17 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! |
| 9456 | Modal logic is multiple systems, shown in the variety of accessibility relations between worlds [Jacquette] |
| Full Idea: Modal logic by its very nature is not monolithic, but fragmented into multiple systems of modal qualifications, reflected in the plurality of accessibility relations on modal model structures or logically possible worlds. | |
| From: Dale Jacquette (Intro to 'Philosophy of Logic' [2002], §3) | |
| A reaction: He implies the multiplicity is basic, and is only 'reflected' in the relations, but maybe the multiplicity is caused by incompetent logicians who can't decide whether possible worlds really are reflexive or symmetrical or transitive in their relations. |
| 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. |
| 9457 | The two main views in philosophy of logic are extensionalism and intensionalism [Jacquette] |
| Full Idea: Philosophy of logic has (roughly) two camps: extensionalists and intensionalists, with the former view dominant. ...There is a close connection between this and eliminativist or reductivist versus folk psychological and intentionalist philosophy of mind. | |
| From: Dale Jacquette (Intro to 'Philosophy of Logic' [2002], §4) | |
| A reaction: Hm. I think I favour intensionalism in the logic, and reductivism about the mind, so I may have a bit of bother here. I'm convinced that this jigsaw can be completed, despite all appearances. |
| 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. |
| 9458 | Extensionalists say that quantifiers presuppose the existence of their objects [Jacquette] |
| Full Idea: Extensionalists hold that quantifiers in predicate logic presuppose the existence of whatever objects can be referred to by constants or bound variables, or enter into true predication of properties. | |
| From: Dale Jacquette (Intro to 'Philosophy of Logic' [2002], §4) | |
| A reaction: I have strong sales resistance to this view. Why should a procedure for correctly reasoning from one proposition to another have anything whatever to do with ontology? A false world picture can be interconnected by perfect logic. |
| 9461 | Intensionalists say meaning is determined by the possession of properties [Jacquette] |
| Full Idea: According to intensionalist semantics the meaning of a proposition is determined by the properties an object possesses. | |
| From: Dale Jacquette (Intro to 'Philosophy of Logic' [2002], §4) | |
| A reaction: This sounds good to me. Extensionalist don't seem to care what sets they put things in, but if property possession comes first, then things will fall into their own sets without any help for us. We can add silly sets afterwards, if we fancy. |
| 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. |
| 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. |
| 9460 | Extensionalist semantics forbids reference to nonexistent objects [Jacquette] |
| Full Idea: In extensionalist semantics only existent objects can be referred to, ...but in everyday thought and discourse we regularly and apparently without undue confusion speak about nonexistent objects. | |
| From: Dale Jacquette (Intro to 'Philosophy of Logic' [2002], §4) | |
| A reaction: This is the reason why Meinong, whose views are presented by Russell as absurd, are undergoing a revival. The full-blown view will even treat 'round squares' as objects about which we can reason - and why not? Don't open a shop which sells them. |
| 9459 | Extensionalist semantics is circular, as we must know the extension before assessing 'Fa' [Jacquette] |
| Full Idea: Extensional semantics is blatantly circular. For 'Fa' to be interpreted as true, we must know that object a belongs to the extension of the predicate F, so we must already know which objects belong to the extension. | |
| From: Dale Jacquette (Intro to 'Philosophy of Logic' [2002], §4) | |
| A reaction: I'm delighted to read this, because it was the first thought that occurred to me when I encountered the theory. Presumably this leads Quine to take predication as basic, because you can't break into the circle. Or, vote for intensionalism? |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |