18 ideas
| 9470 | Modal logic is not an extensional language [Parsons,C] |
| Full Idea: Modal logic is not an extensional language. | |
| From: Charles Parsons (A Plea for Substitutional Quantification [1971], p.159 n8) | |
| A reaction: [I record this for investigation. Possible worlds seem to contain objects] |
| 13418 | The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C] |
| Full Idea: The difficulties historically attributed to the axiom of choice are probably better ascribed to the law of excluded middle. | |
| From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2) | |
| A reaction: The law of excluded middle was a target for the intuitionists, so presumably the debate went off in that direction. |
| 9469 | Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C] |
| Full Idea: I argue (against Quine) that the existential quantifier substitutionally interpreted has a genuine claim to express a concept of existence, which may give the best account of linguistic abstract entities such as propositions, attributes, and classes. | |
| From: Charles Parsons (A Plea for Substitutional Quantification [1971], p.156) | |
| A reaction: Intuitively I have my doubts about this, since the whole thing sounds like a verbal and conventional game, rather than anything with a proper ontology. Ruth Marcus and Quine disagree over this one. |
| 9468 | On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C] |
| Full Idea: For the substitutional interpretation of quantifiers, a sentence of the form '(∃x) Fx' is true iff there is some closed term 't' of the language such that 'Ft' is true. For the objectual interpretation some object x must exist such that Fx is true. | |
| From: Charles Parsons (A Plea for Substitutional Quantification [1971], p.156) | |
| A reaction: How could you decide if it was true for 't' if you didn't know what object 't' referred to? |
| 17447 | Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck] |
| Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal. | |
| From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3 | |
| A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'. |
| 18201 | General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C] |
| Full Idea: The existence of very general principles in mathematics are universally regarded as obvious, where on an empiricist view one would expect them to be bold hypotheses, about which a prudent scientist would maintain reserve. | |
| From: Charles Parsons (Mathematical Intuition [1980], p.152), quoted by Penelope Maddy - Naturalism in Mathematics | |
| A reaction: This is mainly aimed at Quine's and Putnam's indispensability (to science) argument about mathematics. |
| 13419 | If functions are transfinite objects, finitists can have no conception of them [Parsons,C] |
| Full Idea: The finitist may have no conception of function, because functions are transfinite objects. | |
| From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §4) | |
| A reaction: He is offering a view of Tait's. Above my pay scale, but it sounds like a powerful objection to the finitist view. Maybe there is a finitist account of functions that could be given? |
| 13417 | If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C] |
| Full Idea: If experience shows that some aspect of the physical world fails to instantiate a certain mathematical structure, one will modify the theory by sustituting a different structure, while the original structure doesn't lose its status as part of mathematics. | |
| From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2) | |
| A reaction: This seems to be a beautifully simple and powerful objection to the Quinean idea that mathematics somehow only gets its authority from physics. It looked like a daft view to begin with, of course. |
| 19558 | Our own intuitions about whether we know tend to vacillate [Cohen,S] |
| Full Idea: One robust feature of our intuitions about whether we know things is that they tend to vacillate. | |
| From: Stewart Cohen (Contextualism Defended (and reply) [2005], 1) | |
| A reaction: This strikes me as important. If we were tacit invariantists (Idea 19557) we should be able to ask ourselves whether we 'really and truly' know various things, but we can't decide. I know lots about Nietzsche in a pub, and very little in a university. |
| 19561 | We shouldn't jump too quickly to a contextualist account of claims to know [Cohen,S] |
| Full Idea: Maybe contextualists are too quick to appeal to our conflicting intuitions regarding knowledge. | |
| From: Stewart Cohen (Contextualism Defended (and reply) [2005], 1) | |
| A reaction: An important point (from Earl Conee). I thoroughly approve of contextualism, but the whole status of whether a witness or a teacher knows what they are talking about is in danger of collapsing into relativism. This is what peer review is all about. |
| 19563 | The context sensitivity of knowledge derives from its justification [Cohen,S] |
| Full Idea: On my own view, the context sensivity of knowledge is inherited from one of its components, i.e. justification. | |
| From: Stewart Cohen (Contextualism Defended (and reply) [2005], 1) | |
| A reaction: That sounds right, and it reinforces the idea that 'justification' is a more important epistemological concept than 'knowledge'. 'Am I justified in believing p?' Answer: 'it depends how well you have researched it'. |
| 19560 | Contextualism is good because it allows knowledge, but bad because 'knowing' is less valued [Cohen,S] |
| Full Idea: Contextualism is a 'good news, bad news' theory. The good news is that we have lots of knowledge and many surfaces are 'flat'; the bad news is that knowledge and flatness are not all they were cracked up to be. | |
| From: Stewart Cohen (Contextualism Defended (and reply) [2005], 3) | |
| A reaction: That is exactly my position. I lost all interest in whether someone precisely 'knows' or 'does not know' something a long time ago (even in scientific or forensic contexts). In the case of flatness the case is even more obvious. |
| 12893 | Contextualism says sceptical arguments are true, relative to their strict context [Cohen,S] |
| Full Idea: Contextualism explains the appeal of sceptical arguments by allowing that the claims of the sceptic are true, relative to the very strict context in which they are made. | |
| From: Stewart Cohen (Contextualism Defended [2005], p.57) | |
| A reaction: This strikes me a right. I've always thought that global scepticism must be conceded if we are being very strict indeed about justification, but also that it is ridiculous to be that strict. So the epistemological question is 'How strict should we be?' |
| 12896 | Knowledge is context-sensitive, because justification is [Cohen,S] |
| Full Idea: The context-sensitivity of knowledge is inherited from one of its components, i.e. justification. | |
| From: Stewart Cohen (Contextualism Defended [2005], p.68) | |
| A reaction: I think this is exactly right - that there is nothing relative or contextual about what is actually true, or what someone believes, but knowleddge is wholly relative because it rests on shifting standards of justification. |
| 12894 | There aren't invariant high standards for knowledge, because even those can be raised [Cohen,S] |
| Full Idea: The problem for invariantism is that competent speakers, under sceptical pressure, tend to deny that we know even the most conspicuous facts of perception, the clearest memories etc. | |
| From: Stewart Cohen (Contextualism Defended [2005], p.58) | |
| A reaction: This is aimed at Idea 12892. This seems to me a strong response to the rather weak invariantist case (that there is 'really and truly' only one invariant standard for knowledge). Full strength scepticism about everything demolishes all knowledge. |
| 19559 | Contextualists slightly concede scepticism, but only in extremely strict contexts [Cohen,S] |
| Full Idea: Contextualism concedes that there is some truth to skepticism, but contains the damage by holding that skeptical claims are true only relative to atypically strict contexts. | |
| From: Stewart Cohen (Contextualism Defended (and reply) [2005], 1) | |
| A reaction: My attitude to scepticism is that everything we ever affirm should have a footnote saying '...but you never know...', and it should then be ignored. In the strictest context everything is doubted simultaneously (including language), and that is paralysis. |
| 1868 | The world was made as much for animals as for man [Celsus] |
| Full Idea: The world was made as much for the irrational animals as for men. | |
| From: Celsus (On the True Doctrine (Against Christians) [c.178], §V) | |
| A reaction: A good remark. It seems to be a classic distortion of European Christianity that the world is made for us, and that animals only exist to fill our sandwiches. |
| 1867 | Christians presented Jesus as a new kind of logos to oppose that of the philosophers [Celsus] |
| Full Idea: Christians put forth this Jesus not only as the son of God, but as the very Logos - not the pure and holy Logos known to the philosophers, but a new kind of Logos. | |
| From: Celsus (On the True Doctrine (Against Christians) [c.178], III) |