63 ideas
| 14273 | Conditional Proof is only valid if we accept the truth-functional reading of 'if' [Edgington] |
| Full Idea: Conditional Proof seems sound: 'From X and Y, it follows that Z. So from X it follows that if Y,Z'. Yet for no reading of 'if' which is stronger that the truth-functional reading is CP valid, at least if we accept ¬(A&¬B);A; therefore B. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 2.2) | |
| A reaction: See the section of ideas on Conditionals (filed under 'Modality') for a fuller picture of this issue. Edgington offers it as one of the main arguments in favour of the truth-functional reading of 'if' (though she rejects that reading). |
| 10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
| Full Idea: The logic of ZF Set Theory is classical first-order predicate logic with identity. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.121) | |
| A reaction: This logic seems to be unable to deal with very large cardinals, precisely those that are implied by set theory, so there is some sort of major problem hovering here. Boolos is fairly neutral. |
| 10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |
| Full Idea: Maybe the axioms of extensionality and the pair set axiom 'force themselves on us' (Gödel's phrase), but I am not convinced about the axioms of infinity, union, power or replacement. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.130) | |
| A reaction: Boolos is perfectly happy with basic set theory, but rather dubious when very large cardinals come into the picture. |
| 18192 | Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy] |
| Full Idea: For Boolos, the Replacement Axioms go beyond the iterative conception. | |
| From: report of George Boolos (The iterative conception of Set [1971]) by Penelope Maddy - Naturalism in Mathematics I.3 |
| 7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos] |
| Full Idea: We should abandon the idea that the use of plural forms commits us to the existence of sets/classes… Entities are not to be multiplied beyond necessity. There are not two sorts of things in the world, individuals and collections. | |
| From: George Boolos (To be is to be the value of a variable.. [1984]), quoted by Henry Laycock - Object | |
| A reaction: The problem of quantifying over sets is notoriously difficult. Try http://plato.stanford.edu/entries/object/index.html. |
| 10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
| Full Idea: The naïve view of set theory (that any zero or more things form a set) is natural, but inconsistent: the things that do not belong to themselves are some things that do not form a set. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.127) | |
| A reaction: As clear a summary of Russell's Paradox as you could ever hope for. |
| 10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
| Full Idea: According to the iterative conception, every set is formed at some stage. There is a relation among stages, 'earlier than', which is transitive. A set is formed at a stage if and only if its members are all formed before that stage. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.126) | |
| A reaction: He gives examples of the early stages, and says the conception is supposed to 'justify' Zermelo set theory. It is also supposed to make the axioms 'natural', rather than just being selected for convenience. And it is consistent. |
| 13547 | Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) [Boolos, by Potter] |
| Full Idea: Weak Limitation of Size: If there are no more Fs than Gs and the Gs form a collection, then Fs form a collection. Strong Limitation of Size: A property F fails to be collectivising iff there are as many Fs as there are objects. | |
| From: report of George Boolos (Iteration Again [1989]) by Michael Potter - Set Theory and Its Philosophy 13.5 |
| 10699 | Does a bowl of Cheerios contain all its sets and subsets? [Boolos] |
| Full Idea: Is there, in addition to the 200 Cheerios in a bowl, also a set of them all? And what about the vast number of subsets of Cheerios? It is haywire to think that when you have some Cheerios you are eating a set. What you are doing is: eating the Cheerios. | |
| From: George Boolos (To be is to be the value of a variable.. [1984], p.72) | |
| A reaction: In my case Boolos is preaching to the converted. I am particularly bewildered by someone (i.e. Quine) who believes that innumerable sets exist while 'having a taste for desert landscapes' in their ontology. |
| 14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
| Full Idea: Boolos's conception of plural logic is as a reinterpretation of second-order logic. | |
| From: report of George Boolos (On Second-Order Logic [1975]) by Oliver,A/Smiley,T - What are Sets and What are they For? n5 | |
| A reaction: Oliver and Smiley don't accept this view, and champion plural reference differently (as, I think, some kind of metalinguistic device?). |
| 10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
| Full Idea: Boolos has proposed an alternative understanding of monadic, second-order logic, in terms of plural quantifiers, which many philosophers have found attractive. | |
| From: report of George Boolos (To be is to be the value of a variable.. [1984]) by Stewart Shapiro - Philosophy of Mathematics 3.5 |
| 10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
| Full Idea: The metatheory of second-order logic is hopelessly set-theoretic, and the notion of second-order validity possesses many if not all of the epistemic debilities of the notion of set-theoretic truth. | |
| From: George Boolos (On Second-Order Logic [1975], p.45) | |
| A reaction: Epistemic problems arise when a logic is incomplete, because some of the so-called truths cannot be proved, and hence may be unreachable. This idea indicates Boolos's motivation for developing a theory of plural quantification. |
| 10736 | Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo] |
| Full Idea: In an indisputable technical result, Boolos showed how plural quantifiers can be used to interpret monadic second-order logic. | |
| From: report of George Boolos (To be is to be the value of a variable.. [1984], Intro) by Øystein Linnebo - Plural Quantification Exposed Intro |
| 10780 | Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo] |
| Full Idea: Boolos discovered that any sentence of monadic second-order logic can be translated into plural first-order logic. | |
| From: report of George Boolos (To be is to be the value of a variable.. [1984], §1) by Øystein Linnebo - Plural Quantification Exposed p.74 |
| 10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
| Full Idea: One may be of the opinion that no sentence ought to be considered as a truth of logic if, no matter how it is interpreted, it asserts that there are sets of certain sorts. | |
| From: George Boolos (On Second-Order Logic [1975], p.44) | |
| A reaction: My intuition is that in no way should any proper logic assert the existence of anything at all. Presumably interpretations can assert the existence of numbers or sets, but we should be able to identify something which is 'pure' logic. Natural deduction? |
| 10697 | Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos] |
| Full Idea: Indispensable to cross-reference, lacking distinctive content, and pervading thought and discourse, 'identity' is without question a logical concept. Adding it to predicate calculus significantly increases the number and variety of inferences possible. | |
| From: George Boolos (To be is to be the value of a variable.. [1984], p.54) | |
| A reaction: It is not at all clear to me that identity is a logical concept. Is 'existence' a logical concept? It seems to fit all of Boolos's criteria? I say that all he really means is that it is basic to thought, but I'm not sure it drives the reasoning process. |
| 10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
| Full Idea: One may say that '∀x x=x' means 'everything is identical to itself', but one must realise that one's answer has a determinate sense only if the reference (range) of 'everything' is fixed. | |
| From: George Boolos (On Second-Order Logic [1975], p.46) | |
| A reaction: This is the problem now discussed in the recent book 'Absolute Generality', of whether one can quantify without specifying a fixed or limited domain. |
| 13671 | Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro] |
| Full Idea: Boolos proposes that second-order quantifiers be regarded as 'plural quantifiers' are in ordinary language, and has developed a semantics along those lines. In this way they introduce no new ontology. | |
| From: report of George Boolos (To be is to be the value of a variable.. [1984]) by Stewart Shapiro - Foundations without Foundationalism 7 n32 | |
| A reaction: This presumably has to treat simple predicates and relations as simply groups of objects, rather than having platonic existence, or something. |
| 10267 | We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro] |
| Full Idea: Standard second-order existential quantifiers pick out a class or a property, but Boolos suggests that they be understood as a plural quantifier, like 'there are objects' or 'there are people'. | |
| From: report of George Boolos (To be is to be the value of a variable.. [1984]) by Stewart Shapiro - Philosophy of Mathematics 7.4 | |
| A reaction: This idea has potential application to mathematics, and Lewis (1991, 1993) 'invokes it to develop an eliminative structuralism' (Shapiro). |
| 10698 | Plural forms have no more ontological commitment than to first-order objects [Boolos] |
| Full Idea: Abandon the idea that use of plural forms must always be understood to commit one to the existence of sets of those things to which the corresponding singular forms apply. | |
| From: George Boolos (To be is to be the value of a variable.. [1984], p.66) | |
| A reaction: It seems to be an open question whether plural quantification is first- or second-order, but it looks as if it is a rewriting of the first-order. |
| 7806 | Boolos invented plural quantification [Boolos, by Benardete,JA] |
| Full Idea: Boolos virtually patented the new device of plural quantification. | |
| From: report of George Boolos (To be is to be the value of a variable.. [1984]) by José A. Benardete - Logic and Ontology | |
| A reaction: This would be 'there are some things such that...' |
| 10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
| Full Idea: A weak completeness theorem shows that a sentence is provable whenever it is valid; a strong theorem, that a sentence is provable from a set of sentences whenever it is a logical consequence of the set. | |
| From: George Boolos (On Second-Order Logic [1975], p.52) | |
| A reaction: So the weak version says |- φ → |= φ, and the strong versions says Γ |- φ → Γ |= φ. Presumably it is stronger if it can specify the source of the inference. |
| 13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
| Full Idea: Boolos asks why on earth compactness, whatever its virtues, should be definitive of logic itself. | |
| From: report of George Boolos (On Second-Order Logic [1975]) by Ian Hacking - What is Logic? §13 |
| 10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
| Full Idea: The existence of infinitely many natural numbers seems to me no more troubling than that of infinitely many computer programs or sentences of English. There is, for example, no longest sentence, since any number of 'very's can be inserted. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.129) | |
| A reaction: If you really resisted an infinity of natural numbers, presumably you would also resist an actual infinity of 'very's. The fact that it is unclear what could ever stop a process doesn't guarantee that the process is actually endless. |
| 10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
| Full Idea: To the best of my knowledge nothing in mathematics or science requires the existence of very high orders of infinity. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.122) | |
| A reaction: He is referring to particular high orders of infinity implied by set theory. Personally I want to wield Ockham's Razor. Is being implied by set theory a sufficient reason to accept such outrageous entities into our ontology? |
| 10833 | Many concepts can only be expressed by second-order logic [Boolos] |
| Full Idea: The notions of infinity and countability can be characterized by second-order sentences, though not by first-order sentences (as compactness and Skolem-Löwenheim theorems show), .. as well as well-ordering, progression, ancestral and identity. | |
| From: George Boolos (On Second-Order Logic [1975], p.48) |
| 10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
| Full Idea: It is no surprise that we should be able to reason mathematically about many of the things we experience, for they are already 'abstract'. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.129) | |
| A reaction: He has just given a list of exemplary abstract objects (Idea 10489), but I think there is a more interesting idea here - that our experience of actual physical objects is to some extent abstract, as soon as it is conceptualised. |
| 16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
| Full Idea: It seems unavoidable that the facts about logically necessary relations between levels of facts are themselves logically distinct further facts, irreducible to the microphysical facts. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], C) | |
| A reaction: I'm beginning to think that rejecting every theory of reality that is proposed by carefully exposing some infinite regress hidden in it is a rather lazy way to do philosophy. Almost as bad as rejecting anything if it can't be defined. |
| 16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
| Full Idea: Logical supervenience, restricted to individuals, seems to imply strong reduction. It is said that where the B-facts logically supervene on the A-facts, the B-facts simply re-describe what the A-facts describe, and the B-facts come along 'for free'. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], C) | |
| A reaction: This seems to be taking 'logically' to mean 'analytically'. Presumably an entailment is logically supervenient on its premisses, and may therefore be very revealing, even if some people think such things are analytic. |
| 16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
| Full Idea: The root intuition behind nonreductive materialism is that reality is composed of ontologically distinct layers or levels. …The upper levels depend on the physical without reducing to it. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], B) | |
| A reaction: A nice clear statement of a view which I take to be false. This relationship is the sort of thing that drives people fishing for an account of it to use the word 'supervenience', which just says two things seem to hang out together. Fluffy materialism. |
| 16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
| Full Idea: Jessica Wilson (1999) says what makes physicalist accounts different from emergentism etc. is that each individual causal power associated with a supervenient property is numerically identical with a causal power associated with its base property. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], n 11) | |
| A reaction: Hence the key thought in so-called (serious, rather than self-evident) 'emergentism' is so-called 'downward causation', which I take to be an idle daydream. |
| 10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
| Full Idea: Ontological commitment is carried by first-order quantifiers; a second-order quantifier needn't be taken to be a first-order quantifier in disguise, having special items, collections, as its range. They are two ways of referring to the same things. | |
| From: George Boolos (To be is to be the value of a variable.. [1984], p.72) | |
| A reaction: If second-order quantifiers are just a way of referring, then we can see first-order quantifiers that way too, so we could deny 'objects'. |
| 10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
| Full Idea: It's a kind of lunacy to think that sound scientific philosophy demands that we think that we see ink-tracks but not words, i.e. word-types. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.128) | |
| A reaction: This seems to link him with Armstrong's mockery of 'ostrich nominalism'. There seems to be some ambiguity with the word 'see' in this disagreement. When we look at very ancient scratches on stones, why don't we always 'see' if it is words? |
| 10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
| Full Idea: I am rather a fan of abstract objects, and confident of their existence. Smaller numbers, sets and functions don't offend my sense of reality. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.128) | |
| A reaction: The great Boolos is rather hard to disagree with, but I disagree. Logicians love abstract objects, indeed they would almost be out of a job without them. It seems to me they smuggle them into our ontology by redefining either 'object' or 'exists'. |
| 10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
| Full Idea: We twentieth century city dwellers deal with abstract objects all the time, such as bank balances, radio programs, software, newspaper articles, poems, mistakes, triangles. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.129) | |
| A reaction: I find this claim to be totally question-begging, and typical of a logician. The word 'object' gets horribly stretched in these discussions. We can create concepts which have all the logical properties of objects. Maybe they just 'subsist'? |
| 12205 | There are two families of modal notions, metaphysical and epistemic, of equal strength [Edgington] |
| Full Idea: In my view, there are two independent families of modal notions, metaphysical and epistemic, neither stronger than the other. | |
| From: Dorothy Edgington (Two Kinds of Possibility [2004], Abs) | |
| A reaction: My immediate reaction is that epistemic necessity is not necessity at all. 'For all I know' 2 plus 2 might really be 95, and squares may also be circular. |
| 12207 | Metaphysical possibility is discovered empirically, and is contrained by nature [Edgington] |
| Full Idea: Metaphysical necessity derives from distinguishing things which can happen and things which can't, in virtue of their nature, which we discover empirically: the metaphysically possible, I claim, is constrained by the laws of nature. | |
| From: Dorothy Edgington (Two Kinds of Possibility [2004], §I) | |
| A reaction: She claims that Kripke is sympathetic to this. Personally I like the idea that natural necessity is metaphysically necessary (see 'Scientific Essentialism'), but the other way round comes as a bit of a surprise. I will think about it. |
| 12206 | Broadly logical necessity (i.e. not necessarily formal logical necessity) is an epistemic notion [Edgington] |
| Full Idea: So-called broadly logical necessity (by which I mean, not necessarily formal logical necessity) is an epistemic notion. | |
| From: Dorothy Edgington (Two Kinds of Possibility [2004], §I) | |
| A reaction: This is controversial, and is criticised by McFetridge and Rumfitt. Fine argues that 'narrow' (formal) logical necessity is metaphysical. Between them they have got rid of logical necessity completely. |
| 12185 | Logical necessity is epistemic necessity, which is the old notion of a priori [Edgington, by McFetridge] |
| Full Idea: Edgington's position is that logical necessity is an epistemic notion: epistemic necessity which, she claims, is the old notion of the a priori. Like Kripke, she thinks this is two-way independent of metaphysical necessity. | |
| From: report of Dorothy Edgington (Epistemic and Metaphysical Possibility [1985]) by Ian McFetridge - Logical Necessity: Some Issues §1 | |
| A reaction: [her paper was unpublished] She hence thinks an argument can be logically valid, while metaphysically its conclusion may not follow. Dubious, though I think I favour the view that logical necessity is underwritten by metaphysical necessity. |
| 12208 | An argument is only valid if it is epistemically (a priori) necessary [Edgington] |
| Full Idea: Validity is governed by epistemic necessity, i.e. an argument is valid if and only if there is an a priori route from premises to conclusion. | |
| From: Dorothy Edgington (Two Kinds of Possibility [2004], §V) | |
| A reaction: Controversial, and criticised by McFetridge and Rumfitt. I don't think I agree with her. I don't see validity as depending on dim little human beings. |
| 13857 | Truth-functional possibilities include the irrelevant, which is a mistake [Edgington] |
| Full Idea: How likely is a fair die landing on an even number to land six? My approach is, assume an even number, so three possibilities, one a six, so 'one third'; the truth-functional approach is it's true if it is not-even or six, so 'two-thirds'. | |
| From: Dorothy Edgington (Do Conditionals Have Truth Conditions? [1986], 3) | |
| A reaction: The point is that in the truth-functional approach, if the die lands not-even, then the conditional comes out as true, when she says it should be irrelevant. She seems to be right about this. |
| 14281 | A thing works like formal probability if all the options sum to 100% [Edgington] |
| Full Idea: One's degrees of belief in the members of an idealised partition should sum to 100%. That is all there is to the claim that degrees of belief should have the structure of probabilities. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 3.1) |
| 14284 | Conclusion improbability can't exceed summed premise improbability in valid arguments [Edgington] |
| Full Idea: If (and only if) an argument is valid, then in no probability distribution does the improbability of its conclusion exceed the sum of the improbabilities of its premises. We can call this the Probability Preservation Principle. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 3.2) | |
| A reaction: [Ernest Adams is credited with this] This means that classical logic is in some way probability-preserving as well as truth-preserving. |
| 13768 | Validity can preserve certainty in mathematics, but conditionals about contingents are another matter [Edgington] |
| Full Idea: If your interest in logic is confined to applications to mathematics or other a priori matters, it is fine for validity to preserve certainty, ..but if you use conditionals when arguing about contingent matters, then great caution will be required. | |
| From: Dorothy Edgington (Conditionals [2001], 17.2.1) |
| 13853 | It is a mistake to think that conditionals are statements about how the world is [Edgington] |
| Full Idea: The mistake philosophers have made, in trying to understand the conditional, is to assume that its function is to make a statement about how the world is (or how other possible worlds are related to it), true or false, as the case may be. | |
| From: Dorothy Edgington (Do Conditionals Have Truth Conditions? [1986], 1) | |
| A reaction: 'If pigs could fly we would never catch them' may not be about the world, but 'if you press this switch the light comes on' seems to be. Actually even the first one is about the world. I've an inkling that Edgington is wrong about this. Powers! |
| 14270 | Simple indicatives about past, present or future do seem to form a single semantic kind [Edgington] |
| Full Idea: Straightforward statements about the past, present or future, to which a conditional clause is attached - the traditional class of indicative conditionals - do (in my view) constitute a single semantic kind. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 1) | |
| A reaction: This contrasts with Idea 14269, where the future indicatives are group instead with the counterfactuals. |
| 14269 | Maybe forward-looking indicatives are best classed with the subjunctives [Edgington] |
| Full Idea: According to some theorists, the forward-looking 'indicatives' (those with a 'will' in the main clause) belong with the 'subjunctives' (those with a 'would' in the main clause), and not with the other 'indicatives'. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 1) | |
| A reaction: [She cites Gibbard, Dudman and 1988 Bennett; Jackson defends the indicative/subjunctive division, and recent Bennett defends it too] It is plausible to say that 'If you will do x' is counterfactual, since it hasn't actually happened. |
| 13770 | There are many different conditional mental states, and different conditional speech acts [Edgington] |
| Full Idea: As well as conditional beliefs, there are conditional desires, hopes, fears etc. As well as conditional statements, there are conditional commands, questions, offers, promises, bets etc. | |
| From: Dorothy Edgington (Conditionals [2001], 17.3.4) |
| 14275 | Truth-function problems don't show up in mathematics [Edgington] |
| Full Idea: The main defects of the truth-functional account of conditionals don't show up in mathematics. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 2.3) | |
| A reaction: These problems are the paradoxes associated with the material conditional ⊃. Too often mathematical logic has been the tail that wagged the dog in modern philosophy. |
| 13764 | Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? [Edgington] |
| Full Idea: Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? Are they non-truth-functional, like 'because' or 'before'? Do the values of A and B, in some cases, leave open the value of 'If A,B'? | |
| From: Dorothy Edgington (Conditionals [2001], 17.1) | |
| A reaction: I would say they are not truth-functional, because the 'if' asserts some further dependency relation that goes beyond the truth or falsity of A and B. Logical ifs, causal ifs, psychological ifs... The material conditional ⊃ is truth-functional. |
| 13765 | 'If A,B' must entail ¬(A & ¬B); otherwise we could have A true, B false, and If A,B true, invalidating modus ponens [Edgington] |
| Full Idea: If it were possible to have A true, B false, and If A,B true, it would be unsafe to infer B from A and If A,B: modus ponens would thus be invalid. Hence 'If A,B' must entail ¬(A & ¬B). | |
| From: Dorothy Edgington (Conditionals [2001], 17.1) | |
| A reaction: This is a firm defence of part of the truth-functional view of conditionals, and seems unassailable. The other parts of the truth table are open to question, though, if A is false, or they are both true. |
| 14274 | Inferring conditionals from disjunctions or negated conjunctions gives support to truth-functionalism [Edgington] |
| Full Idea: If either A or B is true, then you are intuitively justified in believe that If ¬A, B. If you know that ¬(A&B), then you may justifiably infer that if A, ¬B. The truth-functionalist gets both of these cases (disjunction and negated conjunction) correct. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 2.1) | |
| A reaction: [compressed version] This summarises two of Edgington's three main arguments in favour of the truth-functional account of conditions (along with the existence of Conditional Proof). It is elementary classical logic which supports truth-functionalism. |
| 14276 | The truth-functional view makes conditionals with unlikely antecedents likely to be true [Edgington] |
| Full Idea: The truth-functional view of conditionals has the unhappy consequence that all conditionals with unlikely antecedents are likely to be true. To think it likely that ¬A is to think it likely that a sufficient condition for the truth of A⊃B obtains. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 2.3) | |
| A reaction: This is Edgington's main reason for rejecting the truth-functional account of conditionals. She says it removes our power to discriminate between believable and unbelievable conditionals, which is basic to practical reasoning. |
| 14290 | Doctor:'If patient still alive, change dressing'; Nurse:'Either dead patient, or change dressing'; kills patient! [Edgington] |
| Full Idea: The doctor says "If the patient is still alive in the morning, change the dressing". As a truth-functional command this says "Make it that either the patient is dead in the morning, or change the dressing", so the nurse kills the patient. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 5) | |
| A reaction: Isn't philosophy wonderful? |
| 13855 | A conditional does not have truth conditions [Edgington] |
| Full Idea: A conditional does not have truth conditions. | |
| From: Dorothy Edgington (Do Conditionals Have Truth Conditions? [1986], 1) |
| 13859 | X believes 'if A, B' to the extent that A & B is more likely than A & ¬B [Edgington] |
| Full Idea: X believes that if A, B, to the extent that he judges that A & B is nearly as likely as A, or (roughly equivalently) to the extent that he judges A & B to be more likely than A & ¬B. | |
| From: Dorothy Edgington (Do Conditionals Have Truth Conditions? [1986], 5) | |
| A reaction: This is a formal statement of her theory of conditionals. |
| 14271 | Non-truth-functionalist say 'If A,B' is false if A is T and B is F, but deny that is always true for TT,FT and FF [Edgington] |
| Full Idea: Non-truth-functional accounts agree that 'If A,B' is false when A is true and B is false; and that it is sometimes true for the other three combinations of truth-values; but they deny that the conditional is always true in each of these three cases. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 2.1) | |
| A reaction: Truth-functional connectives like 'and' and 'or' don't add any truth-conditions to the values of the propositions, but 'If...then' seems to assert a relationship that goes beyond its component propositions, so non-truth-functionalists are right. |
| 14272 | I say "If you touch that wire you'll get a shock"; you don't touch it. How can that make the conditional true? [Edgington] |
| Full Idea: Non-truth-functionalists agree that when A is false, 'If A,B' may be either true or false. I say "If you touch that wire, you will get an electric shock". You don't touch it. Was my remark true or false? They say it depends on the wire etc. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 2.1) | |
| A reaction: This example seems to me to be a pretty conclusive refutation of the truth-functional view. How can the conditional be implied simply by my failure to touch the wire (which is what benighted truth-functionalists seem to believe)? |
| 13854 | Conditionals express what would be the outcome, given some supposition [Edgington] |
| Full Idea: It is often necessary to suppose (or assume) that some epistemic possibility is true, and to consider what else would be the case, or would be likely to be the case, given this supposition. The conditional expresses the outcome of such thought processes. | |
| From: Dorothy Edgington (Do Conditionals Have Truth Conditions? [1986], 1) | |
| A reaction: This is the basic Edgington view. It seems to involve an active thought process, and imagination, rather than being the static semantic relations offered by possible worlds analyses. True conditionals state relationships in the world. |
| 14282 | On the supposition view, believe if A,B to the extent that A&B is nearly as likely as A [Edgington] |
| Full Idea: Accepting Ramsey's suggestion that 'if' and 'on the supposition that' come to the same thing, we get an equation which says ...you believe if A,B to the extent that you think that A&B is nearly as likely as A. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 3.1) |
| 14278 | Truth-functionalists support some conditionals which we assert, but should not actually believe [Edgington] |
| Full Idea: There are compounds of conditionals which we confidently assert and accept which, by the lights of the truth-functionalist, we do not have reason to believe true, such as 'If it broke if it was dropped, it was fragile', when it is NOT dropped. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 2.5) | |
| A reaction: [The example is from Gibbard 1981] The fact that it wasn't dropped only negates the nested antecedent, not the whole antecedent. I suppose it also wasn't broken, and both negations seem to be required. |
| 14287 | Does 'If A,B' say something different in each context, because of the possibiites there? [Edgington] |
| Full Idea: A pragmatic constraint might say that as different possibilities are live in different conversational settings, a different proposition may be expressed by 'If A,B' in different conversational settings. | |
| From: Dorothy Edgington (Conditionals (Stanf) [2006], 4.1) | |
| A reaction: Edgington says that it is only the truth of the proposition, not its content, which changes with context. I'm not so sure. 'If Hitler finds out, we are in trouble' says different things in 1914 and 1944. |
| 8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
| Full Idea: Hume's Principle has a structure Boolos calls an 'abstraction principle'. Within the scope of two universal quantifiers, a biconditional connects an identity between two things and an equivalence relation. It says we don't care about other differences. | |
| From: George Boolos (Is Hume's Principle analytic? [1997]), quoted by Michèle Friend - Introducing the Philosophy of Mathematics 3.7 | |
| A reaction: This seems to be the traditional principle of abstraction by ignoring some properties, but dressed up in the clothes of formal logic. Frege tries to eliminate psychology, but Boolos implies that what we 'care about' is relevant. |