15 ideas
8952 | We reach 'reflective equilibrium' when intuitions and theory completely align [Fisher] |
Full Idea: A state of 'reflective equilibrium' is when our theory and our intuitions become completely aligned | |
From: Jennifer Fisher (On the Philosophy of Logic [2008], 12.IV) | |
A reaction: [Rawls made this concept famous] This is a helpful concept in trying to spell out the ideal which is the dream of believers in 'pure reason' - that there is a goal in which everything comes right. The problem is when people have different intuitions! |
8943 | Three-valued logic says excluded middle and non-contradition are not tautologies [Fisher] |
Full Idea: In three-valued logic (L3), neither the law of excluded middle (p or not-p), nor the law of non-contradiction (not(p and not-p)) will be tautologies. If p has the value 'indeterminate' then so will not-p. | |
From: Jennifer Fisher (On the Philosophy of Logic [2008], 07.I) | |
A reaction: I quite accept that the world is full of indeterminate propositions, and that excluded middle and non-contradiction can sometimes be uncertain, but I am reluctant to accept that what is being offered here should be called 'logic'. |
8945 | Fuzzy logic has many truth values, ranging in fractions from 0 to 1 [Fisher] |
Full Idea: In fuzzy logic objects have properties to a greater or lesser degree, and truth values are given as fractions or decimals, ranging from 0 to 1. Not-p is defined as 1-p, and other formula are defined in terms of maxima and minima for sets. | |
From: Jennifer Fisher (On the Philosophy of Logic [2008], 07.II) | |
A reaction: The question seems to be whether this is actually logic, or a recasting of probability theory. Susan Haack attacks it. If logic is the study of how truth is preserved as we move between propositions, then 0 and 1 need a special status. |
8951 | Classical logic is: excluded middle, non-contradiction, contradictions imply all, disjunctive syllogism [Fisher] |
Full Idea: For simplicity, we can say that 'classical logic' amounts to the truth of four sentences: 1) either p or not-p; 2) it is not the case that both p and not-p; 3) from p and not-p, infer q; 4) from p or q and not-p, infer q. | |
From: Jennifer Fisher (On the Philosophy of Logic [2008], 12.I) | |
A reaction: [She says there are many ways of specifying classical logic] Intuition suggests that 2 and 4 are rather hard to dispute, while 1 is ignoring some grey areas, and 3 is totally ridiculous. There is, of course, plenty of support for 3! |
8950 | Logic formalizes how we should reason, but it shouldn't determine whether we are realists [Fisher] |
Full Idea: Even if one is inclined to be a realist about everything, it is hard to see why our logic should be the determiner. Logic is supposed to formalize how we ought to reason, but whether or not we should be realists is a matter of philosophy, not logic. | |
From: Jennifer Fisher (On the Philosophy of Logic [2008], 09.I) | |
A reaction: Nice to hear a logician saying this. I do not see why talk in terms of an object is a commitment to its existence. We can discuss the philosopher's stone, or Arthur's sword, or the Loch Ness monster, or gravitinos, with degrees of commitment. |
8946 | We could make our intuitions about heaps precise with a million-valued logic [Fisher] |
Full Idea: We could construct a 1,000,000-valued logic that would allow our intuitions concerning a heap to vary exactly with the amount of sand in the heap. | |
From: Jennifer Fisher (On the Philosophy of Logic [2008]) | |
A reaction: Presumably only an infinite number of grains of sand would then produce a true heap, and even one grain would count as a bit of a heap, which must both be wrong, so I can't see this helping much. |
16705 | Whiteness isn't created in an alteration, because it is just this-being-white [Oresme] |
Full Idea: If it is said that whiteness begins to be through alteration, this does not hold, because whiteness is nothing other than this-being-white. | |
From: Nicole Oresme (On 'Generation and Corruption' [1349], I.2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 19.3 | |
A reaction: This innocent-looking remark is dynamite, because it rejects the separability of qualities, which threatens the doctrine of Transubstantiation. |
8944 | Vagueness can involve components (like baldness), or not (like boredom) [Fisher] |
Full Idea: Vague terms come in at least two different kinds: those whose constituent parts come in discrete packets (bald, rich, red) and those that don't (beauty, boredom, niceness). | |
From: Jennifer Fisher (On the Philosophy of Logic [2008], 07.II) | |
A reaction: The first group seem to be features of the external world, and the second all occur in the mind. Baldness may be vague, but presumably hairs are (on the whole) not. Nature doesn't care whether someone is actually 'bald' or not. |
5998 | From the necessity of the past we can infer the impossibility of what never happens [Diod.Cronus, by White,MJ] |
Full Idea: Diodorus' Master Argument inferred that since what is past (i.e. true in the past) is necessary, and the impossible cannot follow from the possible, that therefore if something neither is nor ever will be the case, then it is impossible. | |
From: report of Diodorus Cronus (fragments/reports [c.300 BCE]) by Michael J. White - Diodorus Cronus | |
A reaction: The argument is, apparently, no longer fully clear, but it seems to imply determinism, or at least a rejection of the idea that free will and determinism are compatible. (Epictetus 2.19) |
20832 | The Master Argument seems to prove that only what will happen is possible [Diod.Cronus, by Epictetus] |
Full Idea: The Master Argument: these conflict 1) what is past and true is necessary, 2) the impossible does not follow from the possible, 3) something possible neither is nor will be true. Hence only that which is or will be true is possible. | |
From: report of Diodorus Cronus (fragments/reports [c.300 BCE]) by Epictetus - The Discourses 2.19.1 | |
A reaction: [Epictetus goes on to discuss views about which of the three should be given up] It is possible there will be a sea fight tomorrow; tomorrow comes, and no sea fight; so there was necessarily no sea fight; so the impossible followed from the possible. |
8941 | We can't explain 'possibility' in terms of 'possible' worlds [Fisher] |
Full Idea: Explaining 'it is possible that p' by saying p is true in at least one possible world doesn't get me very far. If I don't understand what possibility is, then appealing to possible worlds is not going to do me much good. | |
From: Jennifer Fisher (On the Philosophy of Logic [2008], 06.III) | |
A reaction: This seems so blatant that I assume friends of possible worlds will have addressed the problem. Note that you will also need to understand 'possible' to define necessity as 'true in all possible worlds'. Necessarily-p is not-possibly-not-p. |
8947 | If all truths are implied by a falsehood, then not-p might imply both q and not-q [Fisher] |
Full Idea: If all truths are implied by a falsehood, then 'if there are no trees in the park then there is no shade' and 'if there are no trees in the park there is plenty of shade' both come out as true. Intuitively, though, the second one is false. | |
From: Jennifer Fisher (On the Philosophy of Logic [2008], 08.I) | |
A reaction: The rule that a falsehood implies all truths must be the weakest idea in classical logic, if it actually implies a contradiction. This means we must take an interest in relevance logics. |
14304 | Conditionals are true when the antecedent is true, and the consequent has to be true [Diod.Cronus] |
Full Idea: The connected (proposition) is true when it begins with true and neither could nor can end with false. | |
From: Diodorus Cronus (fragments/reports [c.300 BCE]), quoted by Stephen Mumford - Dispositions 03.4 | |
A reaction: [Mumford got the quote from Bochenski] This differs from the truth-functional account because it says nothing about when the antecedent is false, which fits in also with the 'supposition' view, where A is presumed. This idea adds necessity. |
8949 | In relevance logic, conditionals help information to flow from antecedent to consequent [Fisher] |
Full Idea: A good account of relevance logic suggests that a conditional will be true when the flow of information is such that a conditional is the device that helps information to flow from the antecedent to the consequent. | |
From: Jennifer Fisher (On the Philosophy of Logic [2008], 08.III) | |
A reaction: Hm. 'If you are going out, you'll need an umbrella'. This passes on information about 'out', but also brings in new information. 'If you are going out, I'm leaving you'. What flows is an interpretation of the antecedent. Tricky. |
6024 | Thought is unambiguous, and you should stick to what the speaker thinks they are saying [Diod.Cronus, by Gellius] |
Full Idea: No one says or thinks anything ambiguous, and nothing should be held to be being said beyond what the speaker thinks he is saying. | |
From: report of Diodorus Cronus (fragments/reports [c.300 BCE]) by Aulus Gellius - Noctes Atticae 11.12.2 | |
A reaction: A key argument in favour of propositions, implied in this remark, is that propositions are never ambiguous, though the sentences expressing them may be |