10 ideas
| 11257 | The Pythagoreans were the first to offer definitions [Politis, by Politis] |
| Full Idea: Aristotle praises the Pythagoreans for being the first to offer definitions. | |
| From: report of Vassilis Politis (Aristotle and the Metaphysics [2004]) by Vassilis Politis - Aristotle and the Metaphysics 2.4 | |
| A reaction: This sounds like a hugely important step in the development of Greek philosophy which is hardly ever mentioned. |
| 11235 | 'True of' is applicable to things, while 'true' is applicable to words [Politis] |
| Full Idea: It is crucial not to confuse 'true' with 'true of'. 'True of' is applicable to things, while 'true' is applicable to words. | |
| From: Vassilis Politis (Aristotle and the Metaphysics [2004], 1.4) | |
| A reaction: A beautifully simple distinction which had never occurred to me, and which (being a thoroughgoing realist) I really like. |
| 9540 | A 'value-assignment' (V) is when to each variable in the set V assigns either the value 1 or the value 0 [Hughes/Cresswell] |
| Full Idea: A 'value-assignment' (V) is when to each variable in the set V assigns either the value 1 or the value 0. | |
| From: GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1) | |
| A reaction: In the interpreted version of the logic, 1 and 0 would become T (true) and F (false). The procedure seems to be called nowadays a 'valuation'. |
| 9541 | The Law of Transposition says (P→Q) → (¬Q→¬P) [Hughes/Cresswell] |
| Full Idea: The Law of Transposition says that (P→Q) → (¬Q→¬P). | |
| From: GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1) | |
| A reaction: That is, if the consequent (Q) of a conditional is false, then the antecedent (P) must have been false. |
| 9543 | The rules preserve validity from the axioms, so no thesis negates any other thesis [Hughes/Cresswell] |
| Full Idea: An axiomatic system is most naturally consistent iff no thesis is the negation of another thesis. It can be shown that every axiom is valid, that the transformation rules are validity-preserving, and if a wff α is valid, then ¬α is not valid. | |
| From: GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1) | |
| A reaction: [The labels 'soundness' and 'consistency' seem interchangeable here, with the former nowadays preferred] |
| 9544 | A system is 'weakly' complete if all wffs are derivable, and 'strongly' if theses are maximised [Hughes/Cresswell] |
| Full Idea: To say that an axiom system is 'weakly complete' is to say that every valid wff of the system is derivable as a thesis. ..The system is 'strongly complete' if it cannot have any more theses than it has without falling into inconsistency. | |
| From: GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1) | |
| A reaction: [They go on to say that Propositional Logic is strongly complete, but Modal Logic is not] |
| 11277 | Maybe 'What is being? is confusing because we can't ask what non-being is like [Politis] |
| Full Idea: We may be unfamiliar with the question 'What is being?' because there appear to be no contrastive questions of the form: how do beings differ from things that are not beings? | |
| From: Vassilis Politis (Aristotle and the Metaphysics [2004], 4.1) | |
| A reaction: We can, of course, contrast actual beings with possible beings, or imaginary beings, or even logically impossible beings, but in those cases 'being' strikes me as an entirely inappropriate word. |
| 11248 | Necessary truths can be two-way relational, where essential truths are one-way or intrinsic [Politis] |
| Full Idea: An essence is true in virtue of what the thing is in itself, but a necessary truth may be relational, as the consequence of the relation between two things and their essence. The necessary relation may be two-way, but the essential relation one-way. | |
| From: Vassilis Politis (Aristotle and the Metaphysics [2004], 2.3) | |
| A reaction: He is writing about Aristotle, but has in mind Kit Fine 1994 (qv). Politis cites Plato's answer to the Euthyphro Question as a good example. The necessity comes from the intrinsic nature of goodness/piety, not from the desire of the gods. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |