21 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. |
| 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. |
| 20795 | Some things are their own criterion, such as straightness, a set of scales, or light [Sext.Empiricus] |
| Full Idea: Dogmatists say something can be its own criterion. The straight is the standard of itself, and a set of scales establishes the equality of other things and of itself, and light seems to reveal not just other things but also itself. | |
| From: Sextus Empiricus (Against the Mathematicians [c.180], 442) | |
| A reaction: Each of these may be a bit dubious, but deserves careful discussion. |
| 20794 | How can sceptics show there is no criterion? Weak without, contradiction with [Sext.Empiricus] |
| Full Idea: The dogmatists ask how the sceptic can show there is no criterion. If without a criterion, he is untrustworthy; with a criterion he is turned upside down. He says there is no criterion, but accepts a criterion to establish this. | |
| From: Sextus Empiricus (Against the Mathematicians [c.180], 440) | |
| A reaction: This is also the classic difficulty for foundationalist views of knowledge. Is the foundation justified, or not? |
| 21243 | An existing thing is even greater if its non-existence is inconceivable [Anselm] |
| Full Idea: Something can be thought of as existing, which cannot be thought of as not existing, and this is greater than that which cannot be thought of as not existing. | |
| From: Anselm (Proslogion [1090], Ch 3) | |
| A reaction: This is a necessary addition, to single out the concept of God as special. But you really must give reasons for saying God's non-existence is inconceivable. Atheists seem to manage. |
| 21244 | Conceiving a greater being than God leads to absurdity [Anselm] |
| Full Idea: If some mind could think of something better than thou, the creature would rise above the Creator and judge its Creator; but this is altogether absurd. | |
| From: Anselm (Proslogion [1090], Ch 3) | |
| A reaction: An error, revealing a certain desperation. If a greafer being could be conceived than the being so far imagined as God (a necessarily existing being), that being would BE God, by his own argument (and not some arrogant 'creature'). |
| 21241 | Even the fool can hold 'a being than which none greater exists' in his understanding [Anselm] |
| Full Idea: Even the fool must be convinced that a being than which none greater can be thought exists at least in his understanding, since when he hears this he understands it, and whatever is understood is in the understanding. | |
| From: Anselm (Proslogion [1090], Ch 2) | |
| A reaction: Psalm 14.1: 'The fool hath said in his heart, there is no God'. But how does the fool interpret the words, if he has limited imagination? He might get no further than an attractive film star. He would need prompting to think of a spiritual being. |
| 21242 | If that than which a greater cannot be thought actually exists, that is greater than the mere idea [Anselm] |
| Full Idea: Clearly that than which a greater cannot be thought cannot exist in the understanding alone. For it it is actually in the understanding alone, it can be thought of as existing also in reality, and this is greater. | |
| From: Anselm (Proslogion [1090], Ch 2) | |
| A reaction: The suppressed premise is 'something actually existing is greater than the mere conception of it'. As it stands this is wrong. I can imagine a supreme evil. But see Idea 21243. |
| 1421 | A perfection must be independent and unlimited, and the necessary existence of Anselm's second proof gives this [Malcolm on Anselm] |
| Full Idea: Anselm's second proof works, because he sees that necessary existence (or the impossibility of non-existence) really is a perfection. This is because a perfection requires no dependence or limit or impediment. | |
| From: comment on Anselm (Proslogion [1090], Ch 3) by Norman Malcolm - Anselm's Argument Sect II | |
| A reaction: I have the usual problem, that it doesn't seem to follow that the perfect existence of something bestows a perfection. It may be necessary that 'for every large animal there exists a disease'. Satan may exist necessarily. |
| 21245 | The word 'God' can be denied, but understanding shows God must exist [Anselm] |
| Full Idea: We think of a thing when we say the world, and in another way when we think of the very thing itself. In the second sense God cannot be thought of as nonexistent. No one who understands can think God does not exist. | |
| From: Anselm (Proslogion [1090], Ch 4) | |
| A reaction: It seems open to the atheist to claim the exact opposite - that you can commit to God's existence if it is just a word, but understanding shows that God is impossible (perhaps because of contradictions). How to arbitrate? |
| 21246 | Guanilo says a supremely fertile island must exist, just because we can conceive it [Anselm] |
| Full Idea: Guanilo supposes that we imagine an island surpassing all lands in its fertility. We might then say that we cannot doubt that it truly exists is reality, because anyone can conceive it from a verbal description. | |
| From: Anselm (Proslogion [1090], Reply 3) | |
| A reaction: Guanilo was a very naughty monk, who must have had sleepless nights over this. One could further ask whether an island might have necessary existence. Anselm needs 'a being' to be a special category of thing. |
| 21247 | Nonexistence is impossible for the greatest thinkable thing, which has no beginning or end [Anselm] |
| Full Idea: If anyone does think of something a greater than which cannot be thought, then he thinks of something which cannot be thought of as nonexistent, ...for then it could be thought of as having a beginning and an end. And this is impossible. | |
| From: Anselm (Proslogion [1090], Reply 3) | |
| A reaction: A nice idea, but it has a flip side. If the atheist denies God's existence, then it follows that (because no beginning is possible for such a being) the existence of God is impossible. Anselm adds that contingent existents have parts (unlike God). |
| 1420 | Anselm's first proof fails because existence isn't a real predicate, so it can't be a perfection [Malcolm on Anselm] |
| Full Idea: Anselm's first proof fails, because he treats existence as being a perfection, which it isn't, because that would make it a real predicate. | |
| From: comment on Anselm (Proslogion [1090], Ch 2) by Norman Malcolm - Anselm's Argument Sect I | |
| A reaction: Not everyone accepts Kant's claim that existence cannot be a predicate. They all seem to know what a perfection is. Can the Mona Lisa (an object) not be a perfection? Must it be broken down into perfect predicates? |