14 ideas
| 22764 | Ordinary speech is not exact about what is true; we say we are digging a well before the well exists [Sext.Empiricus] |
| Full Idea: We must allow ordinary speech to use inexact terms, as it does not seek after what is really true but what is supposed to be true. We speak of digging a well or weaving a cloak, but there is no well or cloak when they are being dug or woven. | |
| From: Sextus Empiricus (Against the Logicians (two books) [c.180], II.129) | |
| A reaction: Nice examples. The imprecision is reduced if I say I am creating a well, because that implies something that is not yet complete. If I say I intend to dig a well, is that imprecise because the well does not exist? |
| 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. |
| 22762 | Some properties are inseparable from a thing, such as the length, breadth and depth of a body [Sext.Empiricus] |
| Full Idea: Some properties are inseparable from the things to which they belong - as are length, breadth and depth from bodies, for without their presence it is impossible to perceive Body. | |
| From: Sextus Empiricus (Against the Logicians (two books) [c.180], I.270) | |
| A reaction: For the opposite case he suggests a man running, talking or sleeping. He doesn't mention essential natures, but this is clearly correct. We might say that they are properties which need to be mentioned in a full definition. |
| 22759 | Fools, infants and madmen may speak truly, but do not know [Sext.Empiricus] |
| Full Idea: The fool and the infant and the madman at times say something true, but they do not possess knowledge of the true. | |
| From: Sextus Empiricus (Against the Logicians (two books) [c.180], I.042) | |
| A reaction: This may be correct of someone who is insane, but seems unfair to the fool and the infant. At what age do children begin to know things? If speech was just random nonsense, an accidental truth seems impossible. |
| 22760 | Madmen are reliable reporters of what appears to them [Sext.Empiricus] |
| Full Idea: The madman is a trustworthy criterion of the appearances which occur in madness. | |
| From: Sextus Empiricus (Against the Logicians (two books) [c.180], I.062) | |
| A reaction: It is hard to conceive of an genuinely insane person deliberately misreporting their hallucinations. They are, of course, the sole witness. |
| 22763 | We can only dream of a winged man if we have experienced men and some winged thing [Sext.Empiricus] |
| Full Idea: He who in his sleep dreams of a winged man does not dream so without having seen some winged thing and a man. And in general it is impossible to find in conception anything which one does not possess as known by experience. | |
| From: Sextus Empiricus (Against the Logicians (two books) [c.180], II.058) | |
| A reaction: This precisely David Hume's empiricist account of the formation of concepts. Hume's example is a golden mountain, which he got from Aquinas. How do we dream of faces we have never encountered, or shapes we have never seen? |
| 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. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |