| 2008 | On the Philosophy of Logic |
| p.102 | 8946 | We could make our intuitions about heaps precise with a million-valued logic | |
| 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. |
| 06.III | p.84 | 8941 | We can't explain 'possibility' in terms of 'possible' worlds |
| 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. |
| 07.I | p.95 | 8943 | Three-valued logic says excluded middle and non-contradition are not tautologies |
| 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'. |
| 07.II | p.97 | 8944 | Vagueness can involve components (like baldness), or not (like boredom) |
| 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. |
| 07.II | p.100 | 8945 | Fuzzy logic has many truth values, ranging in fractions from 0 to 1 |
| 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. |
| 08.I | p.107 | 8947 | If all truths are implied by a falsehood, then not-p might imply both q and not-q |
| 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. |
| 08.III | p.117 | 8949 | In relevance logic, conditionals help information to flow from antecedent to consequent |
| 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. |
| 09.I | p.131 | 8950 | Logic formalizes how we should reason, but it shouldn't determine whether we are realists |
| 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. |
| 12.I | p.162 | 8951 | Classical logic is: excluded middle, non-contradiction, contradictions imply all, disjunctive syllogism |
| 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! |
| 12.IV | p.187 | 8952 | We reach 'reflective equilibrium' when intuitions and theory completely align |
| 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! |