20 ideas
| 10061 | The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave] |
| Full Idea: The If-thenist view seems to apply straightforwardly only to the axiomatised portions of mathematics. | |
| From: Alan Musgrave (Logicism Revisited [1977], §5) | |
| A reaction: He cites Lakatos to show that cutting-edge mathematics is never axiomatised. One might reply that if the new mathematics is any good then it ought to be axiomatis-able (barring Gödelian problems). |
| 10065 | Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave] |
| Full Idea: If we identify logic with first-order logic, and mathematics with the collection of first-order theories, then maybe we can continue to maintain the If-thenist position. | |
| From: Alan Musgrave (Logicism Revisited [1977], §5) | |
| A reaction: The problem is that If-thenism must rely on rules of inference. That seems to mean that what is needed is Soundness, rather than Completeness. That is, inference by the rules must work properly. |
| 10049 | Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave] |
| Full Idea: Containing only logical notions is not a necessary condition for being a logical truth, since a logical truth such as 'all men are men' may contain non-logical notions such as 'men'. | |
| From: Alan Musgrave (Logicism Revisited [1977], §3) | |
| A reaction: [He attributes this point to Russell] Maybe it is only a logical truth in its general form, as ∀x(x=x). Of course not all 'banks' are banks. |
| 10050 | A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave] |
| Full Idea: The standard modern view of logical truth is that a statement is logically true if it comes out true in all interpretations in all (non-empty) domains. | |
| From: Alan Musgrave (Logicism Revisited [1977], §3) |
| 10058 | No two numbers having the same successor relies on the Axiom of Infinity [Musgrave] |
| Full Idea: The axiom of Peano which states that no two numbers have the same successor requires the Axiom of Infinity for its proof. | |
| From: Alan Musgrave (Logicism Revisited [1977], §4 n) | |
| A reaction: [He refers to Russell 1919:131-2] The Axiom of Infinity is controversial and non-logical. |
| 10062 | Formalism seems to exclude all creative, growing mathematics [Musgrave] |
| Full Idea: Formalism seems to exclude from consideration all creative, growing mathematics. | |
| From: Alan Musgrave (Logicism Revisited [1977], §5) | |
| A reaction: [He cites Lakatos in support] I am not immediately clear why spotting the remote implications of a formal system should be uncreative. The greatest chess players are considered to be highly creative and imaginative. |
| 10063 | Formalism is a bulwark of logical positivism [Musgrave] |
| Full Idea: Formalism is a bulwark of logical positivist philosophy. | |
| From: Alan Musgrave (Logicism Revisited [1977], §5) | |
| A reaction: Presumably if you drain all the empirical content out of arithmetic and geometry, you are only left with the bare formal syntax, of symbols and rules. That seems to be as analytic as you can get. |
| 10938 | The extremes of essentialism are that all properties are essential, or only very trivial ones [Rami] |
| Full Idea: It would be natural to label one extreme view 'maximal essentialism' - that all of an object's properties are essential - and the other extreme 'minimal' - that only trivial properties such as self-identity of being either F or not-F are essential. | |
| From: Adolph Rami (Essential vs Accidental Properties [2008]) | |
| A reaction: Personally I don't accept the trivial ones as being in any way describable as 'properties'. The maximal view destroys any useful notion of essence. Leibniz is a minority holder of the maximal view. I would defend a middle way. |
| 10940 | An 'individual essence' is possessed uniquely by a particular object [Rami] |
| Full Idea: An 'individual essence' is a property that in addition to being essential is also unique to the object, in the sense that it is not possible that something distinct from that object possesses that property. | |
| From: Adolph Rami (Essential vs Accidental Properties [2008], §5) | |
| A reaction: She cites a 'haecceity' (or mere bare identity) as a trivial example of an individual essence. |
| 10939 | 'Sortal essentialism' says being a particular kind is what is essential [Rami] |
| Full Idea: According to 'sortal essentialism', an object could not have been of a radically different kind than it in fact is. | |
| From: Adolph Rami (Essential vs Accidental Properties [2008], §4) | |
| A reaction: This strikes me as thoroughly wrong. Things belong in kinds because of their properties. Could you remove all the contingent features of a tiger, leaving it as merely 'a tiger', despite being totally unrecognisable? |
| 10934 | Unlosable properties are not the same as essential properties [Rami] |
| Full Idea: It is easy to confuse the notion of an essential property that a thing could not lack, with a property it could not lose. My having spent Christmas 2007 in Tennessee is a non-essential property I could not lose. | |
| From: Adolph Rami (Essential vs Accidental Properties [2008], §1) | |
| A reaction: The idea that having spent Christmas in Tennessee is a property I find quite bewildering. Is my not having spent my Christmas in Tennessee one of my properties? I suspect that real unlosable properties are essential ones. |
| 10933 | Physical possibility is part of metaphysical possibility which is part of logical possibility [Rami] |
| Full Idea: The usual view is that 'physical possibilities' are a natural subset of the 'metaphysical possibilities', which in turn are a subset of the 'logical possibilities'. | |
| From: Adolph Rami (Essential vs Accidental Properties [2008], §1) | |
| A reaction: [She cites Fine 2002 for an opposing view] I prefer 'natural' to 'physical', leaving it open where the borders of the natural lie. I take 'metaphysical' possibility to be 'in all naturally possible worlds'. So is a round square a logical possibility? |
| 10932 | If it is possible 'for all I know' then it is 'epistemically possible' [Rami] |
| Full Idea: There is 'epistemic possibility' when it is 'for all I know'. That is, P is epistemically possible for agent A just in case P is consistent with what A knows. | |
| From: Adolph Rami (Essential vs Accidental Properties [2008], §1) | |
| A reaction: Two problems: maybe 'we' know, and A knows we know, but A doesn't know. And maybe someone knows, but we are not sure about that, which seems to introduce a modal element into the knowing. If someone knows it's impossible, it's impossible. |
| 12608 | Concepts are distinguished by roles in judgement, and are thus tied to rationality [Peacocke] |
| Full Idea: 'Concept' is a notion tied, in the classical Fregean manner, to cognitive significance. Concepts are distinct if we can judge rationally of one, without the other. Concepts are constitutively and definitionally tied to rationality in this way. | |
| From: Christopher Peacocke (Truly Understood [2008], 2.2) | |
| A reaction: It seems to a bit optimistic to say, more or less, that thinking is impossible if it isn't rational. Rational beings have been selected for. As Quine nicely observed, duffers at induction have all been weeded out - but they may have existed, briefly. |
| 12605 | A sense is individuated by the conditions for reference [Peacocke] |
| Full Idea: My basic Fregean idea is that a sense is individuated by the fundamental condition for something to be its reference. | |
| From: Christopher Peacocke (Truly Understood [2008], Intro) | |
| A reaction: For something to actually be its reference (as opposed to imagined reference), truth must be involved. This needs the post-1891 Frege view of such things, and not just the view of concepts as functions which he started with. |
| 12607 | Fregean concepts have their essence fixed by reference-conditions [Peacocke] |
| Full Idea: The Fregean view is that the essence of a concept is given by the fundamental condition for something to be its reference. | |
| From: Christopher Peacocke (Truly Understood [2008], 2.1) | |
| A reaction: Peacocke is a supporter of the Fregean view. How does this work for concepts of odd creatures in a fantasy novel? Or for mistaken or confused concepts? For Burge's 'arthritis in my thigh'? I don't reject the Fregean view. |
| 12609 | Concepts have distinctive reasons and norms [Peacocke] |
| Full Idea: For each concept, there will be some reasons or norms distinctive of that concept. | |
| From: Christopher Peacocke (Truly Understood [2008], 2.3) | |
| A reaction: This is Peacocke's bold Fregean thesis (and it sounds rather Kantian to me). I dislike the word 'norms' (long story), but reasons are interesting. The trouble is the distinction between being a reason for something (its cause) and being a reason for me. |
| 12604 | Any explanation of a concept must involve reference and truth [Peacocke] |
| Full Idea: For some particular concept, we can argue that some of its distinctive features are adequately explained only by a possession-condition that involves reference and truth essentially. | |
| From: Christopher Peacocke (Truly Understood [2008], Intro) | |
| A reaction: He reached this view via the earlier assertion that it is the role in judgement which key to understanding concepts. I like any view of such things which says that truth plays a role. |
| 10060 | Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave] |
| Full Idea: Logical positivists did not adopt old-style logicism, but rather logicism spiced with varying doses of If-thenism. | |
| From: Alan Musgrave (Logicism Revisited [1977], §4) | |
| A reaction: This refers to their account of mathematics as a set of purely logical truths, rather than being either empirical, or a priori synthetic. |
| 12610 | Encountering novel sentences shows conclusively that meaning must be compositional [Peacocke] |
| Full Idea: The phenomenon of understanding sentences one has never encountered before is decisive against theories of meaning which do not proceed compositionally. | |
| From: Christopher Peacocke (Truly Understood [2008], 4.3) | |
| A reaction: I agree entirely. It seems obvious, as soon as you begin to slowly construct a long and unusual sentence, and follow the mental processes of the listener. |