25 ideas
| 9331 | How do we determine which of the sentences containing a term comprise its definition? [Horwich] |
| Full Idea: How are we to determine which of the sentences containing a term comprise its definition? | |
| From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §2) | |
| A reaction: Nice question. If I say 'philosophy is the love of wisdom' and 'philosophy bores me', why should one be part of its definition and the other not? What if I stipulated that the second one is part of my definition, and the first one isn't? |
| 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. |
| 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. |
| 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 |
| 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 |
| 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. |
| 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...' |
| 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'. |
| 11984 | Asserting a possible property is to say it would have had the property if that world had been actual [Plantinga] |
| Full Idea: To say than x has a property in a possible world is simply to say that x would have had the property if that world had been actual. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], I) | |
| A reaction: Plantinga tries to defuse all the problems with identity across possible worlds, by hanging on to subjunctive verbs and modal modifiers. The point, though, was to explain these, or at least to try to give their logical form. |
| 11980 | A possible world is a maximal possible state of affairs [Plantinga] |
| Full Idea: A possible world is just a maximal possible state of affairs. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], I) | |
| A reaction: The key point here is that Plantinga includes the word 'possible' in his definition. Possibility defines the worlds, and so worlds cannot be used on their own to define possibility. |
| 11982 | If possible Socrates differs from actual Socrates, the Indiscernibility of Identicals says they are different [Plantinga] |
| Full Idea: If the Socrates of the actual world has snubnosedness but Socrates-in-W does not, this is surely inconsistent with the Indiscernibility of Identicals, a principle than which none sounder can be conceived. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], I) | |
| A reaction: However, we allow Socrates to differ over time while remaining the same Socrates, so some similar approach should apply here. In both cases we need some notion of what is essential to Socrates. But what unites aged 3 with aged 70? |
| 11983 | It doesn't matter that we can't identify the possible Socrates; we can't identify adults from baby photos [Plantinga] |
| Full Idea: We may say it makes no sense to say that Socrates exists at a world, if there is in principle no way of identifying him. ...But this is confused. To suppose Agnew was a precocious baby, we needn't be able to pick him from a gallery of babies. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], I) | |
| A reaction: This seems a good point, and yet we have a space-time line joining adult Agnew with baby Agnew, and no such causal link is available between persons in different possible worlds. What would be the criterion in each case? |
| 11985 | If individuals can only exist in one world, then they can never lack any of their properties [Plantinga] |
| Full Idea: The Theory of Worldbound Individuals contends that no object exists in more than one possible world; this implies the outrageous view that - taking properties in the broadest sense - no object could have lacked any property that it in fact has. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], II) | |
| A reaction: Leibniz is the best known exponent of this 'outrageous view', though Plantinga shows that Lewis may be seen in the same light, since only counterparts are found in possible worlds, not the real thing. The Theory does seem wrong. |
| 11986 | The counterparts of Socrates have self-identity, but only the actual Socrates has identity-with-Socrates [Plantinga] |
| Full Idea: While Socrates has no counterparts that lack self-identity, he does have counterparts that lack identity-with-Socrates. He alone has that - the property, that is, of being identical with the object that in fact instantiates Socrateity. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], II) | |
| A reaction: I am never persuaded by arguments which rest on such dubious pseudo-properties. Whether or not a counterpart of Socrates has any sort of identity with Socrates cannot be prejudged, as it would beg the question. |
| 11987 | Counterpart Theory absurdly says I would be someone else if things went differently [Plantinga] |
| Full Idea: It makes no sense to say I could have been someone else, yet Counterpart Theory implies not merely that I could have been distinct from myself, but that I would have been distinct from myself had things gone differently in even the most miniscule detail. | |
| From: Alvin Plantinga (Transworld Identity or worldbound Individuals? [1973], II) | |
| A reaction: A counterpart doesn't appear to be 'me being distinct from myself'. We have to combine counterparts over possible worlds with perdurance over time. I am a 'worm' of time-slices. Anything not in that worm is not strictly me. |
| 9333 | A priori belief is not necessarily a priori justification, or a priori knowledge [Horwich] |
| Full Idea: It is one thing to believe something a priori and another for this belief to be epistemically justified. The latter is required for a priori knowledge. | |
| From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §8) | |
| A reaction: Personally I would agree with this, because I don't think anything should count as knowledge if it doesn't have supporting reasons, but fans of a priori knowledge presumably think that certain basic facts are just known. They are a priori justified. |
| 9342 | Understanding needs a priori commitment [Horwich] |
| Full Idea: Understanding is itself based on a priori commitment. | |
| From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §12) | |
| A reaction: This sounds plausible, but needs more justification than Horwich offers. This is the sort of New Rationalist idea I associate with Bonjour. The crucial feature of the New lot is, I take it, their fallibilism. All understanding is provisional. |
| 9332 | Meaning is generated by a priori commitment to truth, not the other way around [Horwich] |
| Full Idea: Our a priori commitment to certain sentences is not really explained by our knowledge of a word's meaning. It is the other way around. We accept a priori that the sentences are true, and thereby provide it with meaning. | |
| From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §8) | |
| A reaction: This sounds like a lovely trump card, but how on earth do you decide that a sentence is true if you don't know what it means? Personally I would take it that we are committed to the truth of a proposition, before we have a sentence for it. |
| 9341 | Meanings and concepts cannot give a priori knowledge, because they may be unacceptable [Horwich] |
| Full Idea: A priori knowledge of logic and mathematics cannot derive from meanings or concepts, because someone may possess such concepts, and yet disagree with us about them. | |
| From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §12) | |
| A reaction: A good argument. The thing to focus on is not whether such ideas are a priori, but whether they are knowledge. I think we should employ the word 'intuition' for a priori candidates for knowledge, and demand further justification for actual knowledge. |
| 9334 | If we stipulate the meaning of 'number' to make Hume's Principle true, we first need Hume's Principle [Horwich] |
| Full Idea: If we stipulate the meaning of 'the number of x's' so that it makes Hume's Principle true, we must accept Hume's Principle. But a precondition for this stipulation is that Hume's Principle be accepted a priori. | |
| From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §9) | |
| A reaction: Yet another modern Quinean argument that all attempts at defining things are circular. I am beginning to think that the only a priori knowledge we have is of when a group of ideas is coherent. Calling it 'intuition' might be more accurate. |
| 9339 | A priori knowledge (e.g. classical logic) may derive from the innate structure of our minds [Horwich] |
| Full Idea: One potential source of a priori knowledge is the innate structure of our minds. We might, for example, have an a priori commitment to classical logic. | |
| From: Paul Horwich (Stipulation, Meaning and Apriority [2000], §11) | |
| A reaction: Horwich points out that to be knowledge it must also say that we ought to believe it. I'm wondering whether if we divided the whole territory of the a priori up into intuitions and then coherent justifications, the whole problem would go away. |