26 ideas
| 15063 | Some sentences depend for their truth on worldly circumstances, and others do not [Fine,K] |
| Full Idea: There is a distinction between worldly and unworldly sentences, between sentences that depend for their truth upon the worldly circumstances and those that do not. | |
| From: Kit Fine (Necessity and Non-Existence [2005], Intro) | |
| A reaction: Fine is fishing around in the area between the necessary, the a priori, truthmakers, and truth-conditions. He appears to be attempting a singlehanded reconstruction of the concepts of metaphysics. Is he major, or very marginal? |
| 13733 | Frege considered definite descriptions to be genuine singular terms [Frege, by Fitting/Mendelsohn] |
| Full Idea: Frege (1893) considered a definite description to be a genuine singular term (as we do), so that a sentence like 'The present King of France is bald' would have the same logical form as 'Harry Truman is bald'. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by M Fitting/R Mendelsohn - First-Order Modal Logic | |
| A reaction: The difficulty is what the term refers to, and they embrace a degree of Meinongianism - that is that non-existent objects can still have properties attributed to them, and so can be allowed some sort of 'existence'. |
| 9874 | Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege] |
| Full Idea: The contradiction in Frege's system is due to the presence of second-order quantification, ..and Frege's explanation of the second-order quantifier, unlike that which he provides for the first-order one, appears to be substitutional rather than objectual. | |
| From: comment on Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], §25) by Michael Dummett - Frege philosophy of mathematics Ch.17 | |
| A reaction: In Idea 9871 Dummett adds the further point that Frege lacks a clear notion of the domain of quantification. At this stage I don't fully understand this idea, but it is clearly of significance, so I will return to it. |
| 18252 | Real numbers are ratios of quantities, such as lengths or masses [Frege] |
| Full Idea: If 'number' is the referent of a numerical symbol, a real number is the same as a ratio of quantities. ...A length can have to another length the same ratio as a mass to another mass. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], III.1.73), quoted by Michael Dummett - Frege philosophy of mathematics 21 'Frege's' | |
| A reaction: This is part of a critique of Cantor and the Cauchy series approach. Interesting that Frege, who is in the platonist camp, is keen to connect the real numbers with natural phenomena. He is always keen to keep touch with the application of mathematics. |
| 18271 | We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege] |
| Full Idea: It cannot be demanded that everything be proved, because that is impossible; but we can require that all propositions used without proof be expressly declared as such, so that we can see distinctly what the whole structure rests upon. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], p.2), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 7 'What' |
| 10623 | Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright] |
| Full Idea: Frege opts for his famous definition of numbers in terms of extensions of the concept 'equal to the concept F', but he then (in 'Grundgesetze') needs a theory of extensions or classes, which he provided by means of Basic Law V. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by B Hale / C Wright - Intro to 'The Reason's Proper Study' §1 |
| 9975 | Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege] |
| Full Idea: Cantor pointed out explicitly to Frege that it is a mistake to take the notion of a set (i.e. of that which has a cardinal number) to simply mean the extension of a concept. ...Frege's later assumption of this was an act of recklessness. | |
| From: comment on Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by William W. Tait - Frege versus Cantor and Dedekind III | |
| A reaction: ['recklessness' is on p.61] Tait has no sympathy with the image of Frege as an intellectual martyr. Frege had insufficient respect for a great genius. Cantor, crucially, understood infinity much better than Frege. |
| 18165 | My Basic Law V is a law of pure logic [Frege] |
| Full Idea: I hold that my Basic Law V is a law of pure logic. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], p.4), quoted by Penelope Maddy - Naturalism in Mathematics I.1 | |
| A reaction: This is, of course, the notorious law which fell foul of Russell's Paradox. It is said to be pure logic, even though it refers to things that are F and things that are G. |
| 15078 | There are levels of existence, as well as reality; objects exist at the lowest level in which they can function [Fine,K] |
| Full Idea: Just as we recognise different levels of reality, so we should recognise different levels of existence. Each object will exist at the lowest level at which it can enjoy its characteristic form of life. | |
| From: Kit Fine (Necessity and Non-Existence [2005], 10) | |
| A reaction: I'm struggling with this claim, despite my sympathy for much of Fine's picture. I'm not sure that the so-called 'levels' of reality have different degrees of reality. |
| 15072 | Bottom level facts are subject to time and world, middle to world but not time, and top to neither [Fine,K] |
| Full Idea: At the bottom are tensed or temporal facts, subject to the vicissitudes of time and hence of the world. Then come the timeless though worldly facts, subject to the world but not to time. Top are transcendental facts, subject to neither world nor time. | |
| From: Kit Fine (Necessity and Non-Existence [2005], 08) | |
| A reaction: For all of Fine's awesome grasp of logic and semantics, when he divides reality up as boldly as this I start to side a bit with the sceptics about modern metaphysics (like Ladyman and Ross). I daresay Fine acknowledges that it is 'speculative'. |
| 15071 | Tensed and tenseless sentences state two sorts of fact, which belong to two different 'realms' of reality [Fine,K] |
| Full Idea: A tensed fact is stated by a tensed sentence while a tenseless fact is stated by a tenseless sentence, and they belong to two 'realms' of reality. That Socrates drank hemlock is in the temporal realm, while 2+2=4 is presumably in the timeless realm. | |
| From: Kit Fine (Necessity and Non-Existence [2005], 07) | |
| A reaction: Put so strongly, I suddenly find sales resistance to his proposal. All my instincts favour one realm, and I take 2+2=4 to be a highly general truth about that realm. It may be a truth of any possible realm, which would distinguish it. |
| 15075 | Modal features are not part of entities, because they are accounted for by the entity [Fine,K] |
| Full Idea: It is natural to suggest that to be a man is to have certain kind of temporal-modal profile. ...but it seems natural that being a man accounts for the profile, ...so one should not appeal to an object's modal features in stating what the object is. | |
| From: Kit Fine (Necessity and Non-Existence [2005], 09) | |
| A reaction: This strikes me as a correct and very helpful point, as I am tempted to think that the modal dispositions of a thing are intrinsic to its identity. If we accept 'powers', must they be modal in character? Fine backs a sortal approach. That's ideology. |
| 15065 | What it is is fixed prior to existence or the object's worldly features [Fine,K] |
| Full Idea: The identity of an object - what it is - is not a worldly matter; essence will precede existence in that the identity of an object may be fixed by its unworldly features even before any question of its existence or other worldly features is considered. | |
| From: Kit Fine (Necessity and Non-Existence [2005], Intro) | |
| A reaction: I'm not clear how this cashes out. If I remove the 'worldly features' of an object, what is there left which establishes identity? Fine carefully avoids talk of 'a priori' knowledge of identity. |
| 15076 | Essential features of an object have no relation to how things actually are [Fine,K] |
| Full Idea: It is the core essential features of the object that will be independent of how things turn out, and they will be independent in the sense of holding regardless of circumstances, not whatever the circumstances. | |
| From: Kit Fine (Necessity and Non-Existence [2005], 09) | |
| A reaction: The distinction at the end seems to be that 'regardless' pays no attention to circumstances, whereas 'whatever' pays attention to all circumstances. In other words, essence has no relationship to how things are. Plausible. Nice to see 'core'. |
| 15073 | Self-identity should have two components, its existence, and its neutral identity with itself [Fine,K] |
| Full Idea: The existential identity of an object with itself needs analysis into two components, one the neutral identity of the object with itself, and the other its existence. The existence of the object appears to be merely a gratuitous addition to its identity. | |
| From: Kit Fine (Necessity and Non-Existence [2005], 08) | |
| A reaction: This is at least a step towards clarification of the notion, which might be seen as just a way of asserting that something 'has an identity'. Fine likes the modern Fregean way of expressing this, as an equality relation. |
| 15074 | We would understand identity between objects, even if their existence was impossible [Fine,K] |
| Full Idea: If there were impossible objects, ones that do not possibly exist, we would have no difficulty in understanding what it is for such objects to be identical or distinct than in the case of possible objects. | |
| From: Kit Fine (Necessity and Non-Existence [2005], 08) | |
| A reaction: Thus, a 'circular square' seems to be the same as a 'square circle'. Fine is arguing for identity to be independent of any questions of existence. |
| 15064 | Proper necessary truths hold whatever the circumstances; transcendent truths regardless of circumstances [Fine,K] |
| Full Idea: We distinguish between the necessary truths proper, those that hold whatever the circumstances, and the transcendent truths, those that hold regardless of the circumstances. | |
| From: Kit Fine (Necessity and Non-Existence [2005], Intro) | |
| A reaction: Fine's project seems to be dividing the necessities which derive from essence from the necessities which tended to be branded in essentialist discussions as 'trivial'. |
| 15070 | It is the nature of Socrates to be a man, so necessarily he is a man [Fine,K] |
| Full Idea: It is of the nature of Socrates to be a man; and from this it appears to follow that necessarily he is a man. | |
| From: Kit Fine (Necessity and Non-Existence [2005], 04) | |
| A reaction: I'm always puzzled by this line of thought, because it is only the intrinsic nature of beings like Socrates which decides in the first place what a 'man' is. How can something help to create a category, and then necessarily belong to that category? |
| 15069 | Possible worlds may be more limited, to how things might actually turn out [Fine,K] |
| Full Idea: An alternative conception of a possible world says it is constituted, not by the totality of facts, or of how things might be, but by the totality of circumstances, or how things might turn out. | |
| From: Kit Fine (Necessity and Non-Existence [2005], 02) | |
| A reaction: The general idea is to make a possible world more limited than in Idea 15068. It only contains properties arising from 'engagement with the world', and won't include timeless sentences. It is a bunch of possibilities, not of actualities? |
| 15068 | The actual world is a totality of facts, so we also think of possible worlds as totalities [Fine,K] |
| Full Idea: We are accustomed think of the actual world as the totality of facts, and so we think of any possible world as being like the actual world in settling the truth-value of every single proposition. | |
| From: Kit Fine (Necessity and Non-Existence [2005], 02) | |
| A reaction: Hence it is normal to refer to a possible world as a 'maximal' set of of propositions (sentences, etc). See Idea 15069 for his proposed alternative view. |
| 9190 | A concept is a function mapping objects onto truth-values, if they fall under the concept [Frege, by Dummett] |
| Full Idea: In later Frege, a concept could be taken as a particular case of a function, mapping every object on to one of the truth-values (T or F), according as to whether, as we should ordinarily say, that object fell under the concept or not. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by Michael Dummett - The Philosophy of Mathematics 3.5 | |
| A reaction: As so often in these attempts at explanation, this sounds circular. You can't decide whether an object truly falls under a concept, if you haven't already got the concept. His troubles all arise (I say) because he scorns abstractionist accounts. |
| 13665 | Frege took the study of concepts to be part of logic [Frege, by Shapiro] |
| Full Idea: Frege took the study of concepts and their extensions to be within logic. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by Stewart Shapiro - Foundations without Foundationalism 7.1 | |
| A reaction: This is part of the plan to make logic a universal language (see Idea 13664). I disagree with this, and with the general logicist view of the position of logic. The logical approach thins concepts out. See Deleuze/Guattari's horror at this. |
| 15077 | It is said that in the A-theory, all existents and objects must be tensed, as well as the sentences [Fine,K] |
| Full Idea: It is said that there is no room in the A-theorists' ontology for a realm of timeless existents. Just as there is a tendency to think that every sentence is tensed, so there is a tendency to think that every object must enjoy a tensed form of existence. | |
| From: Kit Fine (Necessity and Non-Existence [2005], 10) | |
| A reaction: Fine is arguing for certain things to exist or be true independently of time (such as arithmetic, or essential identities). I struggle with the notion of timeless existence. |
| 15067 | A-theorists tend to reject the tensed/tenseless distinction [Fine,K] |
| Full Idea: Most A-theorists have been inclined to reject the tensed/tenseless distinction. | |
| From: Kit Fine (Necessity and Non-Existence [2005], 01) | |
| A reaction: Presumably this is because they reject the notion of 'tenseless' truths. But sentences like 'two and two make four' seem not to be very tensy. |
| 15066 | B-theorists say tensed sentences have an unfilled argument-place for a time [Fine,K] |
| Full Idea: B-theorists regard tensed sentences as incomplete expressions, implicitly containing an unfilled argument-place for the time at which they are to be evaluated. | |
| From: Kit Fine (Necessity and Non-Existence [2005], 01) | |
| A reaction: To distinguish past from future it looks as if you would need two argument-places, not one. Then there are 'used to be' and 'had been' to evaluate. |
| 7482 | Resurrection developed in Judaism as a response to martyrdoms, in about 160 BCE [Anon (Dan), by Watson] |
| Full Idea: The idea of resurrection in Judaism seems to have first developed around 160 BCE, during the time of religious martyrdom, and as a response to it (the martyrs were surely not dying forever?). It is first mentioned in the book of Daniel. | |
| From: report of Anon (Dan) (27: Book of Daniel [c.165 BCE], Ch.7) by Peter Watson - Ideas | |
| A reaction: Idea 7473 suggests that Zoroaster beat them to it by 800 years. |