17 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. |
| 16669 | Everything that exists is either a being, or some mode of a being [Malebranche] |
| Full Idea: It is absolutely necessary that everything in the world be either a being or a mode [maničre] of a being. | |
| From: Nicolas Malebranche (The Search After Truth [1675], III.2.8.ii), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 13.4 |
| 12312 | The real essence of a thing is its powers, or 'dispositional properties' [Copi] |
| Full Idea: With respect to scientific usage, we can say that the real essence of a thing will consist very largely of powers or, in modern terms, dispositional properties. | |
| From: Irving M. Copi (Essence and Accident [1954], p.718) | |
| A reaction: Once again, Copi is a hero. I personally love the word 'powers' in metaphysics (and dislike the word 'properties', which is lost in a fog of confusion). See Molnar on 'powers' and Mumford on 'dispositions'. |
| 10937 | Essential properties are the 'deepest' ones which explain the others [Copi, by Rami] |
| Full Idea: The 'explanatory characterization' says that the essential properties of an object are the object's deepest explanatory properties, which explain the other properties of the object - and which Copi claims is mind-independent. | |
| From: report of Irving M. Copi (Essence and Accident [1954]) by Adolph Rami - Essential vs Accidental Properties §2 | |
| A reaction: It is, of course, normal to see a good explanation as being dependent on the interests of the audience. Perhaps this account should be in terms of causal powers. See Shoemaker on properties. |
| 12308 | In modern science, nominal essence is intended to be real essence [Copi] |
| Full Idea: In the sphere of scientific enquiry the distinction between real and nominal essence tends to disappear; the scientist's classification of things is intended to be in terms of their real essences. | |
| From: Irving M. Copi (Essence and Accident [1954], p.716) | |
| A reaction: Thus we have disputes over what is the 'real' classification of natural kinds such as animals. There is not much point in a classification system that does not at least reflect some aspects of reality. |
| 12303 | Within the four types of change, essential attributes are those whose loss means destruction [Copi] |
| Full Idea: If we can distinguish the different kinds of change (alteration, locomotion, growth, diminution), then we can say that a given attribute is essential to an object if its loss would result in the destruction of that object. | |
| From: Irving M. Copi (Essence and Accident [1954], p.707-8) | |
| A reaction: As Copi is aware, this is a necessary condition for a property for essence, but not sufficient. If an attribute were necessary but non-essential, its loss would also be destruction. We say the essential attributes must also have some explanatory role. |
| 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. |
| 2594 | A true cause must involve a necessary connection between cause and effect [Malebranche] |
| Full Idea: A true cause as I understand it is one such that the mind perceives a necessary connection between it and its effects. | |
| From: Nicolas Malebranche (The Union of Body and Soul [1675], p.116) |
| 12726 | In a true cause we see a necessary connection [Malebranche] |
| Full Idea: A true cause is one in which the mind perceives a necessary connection between the cause and its effect. | |
| From: Nicolas Malebranche (The Search After Truth [1675], 1.649 (450)), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 5 | |
| A reaction: Presumably Hume was ignorant of 'true' causes, since he says he never saw this connection. But then is the perception done by the mind, or by the senses? |
| 12307 | Modern science seeks essences, and is getting closer to them [Copi] |
| Full Idea: Modern science seeks to know the real essences of things, and its increasing successes seem to be bringing it progressively nearer to that goal. | |
| From: Irving M. Copi (Essence and Accident [1954], p.715) | |
| A reaction: This is from a notable pioneering paper, which outlined scientific essentialism even before Marcus and Kripke began to offer a modern account of essence to give it backing. Compare Popper, who thinks essences are will-o-the-wisps. |
| 12310 | Real essences are scientifically knowable, but so are non-essential properties [Copi] |
| Full Idea: Contrary to Locke, I should hold that real essences are in principle knowable, and contrary to Aristotle, I should hold that non-essential or accidental properties can also be objects of scientific knowledge. | |
| From: Irving M. Copi (Essence and Accident [1954], p.717) | |
| A reaction: Copi has just become my hero. Aristotle's account of definition is on the brink of allowing fine-tuned essences, but he thinks universal understanding blocks knowledge of individuals. But cross-referencing of universals pinpoints individuals. |