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18909
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Aristotelian sentences are made up by one of four 'formative' connectors [Aristotle, by Engelbretsen]
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Full Idea:
For Aristotle there are four formatives for sentences: 'belongs to some', 'belongs to every', 'belongs to no', and 'does not belong to every'. These are 'copulae'. Aristotle would have written 'wise belongs to some man'.
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From:
report of Aristotle (Prior Analytics [c.328 BCE]) by George Engelbretsen - Trees, Terms and Truth 3
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A reaction:
A rather set-theoretic reading. This invites a Quinean scepticism about whether wisdom is some entity which can 'belong' to a person. It makes trope theory sound attractive, offering a unique wisdom that is integrated into that particular person.
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8080
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Aristotelian identified 256 possible syllogisms, saying that 19 are valid [Aristotle, by Devlin]
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Full Idea:
Aristotle identified four 'figures' of argument, based on combinations of Subject (S) and Predicate (P) and Middle term (M). The addition of 'all' and 'some', and 'has' and 'has not' got the property, resulted in 256 possible syllogisms, 19 of them valid.
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From:
report of Aristotle (Prior Analytics [c.328 BCE]) by Keith Devlin - Goodbye Descartes Ch.2
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A reaction:
[Compressed version of Devlin] What Aristotle did was astonishing, and must be one of the key ideas of western civilization, even though a lot of his assumptions have been revised or rejected.
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13912
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Aristotle replaced Plato's noun-verb form with unions of pairs of terms by one of four 'copulae' [Aristotle, by Engelbretsen/Sayward]
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Full Idea:
Aristotle replaced the Platonic noun-verb account of logical syntax with a 'copular' account. A sentence is a pair of terms bound together logically (not necessarily grammatically) by one of four 'logical copulae' (every, none, some, not some).
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From:
report of Aristotle (Prior Analytics [c.328 BCE]) by Engelbretsen,G/Sayward,C - Philosophical Logic: Intro to Advanced Topics 8
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A reaction:
So the four copulas are are-all, are-never, are-sometimes, and are-sometime-not. Consider 'men' and 'mortal'. Alternatively, Idea 18909.
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9403
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There are three different deductions for actual terms, necessary terms and possible terms [Aristotle]
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Full Idea:
Since to belong, to belong of necessity, and to be possible to belong are different, ..there will be different deductions for each; one deduction will be from necessary terms, one from terms which belong, and one from possible terms.
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From:
Aristotle (Prior Analytics [c.328 BCE], 29b29-35)
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A reaction:
Fitting and Mendelsohn cite this as the earliest thoughts on modal logic. but Kneale and Kneale say that Aristotle got into a muddle, and so was unable to create a workable system.
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11148
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Deduction is when we suppose one thing, and another necessarily follows [Aristotle]
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Full Idea:
A deduction is a discourse in which, certain things having been supposed, something different from the things supposed results of necessity because these things are so.
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From:
Aristotle (Prior Analytics [c.328 BCE], 24b18)
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A reaction:
Notice that it is modal ('suppose', rather than 'know'), that necessity is involved, which is presumably metaphysical necessity, and that there are assumptions about what would be true, and not just what follows from what.
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8079
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Aristotelian logic has two quantifiers of the subject ('all' and 'some') [Aristotle, by Devlin]
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Full Idea:
Aristotelian logic has two quantifiers of the subject ('all' and 'some'), and two ways to combine the subject with the predicate ('have', and 'have not'), giving four propositions: all-s-have-p, all-s-have-not-p, some-s-have-p, and some-s-have-not-p.
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From:
report of Aristotle (Prior Analytics [c.328 BCE]) by Keith Devlin - Goodbye Descartes Ch.2
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A reaction:
Frege seems to have switched from 'some' to 'at-least-one'. Since then other quantifiers have been proposed. See, for example, Ideas 7806 and 6068.
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13412
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Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf]
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Full Idea:
Not all numbers could possibly have been learned à la Frege-Russell, because we could not have performed that many distinct acts of abstraction. Somewhere along the line a rule had to come in to enable us to obtain more numbers, in the natural order.
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From:
Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.165)
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A reaction:
Follows on from Idea 13411. I'm not sure how Russell would deal with this, though I am sure his account cannot be swept aside this easily. Nevertheless this seems powerful and convincing, approaching the problem through the epistemology.
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13413
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We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf]
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Full Idea:
Both ordinalists and cardinalists, to account for our number words, have to account for the fact that we know so many of them, and that we can 'recognize' numbers which we've neither seen nor heard.
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From:
Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.166)
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A reaction:
This seems an important contraint on any attempt to explain numbers. Benacerraf is an incipient structuralist, and here presses the importance of rules in our grasp of number. Faced with 42,578,645, we perform an act of deconstruction to grasp it.
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13411
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If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf]
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Full Idea:
If we accept the Frege-Russell analysis of number (the natural numbers are the cardinals) as basic and correct, one thing which seems to follow is that one could know, say, three, seventeen, and eight, but no other numbers.
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From:
Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.164)
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A reaction:
It seems possible that someone might only know those numbers, as the patterns of members of three neighbouring families (the only place where they apply number). That said, this is good support for the priority of ordinals. See Idea 13412.
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18911
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Linguistic terms form a hierarchy, with higher terms predicable of increasing numbers of things [Aristotle, by Engelbretsen]
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Full Idea:
According to Aristotle, the terms of a language form a finite hierarchy, where the higher terms are predicable of more things than are lower terms.
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From:
report of Aristotle (Prior Analytics [c.328 BCE]) by George Engelbretsen - Trees, Terms and Truth 3
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A reaction:
I would be a bit cautious about placing something precisely in a hierarchy according to how many things it can be predicated of. It is a start, though, in trying to give a decent account of generality, which is a major concept in philosophy.
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7909
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The Eightfold Path concerns morality, wisdom, and tranquillity [Ashvaghosha]
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Full Idea:
The Eightfold Path has three steps concerning morality - right speech, right bodily action, and right livelihood; three of wisdom - right views, right intentions, and right effort; and two of tranquillity - right mindfulness and right concentration.
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From:
Ashvaghosha (Saundaranandakavya [c.50], XVI)
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A reaction:
Most of this translates quite comfortably into the aspirations of western philosophy. For example, 'right effort' sounds like Kant's claim that only a good will is truly good (Idea 3710). The Buddhist division is interesting for action theory.
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7908
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At the end of a saint, he is not located in space, but just ceases to be disturbed [Ashvaghosha]
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Full Idea:
When an accomplished saint comes to the end, he does not go anywhere down in the earth or up in the sky, nor into any of the directions of space, but because his defilements have become extinct he simply ceases to be disturbed.
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From:
Ashvaghosha (Saundaranandakavya [c.50], XVI)
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A reaction:
To 'cease to be disturbed' is the most attractive account of heaven I have encountered. It all sounds a bit dull though. I wonder, as usual, how they know all this stuff.
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