22 ideas
| 5784 | In its primary and formal sense, 'true' applies to propositions, not beliefs [Russell] |
| Full Idea: We call a belief true when it is belief in a true proposition, ..but it is to propositions that the primary formal meanings of 'truth' and 'falsehood' apply. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], §IV) | |
| A reaction: I think this is wrong. A proposition such as 'it is raining' would need a date-and-time stamp to be a candidate for truth, and an indexical statement such as 'I am ill' would need to be asserted by a person. Of course, books can contain unread truths. |
| 5777 | The truth or falsehood of a belief depends upon a fact to which the belief 'refers' [Russell] |
| Full Idea: I take it as evident that the truth or falsehood of a belief depends upon a fact to which the belief 'refers'. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], p.285) | |
| A reaction: A nice bold commitment to a controversial idea. The traditional objection is to ask how you are going to formulate the 'facts' except in terms of more beliefs, so you ending up comparing beliefs. Facts are a metaphysical commitment, not an acquaintance. |
| 5783 | Propositions of existence, generalities, disjunctions and hypotheticals make correspondence tricky [Russell] |
| Full Idea: The correspondence of proposition and fact grows increasingly complicated as we pass to more complicated types of propositions: existence-propositions, general propositions, disjunctive and hypothetical propositions, and so on. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], §IV) | |
| A reaction: An important point. Truth must not just work for 'it is raining', but also for maths, logic, tautologies, laws etc. This is why so many modern philosophers have retreated to deflationary and minimal accounts of truth, which will cover all cases. |
| 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'. |
| 5780 | The three questions about belief are its contents, its success, and its character [Russell] |
| Full Idea: There are three issues about belief: 1) the content which is believed, 2) the relation of the content to its 'objective' - the fact which makes it true or false, and 3) the element which is belief, as opposed to consideration or doubt or desire. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], §III) | |
| A reaction: The correct answers to the questions (trust me) are that propositions are the contents, the relation aimed at is truth, which is a 'metaphysical ideal' of correspondence to facts, and belief itself is an indefinable feeling. See Hume, Idea 2208. |
| 3158 | Theories of intentionality presuppose rationality, so can't explain it [Dennett] |
| Full Idea: Intentional theory is vacuous as psychology because it presupposes and does not explain rationality or intelligence. | |
| From: Daniel C. Dennett (Brainstorms:Essays on Mind and Psychology [1978], p.15?) | |
| A reaction: Virtually every philosophical theory seems to founder because it presupposes something like the thing it is meant to explain. I agree that 'intentionality' is a slightly airy concept that would probably reduce to something better. |
| 3159 | Beliefs and desires aren't real; they are prediction techniques [Dennett] |
| Full Idea: Intentional systems don't really have beliefs and desires, but one can explain and predict their behaviour by ascribing beliefs and desires to them. This strategy is pragmatic, not right or wrong. | |
| From: Daniel C. Dennett (Brainstorms:Essays on Mind and Psychology [1978], p.7?) | |
| A reaction: If the ascription of beliefs and desires explains behaviour, then that is good grounds for thinking they might be real features of the brain, and even if that is not so, they are real enough as abstractions from brain events, like the 'economic climate'. |
| 5778 | If we object to all data which is 'introspective' we will cease to believe in toothaches [Russell] |
| Full Idea: If privacy is the main objection to introspective data, we shall have to include among such data all sensations; a toothache, for example, is essentially private; a dentist may see the bad condition of your tooth, but does not feel your ache. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], §II) | |
| A reaction: Russell was perhaps the first to see why eliminative behaviourism is a non-starter as a theory of mind. Mental states are clearly a cause of behaviour, so they can't be the same thing. We might 'eliminate' mental states by reducing them, though. |
| 5779 | There are distinct sets of psychological and physical causal laws [Russell] |
| Full Idea: There do seem to be psychological and physical causal laws which are distinct from each other. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], §II) | |
| A reaction: This sounds like the essence of 'property dualism'. Reductive physicalists (like myself) say there is no distinction. Davidson, usually considered a property dualist, claims there are no psycho-physical laws. Russell notes that reduction may be possible. |
| 5781 | Our important beliefs all, if put into words, take the form of propositions [Russell] |
| Full Idea: The important beliefs, even if they are not the only ones, are those which, if rendered into explicit words, take the form of a proposition. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], §III) | |
| A reaction: This assertion is close to the heart of the twentieth century linking of ontology and epistemology to language. It is open to challenges. Why is non-propositional belief unimportant? Do dogs have important beliefs? Can propositions exist non-verbally? |
| 5782 | A proposition expressed in words is a 'word-proposition', and one of images an 'image-proposition' [Russell] |
| Full Idea: I shall distinguish a proposition expressed in words as a 'word-proposition', and one consisting of images as an 'image-proposition'. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], §III) | |
| A reaction: This, I think, is good, though it raises the question of what exactly an 'image' is when it is non-visual, as when a dog believes its owner called. This distinction prevents us from regarding all knowledge and ontology as verbal in form. |
| 5776 | A proposition is what we believe when we believe truly or falsely [Russell] |
| Full Idea: A proposition may be defined as: what we believe when we believe truly or falsely. | |
| From: Bertrand Russell (On Propositions: What they are, and Meaning [1919], p.285) | |
| A reaction: If we define belief as 'commitment to truth', Russell's last six words become redundant. "Propositions are the contents of beliefs", it being beliefs which are candidates for truth, not propositions. (Russell agrees, on p.308!) |