19 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. |
| 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. |
| 15086 | Absolute necessity might be achievable either logically or metaphysically [Hale] |
| Full Idea: Maybe peaceful co-existence between absolute logical necessity and absolute metaphysical necessity can be secured, ..and absolute necessity is their union. ...However, a truth would then qualify as absolutely necessary in two quite different ways. | |
| From: Bob Hale (Absolute Necessities [1996], 4) | |
| A reaction: Hale is addressing a really big question for metaphysic (absolute necessity) which others avoid. In the end he votes for rejecting 'metaphysical' necessity. I am tempted to vote for rejecting logical necessity (as being relative). 'Absolute' is an ideal. |
| 8261 | Maybe not-p is logically possible, but p is metaphysically necessary, so the latter is not absolute [Hale] |
| Full Idea: It might be metaphysically necessary that p but logically possible that not-p, so that metaphysical necessity is not, after all, absolute. | |
| From: Bob Hale (Absolute Necessities [1996]), quoted by E.J. Lowe - The Possibility of Metaphysics 1.5 | |
| A reaction: Lowe presents this as dilemma, but it sounds fine to me. Flying pigs etc. have no apparent logical problems, but I can't conceive of a possible world where pigs like ours fly in a world like ours. Earthbound pigs may be metaphysically necessary. |
| 15081 | A strong necessity entails a weaker one, but not conversely; possibilities go the other way [Hale] |
| Full Idea: One type of necessity may be said to be 'stronger' than another when the first always entails the second, but not conversely. This will obtain only if the possibility of the first is weaker than the possibility of the second. | |
| From: Bob Hale (Absolute Necessities [1996], 1) | |
| A reaction: Thus we would normally say that if something is logically necessary (a very strong claim) then it will have to be naturally necessary. If something is naturally possible, then clearly it will have to be logically possible. Sounds OK. |
| 15080 | 'Relative' necessity is just a logical consequence of some statements ('strong' if they are all true) [Hale] |
| Full Idea: Necessity is 'relative' if a claim of φ-necessary that p just claims that it is a logical consequence of some statements Φ that p. We have a 'strong' version if we add that the statements in Φ are all true, and a 'weak' version if not. | |
| From: Bob Hale (Absolute Necessities [1996], 1) | |
| A reaction: I'm not sure about 'logical' consequence here. It may be necessary that a thing be a certain way in order to qualify for some category (which would be 'relative'), but that seems like 'sortal' necessity rather than logical. |
| 15082 | Metaphysical necessity says there is no possibility of falsehood [Hale] |
| Full Idea: Friends of metaphysical necessity would want to hold that when it is metaphysically necessary that p, there is no good sense of 'possible' (except, perhaps, an epistemic one) in which it is possible that not-p. | |
| From: Bob Hale (Absolute Necessities [1996], 2) | |
| A reaction: We might want to say which possible worlds this refers to (and presumably it won't just be in the actual world). The normal claim would refer to all possible worlds. Adding a '...provided that' clause moves it from absolute to relative necessity. |
| 15085 | 'Broadly' logical necessities are derived (in a structure) entirely from the concepts [Hale] |
| Full Idea: 'Broadly' logical necessities are propositions whose truth derives entirely from the concepts involved in them (together, of course, with relevant structure). | |
| From: Bob Hale (Absolute Necessities [1996], 3) | |
| A reaction: Is the 'logical' part of this necessity bestowed by the concepts, or by the 'structure' (which I take to be a logical structure)? |
| 15088 | Logical necessities are true in virtue of the nature of all logical concepts [Hale] |
| Full Idea: The logical necessities can be taken to be the propositions which are true in virtue of the nature of all logical concepts. | |
| From: Bob Hale (Absolute Necessities [1996], p.10) | |
| A reaction: This is part of his story of essences giving rise to necessities. His proposal sounds narrow, but logical concepts may have the highest degree of generality which it is possible to have. It must be how the concepts connect that causes the necessities. |
| 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. |
| 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. |
| 15087 | Conceptual necessities are made true by all concepts [Hale] |
| Full Idea: Conceptual necessities can be taken to be propositions which are true in virtue of the nature of all concepts. | |
| From: Bob Hale (Absolute Necessities [1996], p.9) | |
| A reaction: Fine endorse essences for these concepts. Could we then come up with a new concept which contradicted all the others, and destroyed the necessity? Yes, presumably. Presumably witchcraft and astrology are full of 'conceptual necessities'. |
| 3914 | Language arranges sensory experience to form a world-order [Whorf] |
| Full Idea: Language first of all is a classification and arrangement of the stream of sensory experience which results in a certain world-order. | |
| From: Benjamin Lee Whorf (Punctual and segmentive Hopi verbs [1936], p.55) | |
| A reaction: This is only true to a limited degree. See Davidson's 'On the very idea of a conceptual scheme'. All humans share a world-order, to some extent. |