Dougherty, M. V. (2004). Aristotle's Four Truth Values. British Journal for the History of Philosophy 12 (4):585-609.
Recent commentators have not overlooked the fact that Aristotle often contends it is important to take into account the views of others when proceeding upon an investigation. Indeed, a number of explicit methodological passages in the Aristotelian corpus seem to promote a method or line of investigation that employs a survey or discussion of the opinions of others. The consideration of methodologically significant opinions, called endoxa by Aristotle, appears to play an important part in Aristotle’s investigative procedures.
Yet what commentators have not always fastened upon is Aristotle’s often-repeated contention that individual views seem to contribute little or nothing to an investigation, but that collectively these views can contribute something substantial. This principle that individual views contribute little, but collectively contribute much, will henceforth be called the ‘Principle of Collective Truth,’ or PCT.
We shall see that the PCT is stated by Aristotle in a number of different contexts. In a political discussion, the principle is used to defend democracy in a qualified way, and it runs thus:
For the many, of whom each individual is not a good man, when they meet together may be better than the few good, if regarded not individually but collectively, just as a feast to which many contribute is better than a dinner provided out of a single purse. (Pol. 3.111281a42–b3)
As a feast to which all the guests contribute is better than a banquet furnished by a single man, so a multitude is a better judge of many things than any individual. (Pol. 3.151286a29–31)5
The principle not only finds an application in political discussions, but is also employed in epistemic contexts. It is significant that Aristotle at times appeals to the PCT to justify or lend credibility to the particular investigative procedure which involves an examination of the opinions of others. We find:
Each individual says something about the nature of things, and while individually they contribute little or nothing to the truth, by the union of all a considerable amount is amassed. (Metaph. 2.1993b1–3)6
The principle that individual contributions to a discussion can contribute to the overall pursuit of truth, yet that individually they contribute little or nothing, leaves us with a paradox. We can bring the paradox before us more clearly by noting that articulations of each polar end of the paradox seem to pervade Aristotle’s writings. We can express the paradox by looking at two seemingly opposing claims:
Error seems to be more natural to living creatures, and the soul spends more time in it. (DA 3.3427b1–2)7
For we say that that which everyone thinks is true; and the man who attacks this belief will hardly have anything more credible to stand on. (EN 10.21173a1–2)8
These two texts appear to express the positions which constitute the difficulty of the PCT. Perhaps we can address the difficulty more precisely. Aristotle appears to contend that, by itself, an individual’s proposition contributes little of worth to the truth but, when somehow combined with the statements of others, it acquires a greater value for truth.
It is not difficult to see that the PCT, when formulated in this way, contains a puzzle. One might formulate the puzzle this way: Aristotle endorses theory P and holds that P is true. Yet P is based on9or agrees with a set of endoxic propositions {q, r, s} and these individual endoxic propositions {q, r, s} themselves contribute little or nothing to the truth. Why, then, would one hold theory P to be true?
I. WHICH AUDIBLE EXPRESSIONS HAVE TRUTH VALUES?
We see, then, that for Aristotle the individually necessary and jointly sufficient conditions for an audible utterance
(AU) to have a truth value can be stated as:
AU has a truth value IFF
i AU is a proposition, and
ii AU asserts a relation between the subject and predicate
II. THE TROUBLE WITH UTTERED PROPOSITIONS
By focusing on Aristotle’s attention to the fact that propositions can be expressively ambiguous, we have discerned that Aristotle is quite aware it may take work to determine the truth value of a proposition. The point of our present inquiry into the PEA has been to show that when Aristotle encounters an endoxon, what the proposition expresses must be determined before it is accepted as either true or false. To put the issue in terms of the vocabulary of De Interpretatione,anendoxon is always encountered as either an oral or written proposition, and it is up to the investigator to locate the t@ ⁄n t cux payfimata to which the smbola constitutive of the proposition correspond. At first such an observation may seem only a little more than obvious, but we shall see that this is an issue to which Aristotle gives tremendous weight in several of his methodological statements concerning philosophic procedure. It is to these such statements that we now turn.
IV. ASSIGNING A TRUTH VALUE TO AN ENDOXON: SOME DIALECTICAL TOOLS
Rather than the two-termed range of simply ‘true’ and ‘false,’ Aristotle has at his disposal a four-fold set of truth values from which to choose. Throughout his writings Aristotle appeals to no fewer than four truth values. This set of true values consists of:
1 wholly true
2. wholly false
3 partially true
4 partially false
Moreover, those who in the case of relative terms do not distinguish to what the object is related, but have described it only so as to include it among too large a number of things, are wrong either wholly or in part; e.g. suppose some one to have defined medicine as a science of what exists. For if medicine be not a science of anything that exists, the definition is clearly altogether false; while if it be a science of some things, but not of others, it is partly false; for it ought to hold of everything. (Top. 6.12149b4–9)58
In this passage, Aristotle describes a scenario in a dialectical debate where the questioner has asked the answerer to agree to the proposition ‘medicine is the science of what is.’ If it were the case that medicine did not deal with any existing subject-matter, then the answerer could reject the proposed definition as wholly false (ıl˙w) ceud3w. Although medicine clearly deals with what is, it does not deal with everything that is. There are many existing things which do not fall under the subject matter of the science of medicine, so the proposition cannot be rejected as wholly false. Rather it must be regarded as partly false (+p2 ti ceud3w). The reason that the proposition cannot be accepted as either wholly true, or wholly false, lies in the fact that the proposition is not properly quantified, or in other words, the proposition is unexplicit with respect to its extension. We might say the proposition suffers from quantifier ambiguity or extensional vagueness. Yet all we have seen in this text is that Aristotle is willing to ascribe a truth value of ‘partly false’ to propositions which are unclear in extension. It appears that Aristotle is treating the designation of ‘partially false’ as a truth value. Are there texts to ground ‘partially true’ as a truth value as well? We turn to another passage for more evidence.
If the question is intelligible and yet it covers many senses, then supposing what it says to be wholly true or wholly false, he [the answerer] should give it an unqualified assent or denial: if, on the other hand, it be partly true and partly false, he should add a comment that it bears different senses, and also that in one it is true, in the other false. (Top. 8.7160a24–8)