7 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] |
| 14742 | It can't be indeterminate whether x and y are identical; if x,y is indeterminate, then it isn't x,x [Salmon,N] |
| Full Idea: Insofar as identity seems vague, it is provably mistaken. If it is vague whether x and y are identical (as in the Ship of Theseus), then x,y is definitely not the same as x,x, since the first pair is indeterminate and the second pair isn't. | |
| From: Nathan Salmon (Reference and Essence: seven appendices [2005], App I) | |
| A reaction: [compressed; Gareth Evans 1978 made a similar point] This strikes me as begging the question in the Ship case, since we are shoehorning the new ship into either the slot for x or the slot for y, but that was what we couldn’t decide. No rough identity? |
| 18885 | Kripke and Putnam made false claims that direct reference implies essentialism [Salmon,N] |
| Full Idea: Kripke and Putnam made unsubstantiated claims, indeed false claims, to the effect that the theory of direct reference has nontrivial essentialist import. | |
| From: Nathan Salmon (Reference and Essence: seven appendices [2005], Pref to Exp Ed) | |
| A reaction: Kripke made very few claims, and is probably innocent of the charge. Most people agree with Salmon that you can't derive metaphysics from a theory of reference. |
| 20713 | God must be fit for worship, but worship abandons morally autonomy, but there is no God [Rachels, by Davies,B] |
| Full Idea: Rachels argues 1) If any being is God, he must be a fitting object of worship, 2) No being could be a fitting object of worship, since worship requires the abandonment of one's role as an autonomous moral agent, so 3) There cannot be a being who is God. | |
| From: report of James Rachels (God and Human Attributes [1971], 7 p.334) by Brian Davies - Introduction to the Philosophy of Religion 9 'd morality' | |
| A reaction: Presumably Lionel Messi can be a fitting object of worship without being God. Since the problem is with being worshipful, rather than with being God, should I infer that Messi doesn't exist? |