13 ideas
| 23367 | Even pointing a finger should only be done for a reason [Epictetus] |
| Full Idea: Philosophy says it is not right even to stretch out a finger without some reason. | |
| From: Epictetus (fragments/reports [c.57], 15) | |
| A reaction: The key point here is that philosophy concerns action, an idea on which Epictetus is very keen. He rather despise theory. This idea perfectly sums up the concept of the wholly rational life (which no rational person would actually want to live!). |
| 11022 | Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read] |
| Full Idea: Gentzen introduced a natural deduction calculus (NK) in 1934. | |
| From: report of Gerhard Gentzen (works [1938]) by Stephen Read - Thinking About Logic Ch.8 |
| 11065 | The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna] |
| Full Idea: Gentzen argued that the inferential role of a logical constant constitutes its meaning. | |
| From: report of Gerhard Gentzen (works [1938]) by Robert Hanna - Rationality and Logic 5.3 | |
| A reaction: Possibly inspired by Wittgenstein's theory of meaning as use? This idea was the target of Prior's famous connective 'tonk', which has the role of implying anything you like, proving sentences which are not logical consequences. |
| 11023 | The logical connectives are 'defined' by their introduction rules [Gentzen] |
| Full Idea: The introduction rules represent, as it were, the 'definitions' of the symbols concerned, and the elimination rules are no more, in the final analysis, than the consequences of these definitions. | |
| From: Gerhard Gentzen (works [1938]), quoted by Stephen Read - Thinking About Logic Ch.8 | |
| A reaction: If an introduction-rule (or a truth table) were taken as fixed and beyond dispute, then it would have the status of a definition, since there would be nothing else to appeal to. So is there anything else to appeal to here? |
| 11213 | Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen] |
| Full Idea: To every logical symbol there belongs precisely one inference figure which 'introduces' the symbol ..and one which 'eliminates' it. The introductions represent the 'definitions' of the symbols concerned, and eliminations are consequences of these. | |
| From: Gerhard Gentzen (works [1938], II.5.13), quoted by Ian Rumfitt - "Yes" and "No" III | |
| A reaction: [1935 paper] This passage is famous, in laying down the basics of natural deduction systems of logic (ones using only rules, and avoiding axioms). Rumfitt questions whether Gentzen's account gives the sense of the connectives. |
| 10067 | Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave] |
| Full Idea: Gentzen proved the consistency of arithmetic from assumptions which transcend arithmetic. | |
| From: report of Gerhard Gentzen (works [1938]) by Alan Musgrave - Logicism Revisited §5 | |
| A reaction: This does not contradict Gödel's famous result, but reinforces it. The interesting question is what assumptions Gentzen felt he had to make. |
| 11984 | Asserting a possible property is to say it would have had the property if that world had been actual [Plantinga] |
| Full Idea: To say than x has a property in a possible world is simply to say that x would have had the property if that world had been actual. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], I) | |
| A reaction: Plantinga tries to defuse all the problems with identity across possible worlds, by hanging on to subjunctive verbs and modal modifiers. The point, though, was to explain these, or at least to try to give their logical form. |
| 11980 | A possible world is a maximal possible state of affairs [Plantinga] |
| Full Idea: A possible world is just a maximal possible state of affairs. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], I) | |
| A reaction: The key point here is that Plantinga includes the word 'possible' in his definition. Possibility defines the worlds, and so worlds cannot be used on their own to define possibility. |
| 11982 | If possible Socrates differs from actual Socrates, the Indiscernibility of Identicals says they are different [Plantinga] |
| Full Idea: If the Socrates of the actual world has snubnosedness but Socrates-in-W does not, this is surely inconsistent with the Indiscernibility of Identicals, a principle than which none sounder can be conceived. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], I) | |
| A reaction: However, we allow Socrates to differ over time while remaining the same Socrates, so some similar approach should apply here. In both cases we need some notion of what is essential to Socrates. But what unites aged 3 with aged 70? |
| 11983 | It doesn't matter that we can't identify the possible Socrates; we can't identify adults from baby photos [Plantinga] |
| Full Idea: We may say it makes no sense to say that Socrates exists at a world, if there is in principle no way of identifying him. ...But this is confused. To suppose Agnew was a precocious baby, we needn't be able to pick him from a gallery of babies. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], I) | |
| A reaction: This seems a good point, and yet we have a space-time line joining adult Agnew with baby Agnew, and no such causal link is available between persons in different possible worlds. What would be the criterion in each case? |
| 11985 | If individuals can only exist in one world, then they can never lack any of their properties [Plantinga] |
| Full Idea: The Theory of Worldbound Individuals contends that no object exists in more than one possible world; this implies the outrageous view that - taking properties in the broadest sense - no object could have lacked any property that it in fact has. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], II) | |
| A reaction: Leibniz is the best known exponent of this 'outrageous view', though Plantinga shows that Lewis may be seen in the same light, since only counterparts are found in possible worlds, not the real thing. The Theory does seem wrong. |
| 11986 | The counterparts of Socrates have self-identity, but only the actual Socrates has identity-with-Socrates [Plantinga] |
| Full Idea: While Socrates has no counterparts that lack self-identity, he does have counterparts that lack identity-with-Socrates. He alone has that - the property, that is, of being identical with the object that in fact instantiates Socrateity. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], II) | |
| A reaction: I am never persuaded by arguments which rest on such dubious pseudo-properties. Whether or not a counterpart of Socrates has any sort of identity with Socrates cannot be prejudged, as it would beg the question. |
| 11987 | Counterpart Theory absurdly says I would be someone else if things went differently [Plantinga] |
| Full Idea: It makes no sense to say I could have been someone else, yet Counterpart Theory implies not merely that I could have been distinct from myself, but that I would have been distinct from myself had things gone differently in even the most miniscule detail. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], II) | |
| A reaction: A counterpart doesn't appear to be 'me being distinct from myself'. We have to combine counterparts over possible worlds with perdurance over time. I am a 'worm' of time-slices. Anything not in that worm is not strictly me. |