Monday, April 22, 2024

What is a term for Aristotle ?

One of the uniquely interesting features of the Topics is that it offers a wealth of examples illustrating the fine logical-grammatical structure of those linguistic expressions considered terms for Aristotle.  The common view that in Aristotle we have essentially a term-logic while in the Stoics we have a proposition- or sentence-logic is untenable. Not only have Bobzien and Shogry shown that the Stoics had a highly developed theory of sub-propositional elements but the evidence points to the Aristotelic term being what we now call a noun-phrase which can include embedded sentences, in particular that-clauses. Thus this opposition is merely apparent

In Plato’s Sophist there is a discussion concerning ’sentences’, ’nouns’ and ’verbs’, sentences being combinations of nouns and verbs, and all sentences must have a ’subject’. Plato gives the example ’Theaetetus, with whom I am now speaking, is flying’. This illustrates how Plato’s concept of ’noun’ corresponds to our ’noun phrase’ and very likely to the Aristotelic term or ’oros’.

1. We must be careful not to confuse Aristotle's convertability and co-extensionality with our modern notions, in particular, first-order notion. Aristotle's convertability  is more of a co-predicability. Thus the Aristotelic 'extent' of a term is not framed using individuals but other terms in general. The extent of a term B is the collection of all terms C for which B can be said of C.  Thus subordinate species and the subordinate species of theses species are all part of the 'extent' of a genus.

2.  Relative idion is a trinary predicate: $RI (x,y,z)$ read: $z$ is the relative idion of $x$ relative to $y$.

4. It will be good to have a complete glossary of all the 'terms' mentioned in the Topics and the relationships between them, either rejected or accepted (and sometimes, unfortunately both) by Aristotle. Examples of terms in book V : bear a very close resemblance to the soul , the primary element wherein the soul is naturally found,  possession of sensation,  being natural sentient, the most rarefied and lightest body, the substance to which "man" belongs as a species, that which is made of body and soul. We at once notice some grammatical issues with this translation, not to mention logical, ontological issues (the flexibility is amazing, even the meta-level predicabilia themselves can be part of the post-determiner of the noun-phrase). How much better is the original Greek. For instance the first term is : to homoiotaton psukhê(i). This appears to be an ellipsis for 'the thing ousia most similar to the soul', that is if we postulate the general structure of the Aristotelic term to be

Genus G + post-modifer

In modern logic the Peano iota operator involves individuals. But for Aristotle it is natural to conceive Peano operators for species, for instance the accepted property of animal as to ek psukhês kai somatos sugkeimenon. But this can be read: the composite consisting of soul and body. Definitions and properties of mass-nouns are not uncommon in the Topics. 

One topic is the following:

forall C.  Subexp(C,B) and Species(C,A) => not Idion(A,B)

Wait a minute ! Are we talking about the linguistic expressions or what they mean ? How dare you put the predicates for subexpression and species and idion all in the same formula !  But what if we want to deal with globs which include both the syntactical, semantic and relational aspects at once ? Fans of ordinary language and ordinary usage,  what do you mean when you say "the word 'cat' " ?   The glob ! Only linguists can invent some fancy brackets to isolate the purely phonetic or orthographic aspect, like /cat/.  Like it or not, Aristotle deals with globs - or perhaps, writing elliptically,  he does not. Maybe our Subexp is wrong, and it should be replaced with semantic inclusion ?

What is the concept of man ?  Does it differ for different people of different cultures at different times and places ? Are we after the invariant in all these concepts ? How does a concept relate to other concepts, to the mind and to the concrete things to which it is predicated ? What is the genesis of concepts and how do they relate to perception ?  What about the different modalities and intentions in which a concept takes part in ? What is predication of essence  and how can one know a concept yet definitions be defeasible ? Surely rationality, bipedalism, etc. are simpler, clearer, concepts and perhaps thus more invariant. But is the genus simpler than the species ? Does predication of essence relate to the essence qua embodied in a concrete substance or to the concept ?

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