10 ideas
| 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] |
| 16730 | If matter is entirely atoms, anything else we notice in it can only be modes [Gassendi] |
| Full Idea: Since these atoms are the whole of the corporeal matter or substance that exists in bodies, if we conceive or notice anything else to exist in these bodies, that is not a substance but only some kind of mode of the substance. | |
| From: Pierre Gassendi (Syntagma [1658], II.1.6.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 22.4 | |
| A reaction: If the atoms have a few qualities of their own, are they just modes? If they are genuine powers, then there can be emergent powers, which are rather more than mere 'modes'. |
| 10356 | Relativism can be seen as about the rationality of different cultural traditions [MacIntyre, by Kusch] |
| Full Idea: MacIntyre formulates relativism in terms of rationality rather than truth or objectivity. Things are rational relative to some particular tradition, but not rational as such. | |
| From: report of Alasdair MacIntyre (Whose Justice? Which Rationality? [1988], p.352) by Martin Kusch - Knowledge by Agreement Ch.19 | |
| A reaction: Personally I had always taken it to be about truth, and I expect any account of rationality to be founded on a notion of truth. There can clearly be cultural traditions of evidence, and possibly even of logic (though I doubt it). |
| 16619 | We observe qualities, and use 'induction' to refer to the substances lying under them [Gassendi] |
| Full Idea: Nothing beyond qualities is perceived by the senses. …When we refer to the substance in which the qualities inhere, we do this through induction, by which we reason that some subject lies under the quality. | |
| From: Pierre Gassendi (Syntagma [1658], II.1.6.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 07.1 | |
| A reaction: He talks of 'induction' (in an older usage), but he seems to mean abduction, since he never makes any observations of the substances being proposed. |
| 23080 | Liberals debate how conservative or radical to be, but don't question their basics [MacIntyre] |
| Full Idea: Contemporary debates within modern political systems are almost exclusively between conservative liberals, liberal liberals, and radical liberals. There is little place for the criticism of the system itself. | |
| From: Alasdair MacIntyre (Whose Justice? Which Rationality? [1988]), quoted by John Kekes - Against Liberalism 01 | |
| A reaction: [No page number given] Kekes seems to be more authoritarian, and MacIntyre is a communitarian (which can be rather authoritarian). I'm dubious about both. |
| 16593 | Atoms are not points, but hard indivisible things, which no force in nature can divide [Gassendi] |
| Full Idea: The vulgar think atoms lack parts and are free of all magnitude, and hence nothing other than a mathematical point, but it is something solid and hard and compact, as to leave no room for division, separation and cutting. No force in nature can divide it. | |
| From: Pierre Gassendi (Syntagma [1658], II.1.3.5), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 03.2 | |
| A reaction: If you gloatingly think the atom has now been split, ask whether electrons and quarks now fit his description. Pasnau notes that though atoms are indivisible, they are not incorruptible, and could go out of existence, or be squashed. |
| 16729 | How do mere atoms produce qualities like colour, flavour and odour? [Gassendi] |
| Full Idea: If the only material principles of things are atoms, having only size, shape, and weight, or motion, then why are so many additional qualities created and existing within the things: color, heat, flavor, odor, and innumerable others? | |
| From: Pierre Gassendi (Syntagma [1658], II.1.5.7), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 22.4 | |
| A reaction: This is pretty much the 'hard question' about the mind-body relation. Bacon said that heat was just motion of matter. I would say that this problem is gradually being solved in my lifetime. |