44 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. |
| 13252 | Some truths have true negations [Beall/Restall] |
| Full Idea: Dialetheism is the view that some truths have true negations. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 7.4) | |
| A reaction: The important thing to remember is that they are truths. Thus 'Are you feeling happy?' might be answered 'Yes and no'. |
| 13247 | A truthmaker is an object which entails a sentence [Beall/Restall] |
| Full Idea: The truthmaker thesis is that an object is a truthmaker for a sentence if and only if its existence entails the sentence. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.5.3) | |
| A reaction: The use of the word 'object' here is even odder than usual, and invites many questions. And the 'only if' seems peculiar, since all sorts of things can make a sentence true. 'There is someone in the house' for example. |
| 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? |
| 13249 | (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically [Beall/Restall] |
| Full Idea: The inference of 'distribution' (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically. It is straightforward to construct a 'stage' at which the LHS is true but the RHS is not. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 6.1.2) | |
| A reaction: This seems to parallel the iterative notion in set theory, that you must construct your hierarchy. All part of the general 'constructivist' approach to things. Is some kind of mad platonism the only alternative? |
| 13243 | Excluded middle must be true for some situation, not for all situations [Beall/Restall] |
| Full Idea: Relevant logic endorses excluded middle, ..but says instances of the law may fail. Bv¬B is true in every situation that settles the matter of B. It is necessary that there is some such situation. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.2) | |
| A reaction: See next idea for the unusual view of necessity on which this rests. It seems easier to assert something about all situations than just about 'some' situation. |
| 13242 | It's 'relevantly' valid if all those situations make it true [Beall/Restall] |
| Full Idea: The argument from P to A is 'relevantly' valid if and only if, for every situation in which each premise in P is true, so is A. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.2) | |
| A reaction: I like the idea that proper inference should have an element of relevance to it. A falsehood may allow all sorts of things, without actually implying them. 'Situations' sound promising here. |
| 13246 | Relevant logic does not abandon classical logic [Beall/Restall] |
| Full Idea: We have not abandoned classical logic in our acceptance of relevant logic. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.4) | |
| A reaction: It appears that classical logic is straightforwardly accepted, but there is a difference of opinion over when it is applicable. |
| 13245 | Relevant consequence says invalidity is the conclusion not being 'in' the premises [Beall/Restall] |
| Full Idea: Relevant consequence says the conclusion of a relevantly invalid argument is not 'carried in' the premises - it does not follow from the premises. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.3.3) | |
| A reaction: I find this appealing. It need not invalidate classical logic. It is just a tougher criterion which is introduced when you want to do 'proper' reasoning, instead of just playing games with formal systems. |
| 13254 | A doesn't imply A - that would be circular [Beall/Restall] |
| Full Idea: We could reject the inference from A to itself (on grounds of circularity). | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 8) | |
| A reaction: [Martin-Meyer System] 'It's raining today'. 'Are you implying that it is raining today?' 'No, I'm SAYING it's raining today'. Logicians don't seem to understand the word 'implication'. Logic should capture how we reason. Nice proposal. |
| 13255 | Relevant logic may reject transitivity [Beall/Restall] |
| Full Idea: Some relevant logics reject transitivity, but we defend the classical view. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 8) | |
| A reaction: [they cite Neil Tennant for this view] To reject transitivity (A?B ? B?C ? A?C) certainly seems a long way from classical logic. But in everyday inference Tennant's idea seems good. The first premise may be irrelevant to the final conclusion. |
| 13250 | Free logic terms aren't existential; classical is non-empty, with referring names [Beall/Restall] |
| Full Idea: A logic is 'free' to the degree it refrains from existential import of its singular and general terms. Classical logic must have non-empty domain, and each name must denote in the domain. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 7.1) | |
| A reaction: My intuition is that logic should have no ontology at all, so I like the sound of 'free' logic. We can't say 'Pegasus does not exist', and then reason about Pegasus just like any other horse. |
| 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. |
| 13235 | Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall] |
| Full Idea: Nowadays we think of the consequence relation itself as the primary subject of logic, and view logical truths as degenerate instances of this relation. Logical truths follow from any set of assumptions, or from no assumptions at all. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.2) | |
| A reaction: This seems exactly right; the alternative is the study of necessities, but that may not involve logic. |
| 13238 | Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall] |
| Full Idea: According to the Peripatetics (Aristotelians), only syllogistic laws stated in variables belong to logic, and not their applications to concrete terms. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.5) | |
| A reaction: [from Lukasiewicz] Seems wrong. I take it there are logical relations between concrete things, and the variables are merely used to describe these relations. Variables lack the internal powers to drive logical necessities. Variables lack essence! |
| 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. |
| 13234 | The view of logic as knowing a body of truths looks out-of-date [Beall/Restall] |
| Full Idea: Through much of the 20th century the conception of logic was inherited from Frege and Russell, as knowledge of a body of logical truths, as arithmetic or geometry was a knowledge of truths. This is odd, and a historical anomaly. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.2) | |
| A reaction: Interesting. I have always taken this idea to be false. I presume logic has minimal subject matter and truths, and preferably none at all. |
| 13232 | Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall] |
| Full Idea: Logic does not study formal languages for their own sake, which is formal grammar. Logic evaluates arguments, and primarily considers formal languages as interpreted. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.1) | |
| A reaction: Hodges seems to think logic just studies formal languages. The current idea strikes me as a much more sensible view. |
| 13241 | The model theory of classical predicate logic is mathematics [Beall/Restall] |
| Full Idea: The model theory of classical predicate logic is mathematics if anything is. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 4.2.1) | |
| A reaction: This is an interesting contrast to the claim of logicism, that mathematics reduces to logic. This idea explains why students of logic are surprised to find themselves involved in mathematics. |
| 13253 | There are several different consequence relations [Beall/Restall] |
| Full Idea: We are pluralists about logical consequence because we take there to be a number of different consequence relations, each reflecting different precisifications of the pre-theoretic notion of deductive logical consequence. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 8) | |
| A reaction: I don't see how you avoid the slippery slope that leads to daft logical rules like Prior's 'tonk' (from which you can infer anything you like). I say that nature imposes logical conquence on us - but don't ask me to prove it. |
| 13240 | A sentence follows from others if they always model it [Beall/Restall] |
| Full Idea: The sentence X follows logically from the sentences of the class K if and only if every model of the class K is also a model of the sentence X. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 3.2) | |
| A reaction: This why the symbol |= is often referred to as 'models'. |
| 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. |
| 13236 | Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall] |
| Full Idea: If mathematical truth reduces to logical truth then it is important what counts as logically true, …but if logicism is not a going concern, then the body of purely logical truths will be less interesting. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.2) | |
| A reaction: Logicism would only be one motivation for pursuing logical truths. Maybe my new 'Necessitism' will derive the Peano Axioms from broad necessary truths, rather than from logic. |
| 13237 | Preface Paradox affirms and denies the conjunction of propositions in the book [Beall/Restall] |
| Full Idea: The Paradox of the Preface is an apology, that you are committed to each proposition in the book, but admit that collectively they probably contain a mistake. There is a contradiction, of affirming and denying the conjunction of propositions. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.4) | |
| A reaction: This seems similar to the Lottery Paradox - its inverse perhaps. Affirm all and then deny one, or deny all and then affirm one? |
| 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. |
| 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) |
| 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 |
| 13244 | Relevant necessity is always true for some situation (not all situations) [Beall/Restall] |
| Full Idea: In relevant logic, the necessary truths are not those which are true in every situation; rather, they are those for which it is necessary that there is a situation making them true. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.2) | |
| A reaction: This seems to rest on the truthmaker view of such things, which I find quite attractive (despite Merricks's assault). Always ask what is making some truth necessary. This leads you to essences. |
| 16719 | The primary qualities are mixed to cause secondary qualities [Burley] |
| Full Idea: Secondary qualities are caused by a mixture of primary qualities. | |
| From: Walter Burley (De formis [1330], pars post p.65), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 21.2 | |
| A reaction: Like paint. He probably has in mind hot, cold, wet and dry as the primary qualities. |
| 13239 | Judgement is always predicating a property of a subject [Beall/Restall] |
| Full Idea: All judgement, for Kant, is essentially the predication of some property to some subject. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.5) | |
| A reaction: Presumably the denial of a predicate could be a judgement, or the affirmation of ambiguous predicates? |
| 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. |
| 13248 | We can rest truth-conditions on situations, rather than on possible worlds [Beall/Restall] |
| Full Idea: Situation semantics is a variation of the truth-conditional approach, taking the salient unit of analysis not to be the possible world, or some complete consistent index, but rather the more modest 'situation'. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.5.4) | |
| A reaction: When I read Davidson (and implicitly Frege) this is what I always assumed was meant. The idea that worlds are meant has crept in to give truth conditions for modal statements. Hence situation semantics must cover modality. |
| 13233 | Propositions commit to content, and not to any way of spelling it out [Beall/Restall] |
| Full Idea: Our talk of propositions expresses commitment to the general notion of content, without a commitment to any particular way of spelling this out. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.1) | |
| A reaction: As a fan of propositions I like this. It leaves open the question of whether the content belongs to the mind or the language. Animals entertain propositions, say I. |
| 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. |