49 ideas
| 22270 | Frege changed philosophy by extending logic's ability to check the grounds of thinking [Potter on Frege] |
| Full Idea: Frege's 1879 logic transformed philosophy because it greatly expanded logic's reach - what thought can achieve unaided - and hence compelled a re-examination of everything previously said about the grounds of thought when logic gives out. | |
| From: comment on Gottlob Frege (Begriffsschrift [1879]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 Intro | |
| A reaction: I loved the gloss on logic as 'what thought can achieve unaided'. I largely see logic in terms of what is mechanically computable. |
| 8939 | We should not describe human laws of thought, but how to correctly track truth [Frege, by Fisher] |
| Full Idea: Frege disagree that logic should merely describe the laws of thought - how people actually did reason. Logic is essentially normative, not descriptive. We want the one logic which successfully tracks the truth. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Jennifer Fisher - On the Philosophy of Logic 1.III | |
| A reaction: This explains Frege's sustained attack on psychologism, and it also explains we he ended up as a platonist about logic - because he wanted its laws to be valid independently of human thinking. A step too far, perhaps. Brains are truth machines. |
| 4971 | I don't use 'subject' and 'predicate' in my way of representing a judgement [Frege] |
| Full Idea: A distinction of subject and predicate finds no place in my way of representing a judgement. | |
| From: Gottlob Frege (Begriffsschrift [1879], §03) | |
| A reaction: Perhaps this sentence could be taken as the beginning of modern analytical philosophy. The old view doesn't seem to me entirely redundant - merely replaced by a much more detailed analysis of what makes a 'subject' and what makes a 'predicate'. |
| 17745 | For Frege, 'All A's are B's' means that the concept A implies the concept B [Frege, by Walicki] |
| Full Idea: 'All A's are B's' meant for Frege that the concept A implies the concept B, or that to be A implies also to be B. Moreover this applies to arbitrary x which happens to be A. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Michal Walicki - Introduction to Mathematical Logic History D.2 | |
| A reaction: This seems to hit the renate/cordate problem. If all creatures with hearts also have kidneys, does that mean that being enhearted logically implies being kidneyfied? If all chimps are hairy, is that a logical requirement? Is inclusion implication? |
| 7728 | Frege has a judgement stroke (vertical, asserting or judging) and a content stroke (horizontal, expressing) [Frege, by Weiner] |
| Full Idea: Frege distinguished between asserting a proposition and expressing it, and he introduced the judgement stroke (a small vertical line, assertion) and the content stroke (a long horizontal line, expression) to represent them. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Joan Weiner - Frege Ch.3 | |
| A reaction: There are also strokes for conditional and denial. |
| 16881 | The laws of logic are boundless, so we want the few whose power contains the others [Frege] |
| Full Idea: Since in view of the boundless multitude of laws that can be enunciated we cannot list them all, we cannot achieve completeness except by searching out those that, by their power, contain all of them. | |
| From: Gottlob Frege (Begriffsschrift [1879], §13) | |
| A reaction: He refers to these laws in the previous sentence as the 'core'. His talk of 'power' is music to my ears, since it implies a direction of explanation. Burge says the power is that of defining other concepts. |
| 7622 | In 1879 Frege developed second order logic [Frege, by Putnam] |
| Full Idea: By 1879 Frege had discovered an algorithm, a mechanical proof procedure, that embraces what is today standard 'second order logic'. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Hilary Putnam - Reason, Truth and History Ch.5 | |
| A reaction: Note that Frege did more than introduce quantifiers, and the logic of predicates. |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| Full Idea: Intuitionists in mathematics deny excluded middle, because it is symptomatic of faith in the transcendent existence of mathematical objects and/or the truth of mathematical statements. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
| A reaction: There are other problems with excluded middle, such as vagueness, but on the whole I, as a card-carrying 'realist', am committed to the law of excluded middle. |
| 7729 | Frege replaced Aristotle's subject/predicate form with function/argument form [Frege, by Weiner] |
| Full Idea: Frege's regimentation is based on the view of the simplest sort of statement as having, not subject/predicate form (as in Aristotle), but function/argument form. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Joan Weiner - Frege | |
| A reaction: This looks like being a crucial move into the modern world, where one piece of information is taken in and dealt with, as in computer procedures. Have educated people reorganised their minds along Fregean lines? |
| 9950 | A quantifier is a second-level predicate (which explains how it contributes to truth-conditions) [Frege, by George/Velleman] |
| Full Idea: The contribution of the quantifier to the truth conditions of sentences of which it is a part cannot be adequately explained if it is treated as other than a second-level predicate (for instance, if it is viewed as name). | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: They suggest that this makes it something like a 'property of properties'. With this account it becomes plausible to think of numbers as quantifiers (since they do, after all, specify quantities). |
| 9991 | For Frege the variable ranges over all objects [Frege, by Tait] |
| Full Idea: For Frege the variable ranges over all objects. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by William W. Tait - Frege versus Cantor and Dedekind XII | |
| A reaction: The point is that Frege had not yet seen the necessity to define the domain of quantification, and this leads him into various difficulties. |
| 10536 | Frege's domain for variables is all objects, but modern interpretations first fix the domain [Dummett on Frege] |
| Full Idea: For Frege there is no need to specify the domain of the individual variables, which is taken as the totality of all objects. This contrasts with the standard notion of an interpretation, which demands that we first fix the domain. | |
| From: comment on Gottlob Frege (Begriffsschrift [1879]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14 | |
| A reaction: What intrigues me is how domains of quantification shift according to context in ordinary usage, even in mid-sentence. I ought to go through every idea in this database, specifying its domain of quantification. Any volunteers? |
| 7730 | Frege introduced quantifiers for generality [Frege, by Weiner] |
| Full Idea: In order to express generality, Frege introduced quantifier notation. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Joan Weiner - Frege | |
| A reaction: This is the birth of predicate logic, beloved of analytical philosophers (but of no apparent interest to phenomenalists, deconstructionists, existentialists?). Generality is what you get from induction (which is, of course, problematic). |
| 7742 | Frege reduced most quantifiers to 'everything' combined with 'not' [Frege, by McCullogh] |
| Full Idea: Frege treated 'everything' as basic, and suggested ways of recasting propositions containing other quantifiers so that this was the only one remaining. He recast 'something' as 'at least one thing', and defined this in terms of 'everything' and 'not'. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Gregory McCullogh - The Game of the Name 1.6 | |
| A reaction: Extreme parsimony seems highly desirable in logic as well as ontology, but it can lead to frustrations, especially over the crucial question of the existence of things quantified over. See Idea 6068. |
| 13824 | Proof theory began with Frege's definition of derivability [Frege, by Prawitz] |
| Full Idea: Frege's formal definition of derivability is perhaps the first investigation in general proof theory. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Dag Prawitz - Gentzen's Analysis of First-Order Proofs 2 n2 | |
| A reaction: In 'On General Proof Theory §1' Prawitz says "proof theory originated with Hilbert" in 1900. Presumably Frege offered a theory, and then Hilbert saw it as a general project. |
| 13609 | Frege produced axioms for logic, though that does not now seem the natural basis for logic [Frege, by Kaplan] |
| Full Idea: Frege's work supplied a set of axioms for logic itself, at least partly because it was a well-known way of presenting the foundations in other disciplines, especially mathematics, but it does not nowadays strike us as natural for logic. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by David Kaplan - Dthat 5.1 | |
| A reaction: What Bostock has in mind is the so-called 'natural' deduction systems, which base logic on rules of entailment, rather than on a set of truths. The axiomatic approach uses a set of truths, plus the idea of possible contradictions. |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| Full Idea: It is surely wise to identify the positions in the natural numbers structure with their counterparts in the integer, rational, real and complex number structures. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2) | |
| A reaction: The point is that this might be denied, since 3, 3/1, 3.00.., and -3*i^2 are all arrived at by different methods of construction. Natural 3 has a predecessor, but real 3 doesn't. I agree, intuitively, with Shapiro. Russell (1919) disagreed. |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| Full Idea: A sequence a1,a2,... of rational numbers is 'Cauchy' if for each rational number ε>0 there is a natural number N such that for all natural numbers m, n, if m>N and n>N then -ε < am - an < ε. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 7.2 n4) | |
| A reaction: The sequence is 'Cauchy' if N exists. |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| Full Idea: There is a dedicated contingent who hold that the category of 'categories' is the proper foundation for mathematics. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.3 n7) | |
| A reaction: He cites Lawvere (1966) and McLarty (1993), the latter presenting the view as a form of structuralism. I would say that the concept of a category will need further explication, and probably reduce to either sets or relations or properties. |
| 17855 | It may be possible to define induction in terms of the ancestral relation [Frege, by Wright,C] |
| Full Idea: Frege's account of the ancestral has made it possible, in effect, to define the natural numbers as entities for which induction holds. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Crispin Wright - Frege's Concept of Numbers as Objects 4.xix | |
| A reaction: This is the opposite of the approach in the Peano Axioms, where induction is used to define the natural numbers. |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| Full Idea: Zermelo said that for each number n, its successor is the singleton of n, so 3 is {{{null}}}, and 1 is not a member of 3. Von Neumann said each number n is the set of numbers less than n, so 3 is {null,{null},{null,{null}}}, and 1 is a member of 3. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2) | |
| A reaction: See Idea 645 - Zermelo could save Plato from the criticisms of Aristotle! These two accounts are cited by opponents of the set-theoretical account of numbers, because it seems impossible to arbitrate between them. |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| Full Idea: The structuralist vigorously rejects any sort of ontological independence among the natural numbers; the essence of a natural number is its relations to other natural numbers. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1) | |
| A reaction: This seems to place the emphasis on ordinals (what order?) rather than on cardinality (how many?). I am strongly inclined to think that this is the correct view, though you can't really have relations if there is nothing to relate. |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| Full Idea: A 'system' is a collection of objects with certain relations among them; a 'pattern' or 'structure' is the abstract form of a system, highlighting the interrelationships and ignoring any features they do not affect how they relate to other objects. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1) | |
| A reaction: Note that 'ignoring' features is a psychological account of abstraction, which (thanks to Frege and Geach) is supposed to be taboo - but which I suspect is actually indispensable in any proper account of thought and concepts. |
| 10607 | Frege's logic has a hierarchy of object, property, property-of-property etc. [Frege, by Smith,P] |
| Full Idea: Frege's general logical system involves a type hierarchy, distinguishing objects from properties from properties-of-properties etc., with every item belonging to a determinate level. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Peter Smith - Intro to Gödel's Theorems 14.1 | |
| A reaction: The Theory of Types went on to apply this hierarchy to classes, where Frege's disastrous Basic Law V flattens the hierarchy of classes, putting them on the same level (Smith p.119) |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| Full Idea: The thesis that principles of arithmetic are derivable from the laws of logic runs against a now common view that logic itself has no ontology. There are no particular logical objects. From this perspective logicism is a non-starter. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 5.1) | |
| A reaction: This criticism strikes me as utterly devastating. There are two routes to go: prove that logic does have an ontology of objects (what would they be?), or - better - deny that arithmetic contains any 'objects'. Or give up logicism. |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| Full Idea: Term Formalism is the view that mathematics is just about characters or symbols - the systems of numerals and other linguistic forms. ...This will cover integers and rational numbers, but what are real numbers supposed to be, if they lack names? | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.1) | |
| A reaction: Real numbers (such as pi and root-2) have infinite decimal expansions, so we can start naming those. We could also start giving names like 'Harry' to other reals, though it might take a while. OK, I give up. |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| Full Idea: Game Formalism likens mathematics to chess, where the 'content' of mathematics is exhausted by the rules of operating with its language. ...This, however, leaves the problem of why the mathematical games are so useful to the sciences. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.2) | |
| A reaction: This thought pushes us towards structuralism. It could still be a game, but one we learned from observing nature, which plays its own games. Chess is, after all, modelled on warfare. |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| Full Idea: The Deductivist version of formalism (sometimes called 'if-thenism') says that the practice of mathematics consists of determining logical consequences of otherwise uninterpreted axioms. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.2) | |
| A reaction: [Hilbert is the source] More plausible than Term or Game Formalism (qv). It still leaves the question of why it seems applicable to nature, and why those particular axioms might be chosen. In some sense, though, it is obviously right. |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| Full Idea: Critics commonly complain that the intuitionist restrictions cripple the mathematician. On the other hand, intuitionist mathematics allows for many potentially important distinctions not available in classical mathematics, and is often more subtle. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 7.1) | |
| A reaction: The main way in which it cripples is its restriction on talk of infinity ('Cantor's heaven'), which was resented by Hilbert. Since high-level infinities are interesting, it would be odd if we were not allowed to discuss them. |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| Full Idea: I classify conceptualists according to what they say about properties or concepts. If someone classified properties as existing independent of language I would classify her as a realist in ontology of mathematics. Or they may be idealists or nominalists. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 2.2.1) | |
| A reaction: In other words, Shapiro wants to eliminate 'conceptualist' as a useful label in philosophy of mathematics. He's probably right. All thought involves concepts, but that doesn't produce a conceptualist theory of, say, football. |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| Full Idea: A definition of a mathematical entity is 'impredicative' if it refers to a collection that contains the defined entity. The definition of 'least upper bound' is impredicative as it refers to upper bounds and characterizes a member of this set. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
| A reaction: The big question is whether mathematics can live with impredicative definitions, or whether they threaten to be viciously circular, and undermine the whole enterprise. |
| 11008 | Existence is not a first-order property, but the instantiation of a property [Frege, by Read] |
| Full Idea: When Kant said that existence was not a property, what he meant was, according to Frege, that existence is not a first-order property - it is not a property of individuals but a property of properties, that the property has an instance. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Stephen Read - Thinking About Logic Ch.5 |
| 14064 | If a statue is identical with the clay of which it is made, that identity is contingent [Gibbard] |
| Full Idea: Under certain conditions a clay statue is identical with the piece of clay of which it is made, and if this is so then the identity is contingent. | |
| From: Allan Gibbard (Contingent Identity [1975], Intro) | |
| A reaction: This initiated the modern debate about statues, and it is an attack on Kripke's claim that if two things are identical, then they are necessarily identical. Kripke seems right about Hesperus and Phosphorus, but not about the statue. |
| 14066 | A 'piece' of clay begins when its parts stick together, separately from other clay [Gibbard] |
| Full Idea: A 'piece' of clay is a portion of clay which comes into existence when all of its parts come to be stuck to each other, and cease to be stuck to any clay which is not a part of the portion. | |
| From: Allan Gibbard (Contingent Identity [1975], I) | |
| A reaction: The sort of gormlessly elementary things that philosophers find themselves having to say, but this is a good basic assertion for a discussion of statue and clay, and I can't think of an objection to it. |
| 14067 | Clay and statue are two objects, which can be named and reasoned about [Gibbard] |
| Full Idea: The piece of clay and the statue are 'objects' - that is to say, they can be designated with proper names, and the logic we ordinarily use will still apply. | |
| From: Allan Gibbard (Contingent Identity [1975], I) | |
| A reaction: An interesting indication of the way that 'object' is used in modern analytic philosophy, which may not be the way that it is used in ordinary English. The number 'seven', for example, seems to be an object by this criterion. |
| 14069 | We can only investigate the identity once we have designated it as 'statue' or as 'clay' [Gibbard] |
| Full Idea: To ask meaningfully what that thing would be, we must designate it either as a statue or as a piece of clay. What that thing would be, apart from the way it is designated, is a question without meaning. | |
| From: Allan Gibbard (Contingent Identity [1975], III) | |
| A reaction: He obviously has a powerful point, but to suggest that we can only investigate a mysterious object once we have designated it as something sounds daft. It would ruin the fun of archaeology. |
| 14076 | Essentialism is the existence of a definite answer as to whether an entity fulfils a condition [Gibbard] |
| Full Idea: Essentialism for a class of entities is that for one entity and a condition which it fulfills, the question of whether it necessarily fulfills the condition has a definite answer apart from the way the entity is specified. | |
| From: Allan Gibbard (Contingent Identity [1975], VII) | |
| A reaction: Yet another definition of essentialism, but resting, as usual in modern discussions, entirely on the notion of necessity. Kit Fine's challenge is that if you investigate the source of the necessity, it turns out to be an essence. |
| 14077 | Essentialism for concreta is false, since they can come apart under two concepts [Gibbard] |
| Full Idea: Essentialism for the class of concrete things is false, since a statue necessarily fulfils a condition as 'Goliath', but only contingently fulfils it as 'lumpl'. On the other hand, essentialism for the class of individual concepts can be true. | |
| From: Allan Gibbard (Contingent Identity [1975], VII) | |
| A reaction: This rests on his definition of essentialism in Idea 14076. He rests his essentialism about concepts on an account given by Carnap ('Meaning and Necessity' §41). The essence of a statue and the essence of a lump of clay do seem distinct. |
| 14070 | A particular statue has sortal persistence conditions, so its origin defines it [Gibbard] |
| Full Idea: A proper name like 'Goliath' denotes a thing in the actual world, and invokes a sortal with certain persistence criteria. Hence its origin makes a statue the statue that it is, and if statues in different worlds have the same beginning, they are the same. | |
| From: Allan Gibbard (Contingent Identity [1975], III) | |
| A reaction: Too neat. There are vague, ambiguous and duplicated origins. Persistence criteria can shift during the existence of a thing (like a club which changes its own constitution). In replicated statues, what is the status of the mould? |
| 14073 | Claims on contingent identity seem to violate Leibniz's Law [Gibbard] |
| Full Idea: The most prominent objection to contingent identity (as in the case of the statue and its clay) is that it violates Leibniz's Law. | |
| From: Allan Gibbard (Contingent Identity [1975], V) | |
| A reaction: Depends what you mean by a property. The trickiest one would be that the statue has (right now) a disposition to be worth a lot, but the clay doesn't. But I don't think that is really a property of the statue. Properties are a muddle. |
| 14065 | Two identical things must share properties - including creation and destruction times [Gibbard] |
| Full Idea: For two things to be strictly identical, they must have all properties in common. That means, among other things, that they must start to exist at the same time and cease to exist at the same time. | |
| From: Allan Gibbard (Contingent Identity [1975], I) | |
| A reaction: I don't accept that coming into existence at time t is a 'property' of a thing. Coincident objects give you the notion of 'existing as' something, which complicates the whole story. |
| 14074 | Leibniz's Law isn't just about substitutivity, because it must involve properties and relations [Gibbard] |
| Full Idea: As a general law of substitutivity of identicals, Leibniz's Law is false. It is a law about properties and relations, that if two things are identical, they have the same properties and relations. It only works in contexts which attribute those. | |
| From: Allan Gibbard (Contingent Identity [1975], V) | |
| A reaction: I'm not convinced about relations, which are not intrinsic properties. Under different descriptions, the relations to human minds might differ. |
| 14072 | Possible worlds identity needs a sortal [Gibbard] |
| Full Idea: Identity across possible worlds makes sense only with respect to a sortal | |
| From: Allan Gibbard (Contingent Identity [1975], IV) | |
| A reaction: See Gibbard's other ideas from this paper. I fear that the sortal invoked is too uncertain and slippery to do any useful job, and I can't see any principled difficulty with naming something before you can think of a sortal for it. |
| 14078 | Only concepts, not individuals, can be the same across possible worlds [Gibbard] |
| Full Idea: It is meaningless to talk of the same concrete thing in different possible worlds, ...but it makes sense to speak of the same individual concept, which is just a function which assigns to each possible world in a set an individual in that world. | |
| From: Allan Gibbard (Contingent Identity [1975], VII) | |
| A reaction: A lovely bold response to the problem of transworld identity, but one which needs investigation. It sounds very promising to me. 'Aristotle' is a cocept, not a name. There is no separate category of 'names'. Wow. (Attach dispositions to concepts?). |
| 14079 | Kripke's semantics needs lots of intuitions about which properties are essential [Gibbard] |
| Full Idea: To use Kripke's semantics, one needs extensive intuitions that certain properties are essential and others accidental. | |
| From: Allan Gibbard (Contingent Identity [1975], X) | |
| A reaction: As usual, we could substitute the word 'necessary' for 'essential' without changing his meaning. If we are always referring to 'our' Hubert Humphrey is speculations about him, then nearly all of his properties will be necessary ones. |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| Full Idea: Rationalism is a long-standing school that can be characterized as an attempt to extend the perceived methodology of mathematics to all of knowledge. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.1) | |
| A reaction: Sometimes called 'Descartes's Dream', or the 'Enlightenment Project', the dream of proving everything. Within maths, Hilbert's Programme aimed for the same certainty. Idea 22 is the motto for the opposition to this approach. |
| 14071 | Naming a thing in the actual world also invokes some persistence criteria [Gibbard] |
| Full Idea: The reference of a name in the actual world is fixed partly by invoking a set of persistence criteria which determine what thing it names. | |
| From: Allan Gibbard (Contingent Identity [1975], III) | |
| A reaction: This is offered as a modification to Kripke, to deal with the statue and clay. I fear that the 'persistence criteria' may be too vague, and too subject to possible change after the origin, to do the job required. |
| 22280 | Frege's account was top-down and decompositional, not bottom-up and compositional [Frege, by Potter] |
| Full Idea: Frege's account was top-down, not bottom-up: he aimed to decompose and discern function-argument structure in already existing sentences, not to explain how those sentences acquired their meanings in the first place. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 03 'Func' | |
| A reaction: This goes with the holistic account of meaning, which leads to Quine's gavagai and Kuhn's obfuscation of science. I recommend compositionality for everthing. |
| 7741 | The predicate 'exists' is actually a natural language expression for a quantifier [Frege, by Weiner] |
| Full Idea: On Frege's logical analysis, the predicate 'exists' is actually a natural language expression for a quantifier. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Joan Weiner - Frege Ch.8 | |
| A reaction: However see Idea 6067, for McGinn's alternative view of quantifiers. In the normal conventions of predicate logic it may be that existence is treated as a quantifier, but that is not the same as saying that existence just IS a quantifier. |