14 ideas
| 6021 | It is only when we say a proposition that we speak truly or falsely [Sext.Empiricus] |
| Full Idea: It is only when we say a proposition that we speak truly or falsely. | |
| From: Sextus Empiricus (Against the Professors (six books) [c.180], 8.74) | |
| A reaction: This makes assertions truth-bearers, rather than propositions. But a proposition can be true or false if it is stamped with a date and/or place. "Shakespeare was born in Stratford on 23rd April 1664". No one needs to assert that. |
| 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. |
| 6020 | 'Man is a rational mortal animal' is equivalent to 'if something is a man, that thing is a rational mortal animal' [Sext.Empiricus] |
| Full Idea: Definitions are identical to universal propositions in meaning, and only differ in syntax, for whoever says 'Man is a rational mortal animal' says the same thing in meaning as whoever says 'If something is a man, that thing is a rational mortal animal'. | |
| From: Sextus Empiricus (Against the Professors (six books) [c.180], 11.8) | |
| A reaction: How strikingly like Bertrand Russell's interest and solutions. Sextus shows a straightforward interest in logical form, of a kind we associate with the twentieth century. Did Sextus Empiricus invent quantification? |
| 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. |
| 6026 | How can you investigate without some preconception of your object? [Sext.Empiricus] |
| Full Idea: A preconception and conception must precede every object of investigation, for how can anyone even investigate without some conception of the object of investigation? | |
| From: Sextus Empiricus (Against the Professors (six books) [c.180], 8.331a) | |
| A reaction: The Duhem-Quine thesis about the 'theory-ladenness of observation' is just a revival of some routine ancient scepticism. As well as a conceptual scheme to accommodate the observation, there must also be some motivation for the investigation. |
| 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. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 6032 | Right actions, once done, are those with a reasonable justification [Sext.Empiricus] |
| Full Idea: Right action is whatever, once it has been done, has a reasonable justification. | |
| From: Sextus Empiricus (Against the Professors (six books) [c.180], 7.158) | |
| A reaction: Why does he add 'once it has been done'? Wouldn't a proposed action be right if it had a reasonable justification? This grows out of the classical and Stoic emphasis on reason in ethics, and leads towards Scanlon's Contractualism. |
| 1517 | The tektraktys (1+2+3+4=10) is the 'fount of ever-flowing nature' [Sext.Empiricus] |
| Full Idea: The tektraktys (1+2+3+4=10) is the 'fount of ever-flowing nature', because nature is a harmony of three concords (4th,5th and octave), and these ratios (4:3, 3:2, and 2:1) are found in the tektraktys. | |
| From: Sextus Empiricus (Against the Professors (six books) [c.180], 7.95) |