History of Logic from Aristotle to Gödel by Raul Corazzon | e-mail: rc
"The central theme of the De interpretatione is the nature of contradiction between assertions. This is a crucially important theme for dialectic, whose regular tasks include that of establishing the contradictory of a proposed thesis, and that of replying to a dilemmatic question by choosing between the affirmation and the negation of a given thesis.(4) The inquiry into language as such, which occupies the first four chapters, is subordinated to this goal.
One apparent obstacle to such a view of the treatise is the (highly suspect) transmitted title, Περί ερμηνείας, which should probably be understood in the sense "On language" (cf. De anima II 8, 420b19-21, where ερμηνεία functions as a synonym of δίάληκτος). A second obstacle is the opening announcement: "First we must determine what a name is, and what a verb is, then what are a negation, an affirmation, an assertion, and a sentence (λόγος)". This programme attaches no special importance to contradiction: affirmation and negation merely appear in the middle of the agenda.(5) In fact though, these two obstacles may helpfully cancel each other out. All we need is the simple hypothesis that the original, lost title of the work (or lecture course) already specified contradiction as the principal theme. There is in fact good reason to think that the authentic title was On affirmation and negation.(6) In that case the opening sentence was unambiguously understood as specifying the series of definitions required as a preliminary to that central theme. Later, when the authentic title was lost, we need only suppose that an early editor was misled by the programmatic opening sentence into identifying language itself as the work's main theme, and inventing its current title, "On language".
As regards the progression in the opening chapters from "name" (δνομα) and "verb" (ρήμα) to "sentence" (λόγος), even this should not really be seen as an investigation of language as such. In ignoring all components of statements other than "names", "verbs", and the negation sign, Aristotle continues and reflects the project in Plato's Sophist 260-264 of investigating statements qua bearers of truth and falsity. (Even the treatment of negation represents the legacy of the Sophist: Aristotle follows Plato (257b-c) in regarding "not" as negating only the word which follows, (7) in contrast with Stoic logic, which uses it to negate an entire proposition). This is a further sign that the dominant theme is a specific one, the relation between certain kinds of assertion, rather than language in general." (pp. 88-89)
(4) My understanding of this and many other aspects of the De int. has been transformed by a recently completed Cambridge doctoral thesis, soon to be published: C.W.A. Whitaker, An analysis of Aristotle's De interpretatione [published in 1996 as: Aristotle's De interpretatione. Contradiction and dialectic. Oxford: Clarendon Press]. He shows that the treatise is to be read in conjunction with the Topics much more than with the Analytics.
(5) The agenda itself does not observe a strictly linear sequence. The first pair, δνoμα/ρήμα, does correspond to chapters 2 and 3 respectively. But άπόφασις καί κατάφασις καί άπόφανσις καί λόγος precisely reverses the order followed in chapters 4-6, starting with the two species, then moving to their genus and finally to the genus of their genus. On this, see Montanari (1984, I: 25-31).
(6) I suggest this because (a) the ancient commentators knew a work by Theophrastus entitled Περί καταφάσεως καί άπoφάσεως, which they said covered the same themes as Int. (Theophrastus frr. 71G, 72A, 79, 8 lB FHSG; cf. schol. in Ar. De int. 94b14-17 Brandis, in Bekker (1961, vol.4), and (b) Theophrastus' other works corresponding to the Organon all had identical titles to the matching Aristotelian texts: he wrote a Categories, a Topics, a Prior Analytics and a Posterior Analytics (frr. 1, 2, 71F, 100B, 104, 112B, 113B, 117, 124A, 127A, 127B FHSG). (Despite frr.frr. 71A and 71E (FHSG), it seems most unlikely that Theophrastus wrote a work actually entitled Περί έρμηνε'ας). An alternative but less plausible hypothesis is that of Maier (1900: 70-1) that it was Theophrastus himself who, finding the Aristotelian treatise already untitled, invented the title Περίκαταφάσεως καί άπoφάσεως. But it is hard to believe that Aristotle's long-term close collaborator on logic and dialectic was ignorant of its authentic title. The likelier story is that it was only after Theophrastus' death that the inauthentic title was invented to fill a gap in the MSS.
(7) This is well demonstrated by Whitaker  cit.
From: David Sedley, Aristotle's De interpretatione and Ancient Semantics, in: Giovanni Manetti (ed.), Knowledge Through Signs. Ancient SemioticTtheories and Practices, Turnhout: Brepols, 1996, pp. 87-108.
"The results so far are as follows. The semantic theory of the De interpretatione places itself at the service of Aristotle's study of contradiction between assertions, and reflects a Platonic debate on the question how beliefs and assertions come to be true or false. It is from this perspective, and not for their own sake, that the theory also addresses itself to the minimum semantic components of assertions, names and verbs. Therefore the semantic passage in chapter 1 is to be thought of as prefixed to the entire work, especially the final chapter, and not specially to chapters 1-4" p. 100
From: David Sedley, Aristotle's De interpretatione and Ancient Semantics, in: Giovanni Manetti (ed.), Knowledge Through Signs. Ancient SemioticTtheories and Practices, Turnhout: Brepols, 1996, pp. 87-108.
Abbreviation: FHSG = Fortenbaugh, Huby, Sharples and Gutas (eds.), Theophrastus of Eresus: Sources for His Life, Writings Thought and Influence, Leiden: Brill 1992 (two volumes).
ORDER OF THE PERI HERMENEIAS.
"Since the enunciation is the principal subject of the Peri Hermeneias the treatise is divided according to the consideration of the enunciation and its parts.(1) After a preliminary chapter on signification and different ways of signifying, (2)Aristotle treats first the principles of the subject i.e., the principles of the enunciation. These are of two kinds: material and formal. The material (or, as St. Thomas refers to them, "quasi material" (3) principles or integral parts of the enunciation are the nom and the verb, the former signifying the substance of a thing and the latter signifying an action or a passion proceeding from a thing. (4) Aristotle defines the noun as a vocal sound which signifies by convention, without time, no part of which signifies separately. (5) "Vocal sound" is the matter or subject on which the signification of the noun is imposed; it distinguishes the noun from sounds not emitted by animals. "Which signifies" distinguishes the noun from nonsense words. "By convention" manifests that this signification of a noun proceeds arbitrarily from the human will; the noun is distinct from sounds which are naturally significant, such as groans and cries. "Without time" distinguishes the noun from the verb, and this last phrase, "no part of which signifies separately," distinguishes the noun from speech (oratio) of which it is a part. The verb is defined in the same way, except that it signifies with time, since it signifies action. It is moreover, distinguished from the participle in that it is always a sign that something is predicated of another. The formal principle of the enunciation is speech, which is its genus.(6) The genus of the enunciation is then called its formal principle, because the more universal in praedicando since it is not of itself contracted to this or that species, is as a form including the species. A genus is logically superior to the species contained under it; since the species are as subjects of which the genus is predicated, the genus is their formal principle.
Having treated the principles of the subject, Aristotle now takes up the subject, i.e., the enunciation, in the rest of the book. This falls into two sections, the first is on the enunciation absolutely considered, (7) the second is on the different kinds of enunciations.(8) The absolute consideration of the enunciation comprises three parts: its definition, (9) its division, (10) and its property of opposition.(11)
The enunciation is defined as speech in which the true or false is found.(12) This definition distinguishes the enunciation from incomplete speech (orationes imperfectae) as well as from questions, commands, prayers, and salutations which do not absolutely signify concepts in which the true or false is found.(13) The first division is into the enunciation which is simply one because what it signifies is one and the enunciation which is one only by conjunction because it signifies many. The latter, called a composite enunciation, is one only secundum quid; simpliciter it is many.(14) The second division is into the species of the enunciation: the affirmation and the negation. This division is primarily of the simple enunciation, but can also be applied ex consequenti to the composite enunciation.(15)
These divisions are followed by a treatment of opposition between the subjective parts of the enunciation, i.e., between affirmation and negation. First, Aristotle shows how enunciations are opposed to each other,(16) and, secondly, he answers a difficulty about whether in future singular enunciations in contingent matter one of the opposed enunciations must be true or false.(17) To show how enunciations are opposed to each other he takes up, first of all, the opposition of affirmation and negation absolutely considered, i.e., without reference to differences arising from the subject. This opposition of affirmation and negation is called contradiction.(18) In this connection, St. Thomas points out that affirmation and negation divide the enunciation on the part of its very form or mode of enunciating, whereas the true and the false divide it in comparison to things, e.g., "The crow is white" is affirmative in its mode of enunciating, but false; "The crow is not white" is negative and true.
...Philosophus assumit duplicem diversitatem enunciationis: quarum prima est ex ipsa forma vel modo enunciandi, secundum quod dictum est quod enunciatio vel est affirmativa, per quam scilicet enunciatur aliquid esse, vel est negative per quam significatur aliquid non esse; secunda diversitas est per comparationem ad rem, ex qua dependet veritas et falsitas intellectus et enunciationis. Cum enim enunciatur aliquid esse vel non esse secundum congruentiam rei, est oratio vera; alioquin est oratio falsa.(19)
Next, Aristotle shows how enunciations are furthermore opposed by reason of their subjects.(20) This involves a new division of enunciations according to the quantity of the subject, i.e., according as something is predicated of many or of one only. Since a subject is either singular or universal, and since a predicate is said of a universal either universally, particularly, or indefinitely, there are four kinds of enunciations: singular, universal, particular, and indefinite.(21) Then, combining the qualities of affirmation and negation with the quantity of the subject, Aristotle shows that an affirmative universal and a negative universal are opposed as contraries, e.g., "Every man is white" and "No man is white."(22) However, when nothing is predicated universally of a universal subject, there cannot be an opposition of contrariety; therefore indefinite enunciations cannot be opposed as contraries.(23) A particular affirmative cannot properly be said to be opposed to a particular negative, because opposition demands the same subject in both enunciations, but a particular enunciation is opposed as a contradictory to the universal of the opposite quality, e.g., "Some man is white" is the contradictory of "No man is white."(24) Next, the author considers how these opposed affirmations and negations are related to truth and falsity: contraries cannot be simultaneously true, etc.(25)
After distinguishing the different modes of opposition, Aristotle shows that there is only one negation opposed to every affirmation, e.g., "Some man is not white" is the only negation of "Every man is white," because it alone removes the very universality of the universal enunciation.(26) Finally, Aristotle takes up the problem of whether one of the opposites must be determinately true .or false in all kinds of enunciations or not.(27) To treat this question it is necessary to observe that enunciations can be divided according to time into present, past, and future and according to their matter into necessary, impossible, and possible or contingent.(28) For enunciations in present or past time, either a universal or its contradictory particular is necessarily true and its opposite is false, in any kind of matter, e.g., "Some man is not white" is necessarily true, if "Every man is white" is false. This is also true for singular enunciations which are opposed as contradictories, e.g., if "This man is white" is true, "This man is not white" is necessarily false. From the truth of a particular affirmation, however, the falsity of its negative cannot be inferred, e.g., "Some man is white" and "Some man is not white" can both be true. But for enunciations in future time a distinction must be made according to the matter of the enunciation. Future enunciations in necessary and impossible matter are determinately true or false in the same way as enunciations in present and past time. Likewise, in contingent matter, universals are false and particulars are true, as for present and past enunciations. It is for singular enunciations in future time that a problem arises, for, although a future singular enunciation in necessary matter is determinately true or false, it does not seem to be so in contingent matter.(29) The answer to this problem and the reasons for the answer take up the rest of this chapter in Aristotle and the rest of the first book of St. Thomas's commentary.
The remainder of the Peri Hermeneias (30) is devoted to the enunciation as it is diversified by the addition of something. First of all, something can be added to a part of the enunciation, i.e., to the subject or to the predicate. Sometimes such an addition does not take away the unity of the enunciation, as when the subject or predicate is rendered infinite by the addition of a negative.(31) Aristotle first takes up the simplest kind of enunciation which consists only of a noun and the verb "is," e.g., "Socrates is." (32) Since only the subject can be made infinite in this kind of enunciation, only two affirmations can be formed from it: "Socrates is" and "Non-Socrates is." There are also the two corresponding negations: "Socrates is not" and "Non-Socrates is not." These enunciations are said to be de secundo adjacente, (33) because "is" is the second diction in the enunciation; "is" signifies that "Socrates" really exists. There are also enunciations de tertio adjacente (34) in which "is" is not the principal predicate but serves to connect the principal predicate with the subject, e.g., "Socrates is white." In such enunciations, the predicate as well as the subject can be made infinite. If an enunciation is constructed from a finite noun, the verb "is," and a predicate which can be either finite or infinite, four enunciations are possible: "Man is just" with its negation, "Man is not just," and "Man is non-just" with its negation, "Man is not non-just." (35) If, on the other hand, the subject is an infinite noun, four enunciations are also possible: "Non-man is just" with its negation, "Non-man is not just" and "Non-man is non-just" with its negation, "Non-man is not non-just." (36) No more than these twelve enunciations are possible. Since the subject of each can be singular, universal, particular, or indefinite, a total of forty-eight enunciations is possible from the point of view taken here. (37) Enunciations whose verbs are adjectival, (38) such as "Socrates runs," are affected by an addition to a part of the enunciation in the same way as simple enunciations, i.e., de secundo adjacente. This is true, despite the fact that from the point of view of what is signified such enunciations are the equivalent of enunciations de tertio adjacente: "Socrates runs" is equivalent to "Socrates is running."
Sometimes an addition takes away the unity of the enunciation. (39) An enunciation is multiple, if what is signified is multiple, even though the enunciation may appear to be simple. An enunciation can be multiple in four ways: (a) when the subject or predicate is one noun which is imposed on several things, which combine into one, but not insofar as they are one (b) when the several which combine into one are the subject or predicate insofar as they are distinct actualities; (c) when one noun is imposed of several things which do not combine into one; and (d) when the several which do not combine into one are the subject or predicate.(40) After distinguishing the multiple enunciations, Aristotle takes up their consequences.(41) He proposes first the problem of why some predicates are true of a subject both when the predicates are taken separately and whey they are joined, while others are true only separately, e.g., from the fact that Socrates is a man and is white it follows that Socrates is a white man but from the fact that he is good and is a musician it does not follow that Socrates is a good musician.(42) The second problem is whether from ay enunciation whose predicate includes several notions it is legitimate to infer several enunciations each having one of the notions for its predicate e.g., from "Socrates is a white man" it follows that he is white and that he is a man, but from "Socrates is a good musician" it does not follow that he is good. (43)
Secondly, an addition can be made, not merely to a part of the enunciation, but to its very composition. Such an addition is a mode, and it distinguishes the modal enunciation from the de inesse enunciation. There are four of these modes: possible, contingent, impossible, and necessary.(44) The introductory paragraphs of Cajetan's commentary explain the distinction between the modal and the de inesse enunciations, which mode make an enunciation modal, the parts of the modal enunciation, and it definition.(45) The text of Aristotle covers the opposition of modals by reason of affirmation and negation(46) as well as their consequences. Thus, to the affirmation, "That man is white is possible," is opposed the negation, "That man is white is not possible."(47) A modal is negative only by addition of a negative to the mode, regardless of whether or not the dictum is negative.(48) The following is an example of the consequence of equipollent modals: that which is necessary to be is, consequently, no possible not to be, not contingent not to be, and impossible not to be.(49) Cajetan concludes this section with some paragraphs on the quantity peculiar to modals and their opposition by virtue of their quantity.(50)
Lastly, Aristotle treats the opposition of enunciations deriving from an addition made to a simple enunciation.(51) In this section, he asks whether the contrary of an affirmative enunciation is the negation of the same predicate or the affirmation of the contrary predicate, e.g., is the contrary of "Every man is just" "No man is just" or "Every man is unjust" ?
DIVISIONS OF THE ENUNCIATION
Six ways of dividing the enunciation can be gathered from the Peri Hermeneias: by reason of unity, quality, quantity, time, matter, and expression or non-expression of the mode of composition.
The first division is into the enunciation that is one (una simpliciter) and that which is composite (una conjunctione). The former is sometimes called categorical, and the latter hypothetical.(52) This is an essential division of the enunciation, because it is a division on the part of the copula.
The second is into affirmation and negation, which St. Thomas frequently asserts is the division of the enunciation into its species.
Quae quidem est divisio generis in species, quia sumitur secundum differentiam praedicati ad quod fertur negatio; praedicatum autem est pars formalis enunciationis; et ideo hujusmodi divisio dicitur pertinere ad qualitatem enunciationis, qualitatem, inquam, essentialem, secundum quod differentia significat quale quid.(53)
The third division is by reason of a difference found in the subject of the enunciation, according as it is said of many or only of one. St. Thomas says this division pertains to the quantity of the enunciation, for quantity follows matter, and the subject is as matter in the enunciation.(54) But when the subject is a universal (i.e., it can be said of many) something can be predicated of it in three ways: universally, if the predicate belongs to the entire multitude in which the universal is found, e.g., "Every man is an animal" ; particularly, if the predicate is said to belong to an indeterminate individual that falls under the universal, e.g., "Some man is white"; or indefinitely, when something is predicated of a universal without any sign of universality or particularity. Thus from the point of view of quantity, the enunciation is divided into singular, universal, particular, and indefinite.(55)
The fourth division of the enunciation is according to time, i.e., into past, present, and future. As the third division was on the part of the subject, this is on the part of the verb, because every enunciation must have a verb or a form of a verb and must, therefore, consignify present past, or future time.(56) Both the third and fourth divisions are accidental because they are according to a part of the enunciation.
The fifth division of the enunciation is according to matter, i.e., according to the relationship of predicate to subject. If the predicate is in the, subject per se, the enunciation is said to be in necessary matter, e.g. "Man is an animal," or "Man is capable of laughter." If it is per s repugnant that the predicate be in the subject, the enunciation is said to be in impossible or remote matter, e.g., "Man is a horse." If the predicate is neither per se repugnant to the subject nor per se contained it, the enunciation is said to be in possible or contingent matter.(57)
The sixth and last division of the enunciation is into the de inesse and the modal enunciation, the former merely stating that the predicate, is or is not in the subject, the latter stating the mode in which the predicate does or does not belong to the subject, i.e., necessarily, impossibly, possibly or contingently.(58)The extremes of this division are the expression o the non-expression of the mode of composition of predicate with subject."
(1) "Principaliter tamen modum scientiae considerantis subjectum et partes subjecti, de quibus per principia propria probat passiones." St. Thomas, In Peri Hermenias, p.377a.
(2) Aristotle, Peri Herm., chap.1; St. Thomas, In Peri Herm., lect.1-3.
(3) lect.4, n.1.
(4) Ibid.; the noun and the verb are treated in Aristotle, chaps. 2, 3; St. Thomas, lect. 4, 5.
(5) It is important to note that nomen or noun includes both the noun substantive and the noun adjective. This is not only true in logic, but is also in accordance with the usage of the older grammarians. Thus, in "Man is white" both "man" am "white" are nouns.
(6) Aristotle, chap. 4, 16b27-35; St. Thomas, lect. 6.
(7) Chap. 4, 17a1-chap. 9.
(8) Chaps. 10-14; in the commentary of St. Thomas, the first is treated in lessons seven to fifteen of what he calls the first book; all the rest in the commentaries of St. Thomas and Cajetan is called the second book.
(9) Chap. 4, 17a1-8.
(10) Chaps. 5-6, 17a26.
(11) Chap. 6, 17a27-chap. 9.6
(12) "Enunciatio est oratio, in qua verum vel falsum est." St. Thomas, lect.7, n.2.
(13) Ibid., n.4.
(14) Ibid., lect.8, n.13.
(15) Ibid., n.19.
(16) Chap. 6, 17a27-chap. 8; St. Thomas, lect.9-12.
(17) Chap. 9; St. Thomas, lect.13-15.
(18) St. Thomas, lect.9, n.8.
(19) Ibid., n.2.
(20) Aristotle, chap.7, 17a37-17b22; St. Thomas, lect.10, 11, nn.1-5.
(21) St. Thomas, lect.10, nn.10, 14, 15, 16.
(22) Ibid., n.18.22
(23) Ibid., n.19.
(24) Ibid., lect.11, nn.2, 3.
(25) Aristotle, chap.7, 17b23-37; St. Thomas, lect.11, nn.6-11.
(26) Chap.7, 17b38-chap.8; St. Thomas, lect.12.
(27) Chap.9; St. Thomas, lect.13-15.
(28) St. Thomas, lect.13, n.3.
(29) Ibid., nn.4, 5, 6.
(30) Aristotle, chaps.10-14; the second book of the commentaries.
(31) Chap.10; St. Thomas and Cajetan, II, lect.1-4.
(32) St. Thomas, lead.
(33) Ibid., lect.2, n.2.
(35) Cajetan, lect.3, nn.1-8.
(36) Ibid., n.9.
(37) Ibid., n.10.
(38) Ibid., nn.12-16.
(39) Aristotle, chap.11; Cajetan, lect.5-7.
(40) Cajetan, lect.5, n.4.
(41) 20b32-21a33; Cajetan, lect.6, 7.
(42) Cajetan, lect.6.
(43) Ibid., lect.7.
(44) Aristotle, chaps.12, 13; Cajetan, lect.8-12.
(45) lect.8, nn.1-6.
(46) Chap.12; Cajetan, lect.8 n.7, lect.9.
(47) Chap.13; Cajetan, lect.10-12, n.9.
(48) Cajetan lect.9, n.5.
(49) Ibid., lect.12, n.7.
(50) Ibid., nn.10-13.
(51) Chap.14; Cajetan, lect.13, 14.
(52) John of Saint Thomas, Cursus philosophicus (ed. Reiser, 3 vols.; Rome: Marietti, 1930), T.I, p.25.
(53) In I Peri Herm., lect.10, n.10.
(55) Ibid., n.13-16.
(56) Ibid., lect.13,
(58) Cajetan, In II Peri Herm., lect.8, n.2.
From: Henri DuLac, "The 'Peri Hermenias'. Its Place in Logic and Its Order", Laval Théologique et Philosophique 5, 1949, pp. 161-169.
"3.2. The expression of thought in speech
3.2.1. As we saw in 2.4.3, one of the words that Plato uses for giving verbal expression to what one holds true in one's mind is the verb apophainesthai. This verb, with gnomon or doxan as the expressed or unexpressed object, was familiar to every Greek and had the quite ordinary meaning of making known one's opinion. It is this word that plays a central role in Aristotle's treatment of the expression of thought in speech, at least in De interpretatione. Together with the noun apophansis, it becomes a more or less technical term for the speech act of making known to others what one holds true in one's mind, of asserting that something is the case. This speech act is either an affirmation or a denial: a kataphasis is an apophansis in which it is asserted that one thing belongs to another, an apophasis is an apophansis in which one thing is separated from another (De int. 17 a 25). Both kataphasis and apophasis are species of the genus phasis: they are forms of saying (phanai) that something is or is not the case.
All these nouns suffer from a process-product ambiguity. Sometimes they indicate the activity of making known one's opinion by means of affirming or denying that something is the case. But they may also designate the utterance which is produced in the course of that activity. So an apophansis is defined as a significant spoken sound about whether something does or does not hold (De int. 17 a 23). The two species of the genus phasis, kataphasis and apophasis, are defined as logos kataphatikos and logos apophatikos, as an affirmative or negative utterance (Cat. 12 b 8). Each is a logos apophantikos, an utterance used in the activity of revealing one's thought (De int. 17 a 8).
It is this utterance, as used for a special purpose, that is the typical unit of the legein-level, the Platonic logos. In contrast with other sorts of expressions which do not yet admit of truth or falsity, a kataphasis or apophasis and a logos apophantikos are the kind of units that are rightly called true or false (Cat. 2 a 7; De int. 17 a 3, 20 a 35).
3.2.2. The other sorts of expressions, which do not yet admit of truth or falsity and are for that reason incomplete and defective, are the units of Plato's onomazein-level, the onomata and rhemata. By uttering an onoma or a rhema one cannot reveal anything by one's utterance in such a way as to be making a statement (De int. 17 a 17). This 'not yet'-character of onomata and rhemata is a point to which Aristotle remarkably often returns.
In Cat. 1 a 16 he distinguishes between expressions whose utterance involves a combination (symploke) and expressions that are uttered without combination. As examples are given: 'Man runs', 'Man wins'; 'Man', 'Ox', 'Runs', 'Wins'. The expressions formed without any combination designate something belonging to one of the categories, and none of them is either true or false (Cat. 2 a 8, 13 b 10).
In De int. 16 a 9 a parallel is drawn between the mental sphere and the verbal sphere. In the mental sphere two kinds of thoughts are found, those
unaccompanied by truth or by falsity and those that necessarily have one or the other. In the verbal sphere onomata and rhemata which are pronounced without any addition -- for instance, 'Man', 'White' -- are like thoughts that are formed without any combination; they are not yet true or false. Even a word such as 'Goat-stag' does not yet signify anything true or false. It does so only when 'is' or 'is not' is added.
That the symploke must be of a special kind is shown by De int 16 b 1. When 'is' or 'is not' is added to a genitive or dative case (Philo's' or 'to-Philo), the combination does not yet yield a truth or falsehood. The oblique cases cannot play the role of naming the subject in a statement-making utterance.
Further examples of the 'not yet'-terminology are De int. 16 b 19 and 17 a 9. Verbs uttered by themselves signify something but they do not yet signify whether something is the case or not (Compare De int. 16 b 28: a word like 'Man' signifies something but not that something is the case or is not the case). The definition (logos) of man, without 'is' or 'was' or 'will be' or something of that kind, is not yet a statement-making utterance.
These passages are sufficient proof that Aristotle, probably inspired by Plato, is fully aware of the incomplete and defective character of onomata and rhemata. Measured against the relative independence of utterances by means of which expression is given to a belief that something is the case, and which therefore admit of truth or falsity, the meaning of onomata and rhemata is imperfect. A composite unit of the legein-level, which has the complete sense of a true or a false thought, is formed only when the open place accompanying each separate onoma or rhema is occupied by a proper complement.
Aristotle defines onomata and rhemata as spoken sounds significant by convention none of whose parts is significant in separation (De int. 16 a 20, 16 b 6; Poetics 1457 a 10, 14). The difference between the two is that an onoma signifies without any reference to time, whereas a rhema additionally signifies time. Moreover, the rhema is a sign of something said of something else, the subject. The verb legein which Aristotle uses in this connection indicates both the predicative and the assertive function of the rhema; if someone says 'Callias runs', the component 'runs' is a sign that the speaker connects the activity of running with Callias, but also that he holds that this predicate actually belongs to Callias, at the time indicated. As for cases like 'Callias is running' or 'Man is just', where the word 'is' occurs as a third element, there the verb 'is' by itself is nothing, but it additionally signifies some combination (synthesis) which cannot be thought without the components (De int 16 b 25). This synthesis, of which the spoken sounds 'is' or 'is not' are the appropriate sign, is the mental activity of bringing together or separating two concepts which, at the same time, is an act of assenting to the combination, or of dissenting from it. Aristotle does not seem to distinguish between merely conceiving of a certain combination, in a neutral state of mind, and actually accepting or rejecting it; for him a synthesis is always a mental assertion. That the copula 'is' has this assertive force is confirmed by Met. 1017 a 31; although Aristotle speaks there of an emphatic use of Is' and 'is not', in the sense of 'Socrates is educated, he really is so', there is reason to believe that this emphatic use is only a strengthening of what is normally present in all cases. For in De int. 21 b 31 it is said that in utterances of the form 'Man is white', 'Man is not white' the parts 'is' and 'is not' determine the true; this presumably means that they lend assertive force to these utterances (The passage is, however, far from clear).
De int. 16 b 20 is also interesting because it is in these lines that we find the first trace of a distinction that later came to be known as the distinction between categorematic and syncategorematic words. Although verbs by themselves do not yet signify whether something is the case or not and therefore do not possess the degree of completeness and independence which is characteristic of the units of the legein-level, it is still true that most of them have a meaning of their own in the sense that both the speaker and the hearer, in pronouncing or hearing the word, will have a definite thought in their minds, a thought that has some kind of self-sufficiency. The copula 'is', on the contrary, is not accompanied by any such distinct and relatively self-sufficient thought; it only adds a certain nuance to the meaning of the words to which it is joined. For this additional way of signifying Aristotle uses the word prossemainein. This verb also occurs in De int 20 a 13, in connection with 'every' and 'no'; these words additionally signify nothing other than that the affirmation or negation is about the name taken universally. Thus we have here the beginning of a trichotomy: expressions signifying that something is the case; verbs and nouns, which do not yet signify that something is the case but have some meaning of their own; and words like 'is', 'every', 'no', which do not signify (semainein) in either of those ways but only contribute to the meaning of other words." pp. 26-29
This chapter clearly shows that the treatment of problems concerning acts and attitudes of holding something true and their objects with which Plato had made a modest but hopeful beginning in Sophist 261-264 was considerably extended and refined by Aristotle's efforts. By way of conclusion I shall give a synopsis of what we have found out about his conception of the bearers of truth and falsity.
In the first place that is true or false which is thought or believed to be the case. This bearer of truth or falsity may be designated by such expressions as doxa, hypolepsis, doxazomenon (doxaston), hypolambanomenon (hypo-lepton), or by a hoti-clause or an accusative and infinitive phrase. In so far as a thought or belief is expressed in words it is perhaps also referred to as the pragma that underlies an affirmation or negation; but Aristotle does not seem to make a clear terminological distinction between the thing believed or asserted and that which is actually the case in reality.
Although it is not denied that logos sometimes stands for that which is asserted, in the contexts that are most relevant to our subject the word usually has the sense of utterance. Utterances that are used to make statements are the second category of bearers of truth and falsity, designated by such expressions as logos apophantikos, logos kataphatikos, logos apophatikos, apophansis, kataphasis, apophasis, and protasis. It is probable that Aristotle in speaking of utterances commonly has in mind what would nowadays be called utterance-tokens. There are, however, some passages in which the bearer of truth or falsity must be taken to be an utterance-type of a certain kind.(*)
As some of the terms for that which is thought or believed and for the utterances used to express it are also employed for the acts or attitudes of judging and believing and for the acts of uttering words with a special intention, the qualifications 'true' and 'false' can easily come to be applied to those acts and attitudes as well. Such cases are, however, exceptional and at any rate derivative." pp. 43-44
(*) For the problem of the so-called future contingencies see Dorothea Frede, Aristoteles and die 'Seeschlacht. Das Problem der Contingentia Futura in De interpretatione 9, Gottingen, 1970.
From: Gabriel Nuchelmans, Theories of Proposition. Ancient and Medieval Conceptions of the Bearers of Truth and Falsity. Amsterdam: North-Holland 1973.