"Developing Series" in Aristotle and Grice

Aristotle's semantic theory is a complex one. Not all words get defined in the same way, via 'specifica differentia and genus'. Some are subtler.

He gives only two examples, though:

one is 'arithmos', which we could translate, harmlessly as 'number'.

Aristotle asks, "Is '1' a number?" -- the fact that numerals were not invented yet allows me to use Arabic material here, extrapolated for your sensibility.

He concludes that '1' is not a number: it's the unity. "Surely we wouldn't say that I have a number of hens if I only own one".

He then goes, "Is two a number?" He concludes that to say that he has "a number of testicles" is 'a gross exaggeration' (he says 'huperbole'). "Two" is the name of the dyad.

"Three is really the first number".

"Then there's 4, 5, 6, etc." This Aristotle calls a 'developing series'. This is not to say that 7 eats 6 and 6 eats 5, etc. The 'meaning' of 'number' _is_ in the developing series.

The other example he gives is

'soul' psukhe (literally, breath)

Plants breathe, animals breathe, man breathes.

There is a 'developing series': the _meaning_ of 'soul' is captured in this developing series. "That a man eats animals and plants is a non-sequitur", he adds, "the sequence is needed to give "transitional" meaning to our talk about living things".

Grice found this fascinating and spent five minutes discussing it in his presidential address of the pacific division of the A. P. A. in March 1975. Cheers.

JL