Re: Peirce List Discussion • Phyllis Chiasson
A more complete excerpt and the translator’s notes are very helpful here.
A probability (εικος) is not the same as a sign (σηµειον). The former is a generally accepted premiss ; for that which people know to happen or not to happen, or to be or not to be, usually in a particular way, is a probability : e.g., that the envious are malevolent or that those who are loved are affectionate. A sign, however, means a demonstrative premiss which is necessary or generally accepted.1 That which coexists with something else, or before or after whose happening something else has happened, is a sign of that something’s having happened or being.
An enthymeme is a syllogism from probabilities or signs ; and a sign can be taken in three ways — in just as many ways as there are of taking the middle term in the several figures : either as in the first figure or as in the second or as in the third.
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E.g., the proof that a woman is pregnant because she has milk is by the first figure ; for the middle term is ‘having milk’. A stands for ‘pregnant’, B for ‘having milk’, and C for ‘woman’.
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The proof that the wise are good because Pittacus was good is by the third figure. A stands for ‘good’, B for ‘the wise’, and C for Pittacus. Then it is true to predicate both A and B of C ; only we do not state the latter, because we know it, whereas we formally assume the former.
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The proof that a woman is pregnant because she is sallow is intended to be by the middle figure ; for since sallowness is a characteristic of woman in pregnancy, and is associated with this particular woman, they suppose that she is proved to be pregnant. A stands for ‘sallowness’, B for ‘being pregnant’, C for ‘woman’.
If only one premiss is stated, we get only a sign ; but if the other premiss is assumed as well, we get a syllogism,2 e.g., that Pittacus is high-minded, because those who love honour are high-minded, and Pittacus loves honour ; or again that the wise are good, because Pittacus is good and also wise.
In this way syllogisms can be effected ; but whereas a syllogism in the first figure cannot be refuted if it is true, since it is universal, a syllogism in the last figure can be refuted even if the conclusion is true, because the syllogism is neither universal nor relevant to our purpose.3 For if Pittacus is good, it is not necessary for this reason that all other wise men are good. A syllogism in the middle figure is always and in every way refutable, since we never get a syllogism with the terms in this relation4 ; for it does not necessarily follow, if a pregnant woman is sallow, and this woman is sallow, that she is pregnant. Thus truth can be found in all signs, but they differ in the ways which have been described.
We must either classify signs in this way, and regard their middle term as an index (τεκµηριον)5 (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes6 as ‘signs’, and that which is drawn from the middle as an ‘index’. For the conclusion which is reached through the first figure is most generally accepted and most true. (Aristotle, Prior Analytics 2.27, 70a3–70b6).
Translator’s Notes
- If referable to one phenomenon only, a sign has objective necessity ; if to more than one, its value is a matter of opinion.
- Strictly an enthymeme.
- If the signs of an enthymeme in the first figure are true, the conclusion is inevitable. Aristotle does not mean that the conclusion is universal, but that the universality of the major premiss implies the validity of the minor and conclusion. The example (<all> those who have honour, etc.) quoted for the third figure contains no universal premiss or sign, and fails to establish a universal conclusion.
- i.e. when both premisses are affirmative.
- Signs may be classified as irrefutable (1st figure) and refutable (2nd and 3rd figures), and the name ‘index’ may be attached to their middle terms, either in all figures or (more probably) only in the first, where the middle is distinctively middle.
- Alternatively the name ‘sign’ may be restricted to the 2nd and 3rd figures, and may be replaced by ‘index’ in the first.
Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.
Related content in Appendix A of Theme One Program • User Guide.
for 
for 
is a boolean function 
defined as follows:
if and only if exactly one of the arguments 
equals 
via functional composition but the rest of the family is worth keeping around for many practical purposes.
may be written for 
since the number of arguments determines the rank of the operator. In some contexts even the letter 
may be omitted, writing just the argument list 
in which case it helps to use a distinctive typeface for the list delimiters, as 
arguments can be expressed in terms of minimal negation operators as 
and this is conveniently abbreviated as a concatenation of arguments 
is a triadic relation of the form 
where 
is a set of formal objects under consideration and 
and 
are two formal languages used to denote those objects. It is common practice to cut one’s teeth on the special case 
before moving on to more solid diets.
Inquiry Into Inquiry 