐπὶ πᾶσιν, ἀλλ᾿ ἤτοι ποιὸν ἢ πρός τι ἢ ποσὸν ἢ τῶν τοιούτων τι σημαίνειν.
It is clear, then, that one must not grant that what is commonly predicated of all is a 'this', but that it signifies either a quality, or a relation, or a quantity, or something of this sort.

Notes

  1. ¦8¦Ἆρ᾿ ᾗ μὴ ἔχει χειρὶ τύπτοι ἄν; — The question "Would a man strike with a hand which he does not have?" contains a structural ambiguity. The phrase ᾗ μὴ ἔχει can mean either "with the hand which (of two) he does not have (e.g. his missing left hand, while striking with his available right hand)" or "in a way or with a hand that he does not possess at all." In the former sense, it is physically possible; in the latter, it is impossible.
  2. ¦9¦οὐ πρὸς τὸν λόγον ἀλλὰ πρὸς τὸν ἄνθρωπον λύουσιν — A crucial distinction in Aristotelian logic: "solving not against the argument but against the person." Rather than pointing out the logical fallacy in the argument itself (such as a category mistake, which is a solution πρὸς τὸν λόγον), these opponents merely exploit some feature of the questioner's presentation or the respondent's character to silence them, which is a solution πρὸς τὸν ἄνθρωπον.
  3. ¦11¦Ὦν δὲ τὸ μὲν εὗρε τὸ δ᾿ ἔμαθε, τὰ ἄμφω οὐδέτέρον — The genitive relative pronoun ὧν ("of which") functions as a partitive genitive, split into "the one" (τὸ μέν) and "the other" (τὸ δέ) within the relative clause. The subject of the main clause, "both" (τὰ ἄμφω), is neither wholly found nor wholly learned, showing that the disjunctive premise "either by learning or by finding" is fallacious because it confuses the collective "all" (τὰ ἅπαντα) with the distributive "each" (τὸ ἅπαν).
  4. ¦12¦οὐ τὸ ἐκτίθεσθαι δὲ ποιεῖ τὸν τρίτον ἄνθρωπον, ἀλλ᾿ αὑτὸ [or τὸ ὅπερ] τόδε τι εἶναι συγχωρεῖν — An analysis of the cause of the "Third Man" argument (the regress that requires an infinite chain of "men" beyond Callias and the Form of Man). Aristotle points out that the act of "setting out" (abstracting) the common term is not what causes the infinite regress, but rather the granting that this abstracted common term ("man") is itself a particular substance (a τόδε τι).

Cite this passage

Aristotle, On Sophistical Refutations §22#2. Humanitext Reader, https://reader.humanitext.ai/en/text/urn:cts:greekLit:tlg0086.tlg040.humanitext-grc1:22%232

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