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. |
| 3654 | The pineal gland links soul to body, and unites the two symmetrical sides of the body [Descartes, by PG] |
| Full Idea: The soul is united with the body in just one place, a gland (the pineal) in the centre of the brain. It is placed so that its slightest movement will affect the passions, and it plays the essential role of uniting the two symmetrical sides of the body. | |
| From: report of René Descartes (The Passions of the Soul [1649], §31) by PG - Db (ideas) | |
| A reaction: See Idea 4862 for Spinoza's nice response to Descartes' proposal. If Descartes had followed brain research for the last four hundred years, at what point would he have wavered? If every single part of the brain seems to 'interact', dualism looks unlikely. |
| 4015 | For Descartes passions are God-given preservers of the mind-body union [Descartes, by Taylor,C] |
| Full Idea: Descartes sees passions not as opinions, but as functional devices that the Creator has designed for us to help preserve the body-soul substantial union. | |
| From: report of René Descartes (The Passions of the Soul [1649]) by Charles Taylor - Sources of the Self §8 | |
| A reaction: I wonder what Descartes would have made of the theory of evolution? |
| 4313 | Are there a few primary passions (say, joy, sadness and desire)? [Descartes, by Cottingham] |
| Full Idea: Descartes says there are six primary passions (wonder, love, hatred, desire, joy and sadness); Spinoza says there are just three (joy, sadness and desire). | |
| From: report of René Descartes (The Passions of the Soul [1649]) by John Cottingham - The Rationalists p.172 | |
| A reaction: A dubious project. However, it is now agreed that there are a few (six?) basic universal facial expressions, to which these passions may correspond. |
| 23989 | There are six primitive passions: wonder, love, hatred, desire, joy and sadness [Descartes, by Goldie] |
| Full Idea: Descartes said there are six primitive passions, namely wonder, love, hatred, desire, joy and sadness. The others are either species of these, or composed of them. | |
| From: report of René Descartes (The Passions of the Soul [1649], 353) by Peter Goldie - The Emotions 4 'Evidence' | |
| A reaction: [not sure about ref] It's a nice touch to add 'wonder', which doesn't make it onto anyone else's list. |
| 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. |
| 20037 | Merely willing to walk leads to our walking [Descartes] |
| Full Idea: Our merely willing to walk has the consequence that our legs move and we walk. | |
| From: René Descartes (The Passions of the Soul [1649], 18), quoted by Rowland Stout - Action 1 'Volitionism' | |
| A reaction: Stout attributes this to Descartes' dualism, as if legs are separate from persons. Stout says the idea of a prior mental act is not usually now considered as part of an action, or even to exist at all. If the volition is intentional, there is a regress. |
| 16763 | We don't die because the soul departs; the soul departs because the organs cease functioning [Descartes] |
| Full Idea: We ought to hold, on the contrary, that the soul takes its leave when we die only because this heat ceases and the organs that bring about bodily movement decay. | |
| From: René Descartes (The Passions of the Soul [1649], I.5), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 24.5 | |
| A reaction: This sounds like a pretty major change in our concept of death, given that we all now agree with Descartes. |
| 4016 | Descartes makes strength of will the central virtue [Descartes, by Taylor,C] |
| Full Idea: Descartes makes strength of will the central virtue. | |
| From: report of René Descartes (The Passions of the Soul [1649]) by Charles Taylor - Sources of the Self §8 | |
| A reaction: Presumably strength of will can serve evil ends, so this is a bit confusing. |
| 22252 | Capitalism may actually be the best way to foster community [Conway,D] |
| Full Idea: Not only is there no good reason for supposing capitalism inimical to community, but there is reason to think it more conducive to community than the feasible alternatives to it. | |
| From: David Conway (Capitalism and Community [1996], I) | |
| A reaction: Conway is defending an obviously unorthodox view, while attacking the hopes of communitarians. |
| 22253 | Capitalism is just the market, with optional limited government, and perhaps democracy [Conway,D] |
| Full Idea: There are three types of capitalism: 1) the market - private ownership, labor contracts and profit, 2) limited government - the state provides goods the market cannot do, 3) limited government with democracy - with political freedom and elections. | |
| From: David Conway (Capitalism and Community [1996], II) | |
| A reaction: [compressed] I would have thought that capitalism is compatible with a fair degree of workplace democracy, which would make a fourth type. |
| 22256 | Capitalism prefers representative democracy, which avoids community decision-making [Conway,D] |
| Full Idea: By opting for representative rather than direct democracy, capitalism is said to preclude political community, for which the citizens of a state must possess a common will, which needs their direct participation in decisions. | |
| From: David Conway (Capitalism and Community [1996], V) | |
| A reaction: Conway does not accept this claim. I'm beginning to wonder whether the famous British electoral system is actually a capitalist conspiracy against the people. |
| 22255 | Capitalism breaks up extended families, and must then provide welfare for the lonely people [Conway,D] |
| Full Idea: It is said that capitalism encourages the breakup of extended families, which creates the need for extensive state welfare for those indigent members of society who can no longer rely on their own family to take care of them. | |
| From: David Conway (Capitalism and Community [1996], V) | |
| A reaction: Conway does not accept this claim. It seems to simplistic to say that capitalism is the sole culprit. Any rise of mechanisation in agriculture would break up rural extended families. |
| 22257 | Capitalism is anti-community, by only valuing individuals, and breaking up families [Conway,D] |
| Full Idea: Communitarns say capitalism is inimical to family community, because it encourages an individualistic mentality which only values self-fulfilment, and because it demands labour mobility which is disruptive of families. | |
| From: David Conway (Capitalism and Community [1996], VI) | |
| A reaction: Chicken-and-egg with the first one. Small entrepreneurs are individualists who seek their own gain. It is big capitalism that sucks in the others. Traditional community is based on labour-intensive agriculture. |