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| 22317 | Truth does not admit of more and less |
| Full Idea: What is only half true is untrue. Truth does not admit of more and less. | |||
| From: Gottlob Frege (works [1890], CP 353), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 48 'Truth' | |||
| A reaction: What about a measurement which is accurate to three decimal places? Maybe being 'close to' the truth is not the same as being 'more' true. The truth about a distance between two points is unknowable? |
| 13455 | Frege did not think of himself as working with sets |
| Full Idea: Frege did not think of himself as working with sets. | |||
| From: report of Gottlob Frege (works [1890]) by William D. Hart - The Evolution of Logic 1 | |||
| A reaction: One can hardly blame him, given that set theory was only just being invented. |
| 16895 | The null set is indefensible, because it collects nothing |
| Full Idea: Frege regarded the null set as an indefensible entity from the point of view of iterative set theory. It collects nothing. | |||
| From: report of Gottlob Frege (works [1890]) by Tyler Burge - Frege on Apriority (with ps) 2 | |||
| A reaction: The null set defines the possibility that something could be collected. At the very least, it introduces curly brackets into the language. |
| 3328 | Frege proposed a realist concept of a set, as the extension of a predicate or concept or function |
| Full Idea: Contrary to Dedekind's anti-realism, Frege proposed a realist definition of a set as the extension of a predicate (or concept, or function). | |||
| From: report of Gottlob Frege (works [1890]) by José A. Benardete - Metaphysics: the logical approach Ch.13 |
| 9179 | Frege frequently expressed a contempt for language |
| Full Idea: Frege frequently expressed a contempt for language. | |||
| From: report of Gottlob Frege (works [1890], p.228) by Michael Dummett - Frege's Distinction of Sense and Reference p.228 | |||
| A reaction: This strikes me as exactly the right attitude for a logician to have. Russell seems to have agreed. Attitudes to vagueness are the test case. Over-ambitious modern logicians dream of dealing with vagueness. Forget it. Stick to your last. |
| 13473 | Frege thinks there is an independent logical order of the truths, which we must try to discover |
| Full Idea: Frege thinks there is a single right deductive order of the truths. This is not an epistemic order, but a logical order, and it is our job to arrange our beliefs in this order if we can make it out. | |||
| From: report of Gottlob Frege (works [1890]) by William D. Hart - The Evolution of Logic 2 | |||
| A reaction: Frege's dream rests on the belief that there exists a huge set of logical truths. Pluralism, conventionalism, constructivism etc. about logic would challenge this dream. I think the defence of Frege must rest on Russellian rooting of logic in nature. |
| 3319 | Frege gives a functional account of predication so that we can dispense with predicates |
| Full Idea: The whole point of Frege's functional account of predication lies in its allowing us to dispense with all properties across the board. | |||
| From: report of Gottlob Frege (works [1890]) by José A. Benardete - Metaphysics: the logical approach Ch.9 |
| 6076 | For Frege, predicates are names of functions that map objects onto the True and False |
| Full Idea: For Frege, a predicate does not refer to the objects of which it is true, but to the function that maps these objects onto the True and False; ..a predicate is a name for this function. | |||
| From: report of Gottlob Frege (works [1890]) by Colin McGinn - Logical Properties Ch.3 | |||
| A reaction: McGinn says this is close to the intuitive sense of a property. Perhaps 'predicates are what make objects the things they are?' |
| 9871 | Frege always, and fatally, neglected the domain of quantification |
| Full Idea: Frege persistently neglected the question of the domain of quantification, which proved in the end to be fatal. | |||
| From: comment on Gottlob Frege (works [1890]) by Michael Dummett - Frege philosophy of mathematics Ch.16 | |||
| A reaction: The 'fatality' refers to Russell's paradox, and the fact that not all concepts have extensions. Common sense now says that this is catastrophic. A domain of quantification is a topic of conversation, which is basic to all language. Cf. Idea 9874. |
| 16884 | Basic truths of logic are not proved, but seen as true when they are understood |
| Full Idea: In Frege's view axioms are basic truth, and basic truths do not need proof. Basic truths can be (justifiably) recognised as true by understanding their content. | |||
| From: report of Gottlob Frege (works [1890]) by Tyler Burge - Frege on Knowing the Foundations 1 | |||
| A reaction: This is the underpinning of the rationalism in Frege's philosophy. |
| 3331 | If '5' is the set of all sets with five members, that may be circular, and you can know a priori if the set has content |
| Full Idea: There is a suspicion that Frege's definition of 5 (as the set of all sets with 5 members) may be infected with circularity, …and how can we be sure on a priori grounds that 4 and 5 are not both empty sets, and hence identical? | |||
| From: comment on Gottlob Frege (works [1890]) by José A. Benardete - Metaphysics: the logical approach Ch.14 |
| 16880 | Frege aimed to discover the logical foundations which justify arithmetical judgements |
| Full Idea: Frege saw arithmetical judgements as resting on a foundation of logical principles, and the discovery of this foundation as a discovery of the nature and structure of the justification of arithmetical truths and judgments. | |||
| From: report of Gottlob Frege (works [1890]) by Tyler Burge - Frege on Knowing the Foundations Intro | |||
| A reaction: Burge's point is that the logic justifies the arithmetic, as well as underpinning it. |
| 8689 | Eventually Frege tried to found arithmetic in geometry instead of in logic |
| Full Idea: After the problem with Russell's paradox, Frege did not publish for fourteen years, and he then tried to re-found arithmetic in Euclidean geometry, rather than in logic. | |||
| From: report of Gottlob Frege (works [1890], 3.4) by Michèle Friend - Introducing the Philosophy of Mathematics 3.4 | |||
| A reaction: I take it that his new road would have led him to modern Structuralism, so I think he was probably on the right lines. Unfortunately Frege had already done enough for one good lifetime. |
| 5657 | Frege's logic showed that there is no concept of being |
| Full Idea: Frege's quantificational logic vindicates Kant's insight that existence is not a predicate and leads to fallacies when treated as one; and we might also say, despite Hegel, that there is no concept of being. | |||
| From: report of Gottlob Frege (works [1890]) by Roger Scruton - Short History of Modern Philosophy Ch.17 | |||
| A reaction: I notice that Colin McGinn has questioned the value of quantificational logic. It is difficult to assert that 'there is no concept of x', if several people have written large books about it. |
| 3318 | Frege made identity a logical notion, enshrined above all in the formula 'for all x, x=x' |
| Full Idea: It was Frege who first made identity a logical notion, enshrining it above all in the formula (x) x=x. | |||
| From: report of Gottlob Frege (works [1890]) by José A. Benardete - Metaphysics: the logical approach Ch.9 |
| 16885 | To understand a thought, understand its inferential connections to other thoughts |
| Full Idea: Frege famously realised that understanding a thought requires understanding its inferential connections to other thoughts. | |||
| From: report of Gottlob Frege (works [1890]) by Tyler Burge - Frege on Knowing the Foundations 1 | |||
| A reaction: If true, this is probably our greatest advance in grasping the concept of 'understanding' since Aristotle - but is it true? It is a striking and interesting idea, and central to the importance of Frege in modern analytic philosophy. |
| 16887 | Frege's concept of 'self-evident' makes no reference to minds |
| Full Idea: Frege's terms that translate 'self-evident' usually make no explicit reference to actual minds. | |||
| From: report of Gottlob Frege (works [1890]) by Tyler Burge - Frege on Knowing the Foundations 4 | |||
| A reaction: This follows the distinction in Aquinas, between things that are intrinsically self-evident, and things that are self-evident to particular people. God, presumably, knows all of the former. |
| 16894 | An apriori truth is grounded in generality, which is universal quantification |
| Full Idea: Generality for Frege is simply universal quantification; what makes a truth apriori is that its ultimate grounds are universally quantified. | |||
| From: report of Gottlob Frege (works [1890]) by Tyler Burge - Frege on Apriority (with ps) 2 |
| 16882 | The building blocks contain the whole contents of a discipline |
| Full Idea: The ultimate building blocks of a discipline contain, as it were in a nutshell, its whole contents. | |||
| From: Gottlob Frege (works [1890]), quoted by Tyler Burge - Frege on Knowing the Foundations 1 | |||
| A reaction: [Burge gives a reference] I would describe this nutshell as the 'essence' of the subject, and it fits Aristotle's concept of an essence perfectly. Does it fit biology or sociology, in the way it might fit maths or logic? Think of DNA or cells in biology. |
| 5816 | Frege said concepts were abstract entities, not mental entities |
| Full Idea: Frege, rebelling against 'psychologism', identified concepts (and hence 'intensions' or meanings) with abstract entities rather than mental entities. | |||
| From: report of Gottlob Frege (works [1890]) by Hilary Putnam - Meaning and Reference p.119 | |||
| A reaction: This, of course, assumes that 'abstract' entities and 'mental' entities are quite distinct things. A concept is presumably a mental item which has content, and the word 'concept' is simply ambiguous, between the container and the contents. |
| 7307 | A thought is not psychological, but a condition of the world that makes a sentence true |
| Full Idea: For Frege, a thought is not something psychological or subjective; rather, it is objective in the sense that it specifies some condition in the world the obtaining of which is necessary and sufficient for the truth of the sentence that expresses it. | |||
| From: report of Gottlob Frege (works [1890]) by Alexander Miller - Philosophy of Language 2.2 | |||
| A reaction: It is worth emphasising Russell's anti-Berkeley point about 'ideas', that the idea is in the mind, but its contents are in the world. Since the contents are what matter, this endorses Frege, and also points towards modern externalism. |
| 7309 | Frege's 'sense' is the strict and literal meaning, stripped of tone |
| Full Idea: Frege held that "and" and "but" have the same 'sense' but different 'tones' (note: they have the same truth tables); the sense of an expression is what a sentence strictly and literally means, stripped of its tone. | |||
| From: report of Gottlob Frege (works [1890]) by Alexander Miller - Philosophy of Language 2.6 | |||
| A reaction: It seems important when studying Frege to remember what has been stripped out. In "he is a genius and he plays football", if you substitute 'but' for 'and', the new version says (literally?) something very distinctive about football. |
| 7312 | 'Sense' solves the problems of bearerless names, substitution in beliefs, and informativeness |
| Full Idea: Frege's introduction of 'sense' was motivated by the desire to solve three problems: the problem of bearerless names, the problem of substitution in belief contexts, and the problem of informativeness. | |||
| From: report of Gottlob Frege (works [1890]) by Alexander Miller - Philosophy of Language 2.9 | |||
| A reaction: A proposal which solves three problems sounds pretty good! These three problems can be used to test the counter-proposals of Russell and Kripke. |
| 7725 | 'P or not-p' seems to be analytic, but does not fit Kant's account, lacking clear subject or predicate |
| Full Idea: 'It is raining or it is not raining' appears to true because of the general principle 'p or not-p', so it is analytic; but this does not fit Kant's idea of an analytic truth, because it is not obvious that it has a subject concept or a predicate concept. | |||
| From: report of Gottlob Frege (works [1890]) by Joan Weiner - Frege Ch.2 | |||
| A reaction: The general progress of logic seems to be a widening out to embrace problem sentences. However, see Idea 7315 for the next problem that arises with analyticity. All this culminates in Quine's attack (e.g. Idea 1624). |
| 7316 | Analytic truths are those that can be demonstrated using only logic and definitions |
| Full Idea: Frege (according to Quine) characterises analytic truths as those that can be demonstrated or proved using only logical laws and definitions as premises. | |||
| From: report of Gottlob Frege (works [1890]) by Alexander Miller - Philosophy of Language 4.2 | |||
| A reaction: This is the big shift away from the Kantian version (predicate contained in the subject) towards a modern version, perhaps fixed by a truth table giving true for all values. |
| 3307 | Frege put forward an ontological argument for the existence of numbers |
| Full Idea: Frege put forward an ontological argument for the existence of numbers. | |||
| From: report of Gottlob Frege (works [1890]) by José A. Benardete - Metaphysics: the logical approach Ch.4 |