display all the ideas for this combination of texts
12 ideas
| 10111 | Asserting Excluded Middle is a hallmark of realism about the natural world [George/Velleman] |
| Full Idea: A hallmark of our realist stance towards the natural world is that we are prepared to assert the Law of Excluded Middle for all statements about it. For all statements S, either S is true, or not-S is true. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4) | |
| A reaction: Personally I firmly subscribe to realism, so I suppose I must subscribe to Excluded Middle. ...Provided the statement is properly formulated. Or does liking excluded middle lead me to realism? |
| 4730 | For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady] |
| Full Idea: Aristotle apparently believed that the subject-predicate structure of Greek reflected the substance-accident nature of reality. | |
| From: report of Aristotle (works [c.330 BCE]) by Paul O'Grady - Relativism Ch.4 | |
| A reaction: We need not assume that Aristotle is wrong. It is a chicken-and-egg. There is something obvious about subject-predicate language, if one assumes that unified objects are part of nature, and not just conventional. |
| 12664 | A truth-table, not inferential role, defines 'and' [Fodor] |
| Full Idea: I'm inclined to think that 'and' is defined by its truth-table (and not, for example, by its 'inferential-role'). | |
| From: Jerry A. Fodor (LOT 2 [2008], Ch.7) | |
| A reaction: Sounds right, on my general principle that something can only have a function if it has an intrinsic nature. The truth-table just formalises normal understanding of 'and', according to what it makes true. |
| 12648 | Names in thought afford a primitive way to bring John before the mind [Fodor] |
| Full Idea: Names in thought (in contrast to, say, descriptions in thought) afford a primitive way of bringing John before the mind. | |
| From: Jerry A. Fodor (LOT 2 [2008], Ch.3 App) | |
| A reaction: I think the 'file' account of concepts which Fodor has now latched onto gives a wonderful account of names. They are simple if you haven't opened the file yet (like 'Louis', in Evans's example). |
| 12650 | 'Paderewski' has two names in mentalese, for his pianist file and his politician file [Fodor] |
| Full Idea: Paderewski (as pianist and as politician) has two names in Mentalese. If you think there are two Paderewskis, it's important that what you get when you retrieve the pianist file differs from the politician file. You can then merge the two files. | |
| From: Jerry A. Fodor (LOT 2 [2008], Ch.3 App) | |
| A reaction: The same will apply to 'Hespherus' and 'Phosphorus'. We can re-separate the 'morning star' and 'evening star' files if we wish to discuss ancient Egyptian attitudes to such things. I love this idea of Fodor's. Explanations flow from it. |
| 10129 | A 'model' is a meaning-assignment which makes all the axioms true [George/Velleman] |
| Full Idea: A 'model' of a theory is an assignment of meanings to the symbols of its language which makes all of its axioms come out true. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) | |
| A reaction: If the axioms are all true, and the theory is sound, then all of the theorems will also come out true. |
| 10105 | Differences between isomorphic structures seem unimportant [George/Velleman] |
| Full Idea: Mathematicians tend to regard the differences between isomorphic mathematical structures as unimportant. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3) | |
| A reaction: This seems to be a pointer towards Structuralism as the underlying story in mathematics. The intrinsic character of so-called 'objects' seems unimportant. How theories map onto one another (and onto the world?) is all that matters? |
| 12656 | P-and-Q gets its truth from the truth of P and truth of Q, but consistency isn't like that [Fodor] |
| Full Idea: The truth of P-and-Q is (roughly) a function of the truth of P and the truth of Q; but the consistency of P&Q isn't a function of the consistency of P and the consistency of Q. | |
| From: Jerry A. Fodor (LOT 2 [2008], Ch.4.5 n33) | |
| A reaction: This is a nice deep issue. Fodor is interested in artificial intelligence at this point, but I am interested in the notion of coherence, as found in good justifications. Even consistency isn't elementary logic, never mind coherence. |
| 10119 | Consistency is a purely syntactic property, unlike the semantic property of soundness [George/Velleman] |
| Full Idea: Consistency is a purely syntactic property, unlike the semantic property of soundness. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 10126 | A 'consistent' theory cannot contain both a sentence and its negation [George/Velleman] |
| Full Idea: If there is a sentence such that both the sentence and its negation are theorems of a theory, then the theory is 'inconsistent'. Otherwise it is 'consistent'. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) |
| 10120 | Soundness is a semantic property, unlike the purely syntactic property of consistency [George/Velleman] |
| Full Idea: Soundness is a semantic property, unlike the purely syntactic property of consistency. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6) |
| 10127 | A 'complete' theory contains either any sentence or its negation [George/Velleman] |
| Full Idea: If there is a sentence such that neither the sentence nor its negation are theorems of a theory, then the theory is 'incomplete'. Otherwise it is 'complete'. | |
| From: A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.7) | |
| A reaction: Interesting questions are raised about undecidable sentences, irrelevant sentences, unknown sentences.... |