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to speak the truth or to lie, for example "Socrates is a man"—for see, this is true—or "Socrates is not a man"—for see, this is false. Affirmation is a statement signifying what belongs to something, for example "Socrates is walking". Affirmation again is a declarative statement of something about something. Negation is a statement signifying what <not> belongs to something, for example "Socrates is not walking". Contradiction is the conflict of two propositions dividing the true and the false in every matter and at every time, for example "every man is just", "not every man is just"; of these one is necessarily true and the other false. A proposition is a declarative statement of something from something, which is a negation, or of something about something, which is an affirmation. -A term is that into which the proposition is resolved, for example the proposition is "Socrates is walking"; this proposition is resolved into "Socrates" and into "is walking". Each of them, therefore, as a part of a proposition, is a term. -A syllogism is a discourse in which, certain things being posited, something other than what is posited necessarily follows from their being so; and by "posited" I meant "agreed upon", and by "from their being so" I say, that is, that the conclusion comes about because of the preceding propositions, not needing any other external constitution or term. -A lemma is that which is taken as agreed upon for the establishment of something. It should be known that these five in their substance do not differ at all from one another, namely: declaration, proposition, problem, objection, conclusion; for when I simply declare that the soul is immortal, it is called a declaration. But when it is taken as part of a syllogism, then to say "the soul is immortal" is a proposition. And when someone objects to the proposition, asking: Whence is it clear that the soul is immortal? then such a thing is called an objection. And when again we propose for inquiry: Is the soul immortal? it is called a problem. But when it is inferred from a proposition, it is called a conclusion, for example: The soul is ever-moving, the ever-moving is immortal, it remains from these propositions: Therefore the soul is immortal; this is the conclusion. A problem is a theorem tending toward choice and avoidance with a view to theory and knowledge. -A query is a question requiring a detailed answer. - It should be known that a questioning discourse differs from an inquiring one, because for the questioning one a quick answer follows, that is, a short one, but for the inquiring one a delayed and lengthy answer follows, that is, one with many words. -An objection is that which from the first starting-point, that is, from the premises, overthrows the argument. -A counter-argument, on the other hand, is that which accepts the argument as true, but shows that it does no harm to the matter at hand, as for instance we wish to show. A heresy is an untrue opinion concerning faith. A heresy is the opinion of several people who agree with each other but disagree with others. -A common notion is that which is agreed upon by all, for example that God exists. -A thesis is a paradoxical supposition of one of those known in philosophy, that is, a strange notion, such as the argument of Parmenides, that he said being is one, and that of Heraclitus, that all things are in motion. 19 Concerning the four dialectical methods It should be known that there are four dialectical, or logical, methods: 1. divisive, which divides the genus into species by means of differences; 2. definitive, which from the genus and the differences it divided, as the divisive method defines the subject; 3. analytic, which resolves the more composite into the simpler, that is, the body into the humors, the humors into the fruits, the fruits into the four elements, the four elements into matter and form; 4. demonstrative, which by means of some middle term demonstrates the matter at hand; for example, it is proposed for me to show that the soul is immortal; I take some middle term, the ever-moving, and I reason thus: The soul is ever-moving; the

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τὸ ἀληθεύειν ἐστὶν ἢ τὸ ψεύδεσθαι οἷον «Σωκράτης ἄνθρωπός ἐστιν»-ἰδοὺ γὰρ ἀληθεύει-ἢ «Σωκράτης οὐκ ἔστιν ἄνθρωπος»-ἰδοὺ γὰρ ψεύδεται. Κατάφασίς ἐστι λόγος σημαίνων, τί τινι ὑπάρχει οἷον «Σωκράτης βαδίζει». Κατάφασις πάλιν ἐστὶ λόγος ἀποφαντικός τινος κατά τινος. Ἀπόφασίς ἐστι λόγος σημαίνων, τί τινι <οὐχ> ὑπάρχει οἷον «Σωκράτης οὐ βαδίζει». Ἀντίφασις ἐστι μάχη δύο προτάσεων μεριζουσῶν τὸ ἀληθὲς καὶ τὸ ψεῦδος ἐπὶ πάσης ὕλης καὶ ἐπὶ παντὸς χρόνου οἷον «πᾶς ἄνθρωπος δίκαιός ἐστιν», «οὐ πᾶς ἄνθρωπος δίκαιός ἐστιν»· πάντως τούτων ἡ μέν ἐστιν ἀληθὴς ἡ δὲ ψευδής. Πρότασίς ἐστι λόγος ἀποφαντικός τινος ἀπό τινος, ὅπερ ἐστὶν ἀπόφασις, ἤ τινος κατά τινος, ὅπερ ἐστὶ κατάφασις. -Ορος ἐστίν, εἰς ὃν ἀναλύεται ἡ πρότασις, οἷον πρότασίς ἐστι «Σωκράτης βαδίζει»· αὕτη ἡ πρότασις ἀναλύεται εἰς τὸ «Σωκράτης» καὶ εἰς τὸ «βαδίζει». Ἕκαστον οὖν αὐτῶν ὡς μέρος προτάσεως ὅρος ἐστί. -Συλλογισμός ἐστι λόγος, ἐν ᾧ τεθέντων τινῶν ἕτερον ἐξ ἀνάγκης τῶν κειμένων συμβαίνει διὰ τὰ κείμενα· «τεθέντων» δὲ εἶπον ἀντὶ τοῦ «ὁμολογηθέντων», τὸ δὲ «διὰ τὰ κείμενά» φημι, τουτέστιν ὅτι διὰ τὰς προκειμένας προτάσεις γίνεται τὸ συμπέρασμα μὴ δεόμενον ἔξωθεν ἑτέρας τινὸς συστάσεως ἢ ὅρου. -Λημμάτιόν ἐστιν, ὅπερ εἴληπται ὡς ὁμολογούμενον πρὸς κατασκευήν τινος. Ἰστέον δέ, ὅτι τὰ πέντε ταῦτα κατὰ τὴν ὑπόστασιν οὐδὲν ἀλλήλων διενηνόχασιν οἷον ἀπόφανσις, πρότασις, πρόβλημα, ἔνστασις, συμπέρασμα· ὅταν μὲν γὰρ ἁπλῶς ἀποφαίνωμαι, ὅτι ἡ ψυχὴ ἀθάνατός ἐστιν, ἀπόφανσις λέγεται. Ὅτε δὲ ὡς μέρος συλλογισμοῦ ληφθῇ, τότε πρότασίς ἐστι τὸ λέγειν «ἡ ψυχὴ ἀθάνατός ἐστιν». Ἡνίκα δέ τις ἐνίσταται πρὸς τὴν πρότασιν ζητῶν· Πόθεν δῆλον, ὅτι ἡ ψυχὴ ἀθάνατός ἐστι; τότε τὸ τοιοῦτον ἔνστασις προσαγορεύεται. Ἡνίκα δὲ πάλιν προτείνομεν εἰς ζήτησιν· Ἆρά γε ἡ ψυχὴ ἀθάνατός ἐστιν; καλεῖται πρόβλημα. Ὅτε δὲ ἐκ προτάσεως συνάγεται, καλεῖται συμπέρασμα, οἷον· Ἡ ψυχὴ ἀεικίνητος, τὸ ἀεικίνητον ἀθάνατον, λοιπὸν ἐκ τῶν προτάσεων τούτων· Ἄρα γε ἡ ψυχὴ ἀθάνατος· τουτέστι τὸ συμπέρασμα. Πρόβλημά ἐστι θεώρημα συντεῖνον εἰς αἵρεσιν καὶ φυγὴν πρὸς θεωρίαν καὶ γνῶσιν. -Πύσμα ἐστὶν ἐρώτημα διεξοδικὴν ἀπαιτοῦν ἀπόκρισιν. - Ἰστέον, ὡς διαφέρει ὁ ἐρωτηματικὸς λόγος τοῦ πυσματικοῦ, ὅτι τῷ μὲν ἐρωτηματικῷ ταχεῖα ἕπεται ἡ ἀπόκρισις ἤγουν δι' ὀλίγου, τῷ δὲ πυσματικῷ χρονία καὶ διὰ πολλοῦ ἕπεται ἡ ἀπόκρισις ἤγουν διὰ πολλῶν λόγων. -Ενστασις ἡ ἐκ πρώτης βαλβῖδος ἤγουν ἐκ προοιμίων ἀνατρέπουσα τὸν λόγον. -̓Αντιπαράστασις δὲ ἡ δεχομένη μὲν τὸν λόγον ὡς ἀληθῆ, δεικνύουσα δέ, ὡς οὐδὲν βλάπτει πρὸς τὸ προκείμενον, οἷον θελόντων ἡμῶν δεῖξαι. Αἵρεσίς ἐστι περὶ πίστεως οὐκ ἀληθὴς δόξα. Αἵρεσίς ἐστι δόξα πλειόνων ἀνθρώπων πρὸς ἀλλήλους μὲν συμφωνούντων πρὸς ἑτέρους δὲ διαφωνούντων. -Κοινὴ δὲ ἔννοιά ἐστιν ἡ παρὰ πάντων ὁμολογουμένη, οἷον ὅτι ἔστι θεός. -Θέσις δέ ἐστι παράδοξος ὑπόληψίς τινος τῶν ἐν φιλοσοφίᾳ γνωρίμων ἤγουν ξένη ἔννοια οἷον ὡς Παρμενίδου λόγος, ὅτι ἓν ἔλεγε τὸ ὄν, καὶ ὡς ὁ Ἡρακλείτου, ὅτι πάντα κινεῖται. 19 Περὶ τῶν τεσσάρων διαλεκτικῶν μεθόδων Ἰστέον, ὡς τέσσαρές εἰσι διαλεκτικαὶ μέθοδοι ἤγουν λογικαί· αʹ διαιρετική, ἥτις διαιρεῖ τὸ γένος εἰς εἴδη διὰ μέσων τῶν διαφορῶν· βʹ ὁριστική, ἥτις ἀπὸ τοῦ γένους καὶ τῶν διαφορῶν διεῖλε, ὡς ἡ διαιρετικὴ ὁρίζεται τὸ ὑποκείμενον· γʹ ἀναλυτικὴ ἡ τὸ συνθετικώτερον ἀναλύουσα εἰς τὰ ἁπλούστερα, ἤγουν τὸ σῶμα εἰς τοὺς χυμούς, τοὺς χυμοὺς εἰς τοὺς καρπούς, τοὺς καρποὺς εἰς τὰ τέσσαρα στοιχεῖα, τὰ τέσσαρα στοιχεῖα εἰς ὕλην καὶ εἶδος· δʹ ἀποδεικτικὴ ἡ διὰ μέσου τινὸς δεικνύουσα τὸ προκείμενον· οἷον πρόκειταί μοι δεῖξαι, ὅτι ἡ ψυχὴ ἀθάνατός ἐστι· λαμβάνω τι μέσον, τὸ ἀεικίνητον, καὶ συλλογίζομαι οὕτως· Ἡ ψυχὴ ἀεικίνητος· τὸ