11 ideas
| 8616 | How can multiple statements, none of which is tenable, conjoin to yield a tenable conclusion? [Elgin] |
| Full Idea: How can multiple statements, none of which is tenable, conjoin to yield a tenable conclusion? How can their relation to other less than tenable enhance their tenability? | |
| From: Catherine Z. Elgin (Non-foundationalist epistemology [2005], p.157) | |
| A reaction: Her example is witnesses to a crime. Bayes Theorem appears to deal with individual items. "The thief had green hair" becomes more likely with multiple testimony. This is a very persuasive first step towards justification as coherence. |
| 8617 | Statements that are consistent, cotenable and supportive are roughly true [Elgin] |
| Full Idea: The best explanation of coherence (where the components of a coherent account must be mutually consistent, cotenable and supportive) is that the account is at least roughly true. | |
| From: Catherine Z. Elgin (Non-foundationalist epistemology [2005], p.158) | |
| A reaction: Note that she is NOT employing a coherence account of truth (which I take to be utterly wrong). It is notoriously difficult to define coherence. If the components must be 'tenable', they have epistemic status apart from their role in coherence. |
| 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. |
| 8618 | Coherence is a justification if truth is its best explanation (not skill in creating fiction) [Elgin] |
| Full Idea: The best explanation of the coherence of 'Middlemarch' lies in the novelist's craft. Coherence conduces to epistemic acceptability only when the best explanation of the coherence of a constellation of claims is that they are (at least roughly) true. | |
| From: Catherine Z. Elgin (Non-foundationalist epistemology [2005], p.160) | |
| A reaction: Yes. This combines my favourite inference to the best explanation (the favourite tool of us realists) with coherence as justification, where coherence can, crucially, have a social dimension. I begin to think this is the correct account of justification. |
| 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. |