12 ideas
6710 | You can only define a statement that something is 'true' by referring to its functional possibilities [James] |
Full Idea: Pragmatism insists that statements and beliefs are inertly and statically true only by courtesy: they practically pass for true; but you cannot define what you mean by calling them true without referring to their functional possibilities. | |
From: William James (The Meaning of the Word "Truth" [1907], p.2) | |
A reaction: I think this clarifies an objection to pragmatism, because all functional definitions (e.g. of the mind, or of moral behaviour) are preceded by the question of WHY this thing is able to function in this way. What special quality makes this possible? |
22305 | If the hypothesis of God is widely successful, it is true [James] |
Full Idea: On pragmatistic principles, if the hypothesis of God works satisfactorily in the widest sense of the word, it is true. | |
From: William James (The Meaning of the Word "Truth" [1907], p.299), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 35 'Prag' | |
A reaction: How you get from 'widely satisfactory' to 'true' is beyond my comprehension. This is dangerous nonsense. This view of truth seems to be a commonplace in American culture. Peirce hurray! James boo! James accepted verification, where possible. |
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. |
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. |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |