39 ideas
| 4465 | Note that "is" can assert existence, or predication, or identity, or classification [PG] |
| Full Idea: There are four uses of the word "is" in English: as existence ('he is at home'), as predication ('he is tall'), as identity ('he is the man I saw'), and as classification ('he is British'). | |
| From: PG (Db (ideas) [2031]) | |
| A reaction: This seems a nice instance of the sort of point made by analytical philosophy, which can lead to horrible confusion in other breeds of philosophy when it is overlooked. |
| 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. |
| 4686 | Fallacies are errors in reasoning, 'formal' if a clear rule is breached, and 'informal' if more general [PG] |
| Full Idea: Fallacies are errors in reasoning, labelled as 'formal' if a clear rule has been breached, and 'informal' if some less precise error has been made. | |
| From: PG (Db (ideas) [2031]) | |
| A reaction: Presumably there can be a grey area between the two. |
| 7415 | Question-begging assumes the proposition which is being challenged [PG] |
| Full Idea: To beg the question is to take for granted in your argument that very proposition which is being challenged | |
| From: PG (Db (ideas) [2031]) | |
| A reaction: An undoubted fallacy, and a simple failure to engage in the rational enterprise. I suppose one might give a reason for something, under the mistaken apprehension that it didn't beg the question; analysis of logical form is then needed. |
| 7414 | What is true of a set is also true of its members [PG] |
| Full Idea: The fallacy of division is the claim that what is true of a set must therefore be true of its members. | |
| From: PG (Db (ideas) [2031]) | |
| A reaction: Clearly a fallacy, but if you only accept sets which are rational, then there is always a reason why a particular is a member of a set, and you can infer facts about particulars from the nature of the set |
| 6696 | The Ad Hominem Fallacy criticises the speaker rather than the argument [PG] |
| Full Idea: The Ad Hominem Fallacy is to criticise the person proposing an argument rather than the argument itself, as when you say "You would say that", or "Your behaviour contradicts what you just said". | |
| From: PG (Db (ideas) [2031]) | |
| A reaction: Nietzsche is very keen on ad hominem arguments, and cheerfully insults great philosophers, but then he doesn't believe there is such a thing as 'pure argument', and he is a relativist. |
| 4687 | Minimal theories of truth avoid ontological commitment to such things as 'facts' or 'reality' [PG] |
| Full Idea: Minimalist theories of truth are those which involve minimum ontological commitment, avoiding references to 'reality' or 'facts' or 'what works', preferring to refer to formal relationships within language. | |
| From: PG (Db (ideas) [2031]) | |
| A reaction: Personally I am suspicious of minimal theories, which seem to be designed by and for anti-realists. They seem too focused on language, when animals can obviously formulate correct propositions. I'm quite happy with the 'facts', even if that is vague. |
| 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. |
| 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. |
| 6516 | Monty Hall Dilemma: do you abandon your preference after Monty eliminates one of the rivals? [PG] |
| Full Idea: The Monty Hall Dilemma: Three boxes, one with a big prize; pick one to open. Monty Hall then opens one of the other two, which is empty. You may, if you wish, switch from your box to the other unopened box. Should you? | |
| From: PG (Db (ideas) [2031]) | |
| A reaction: The other two boxes, as a pair, are more likely contain the prize than your box. Monty Hall has eliminated one of them for you, so you should choose the other one. Your intuition that the two remaining boxes are equal is incorrect! |
| 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 |
| 24054 | Everything has a probability, something will happen, and probabilities add up [PG] |
| Full Idea: The three Kolgorov axioms of probability: the probability of an event is a non-negative real number; it is certain that one of the 'elementary events' will occur; and the unity of probabilities is the sum of probability of parts ('additivity'). | |
| From: PG (Db (ideas) [2031]) | |
| A reaction: [My attempt to verbalise them; they are normally expressed in terms of set theory]. Got this from a talk handout, and Wikipedia. |
| 3875 | If reality is just what we perceive, we would have no need for a sixth sense [PG] |
| Full Idea: Reality must be more than merely what we perceive, because a sixth sense would enhance our current knowledge, and a seventh, and so on. | |
| From: PG (Db (ideas) [2031]) |
| 3876 | If my team is losing 3-1, I have synthetic a priori knowledge that they need two goals for a draw [PG] |
| Full Idea: If my football team is losing 3-1, I seem to have synthetic a priori knowledge that they need two goals to achieve a draw | |
| From: PG (Db (ideas) [2031]) |
| 335 | Do the gods also hold different opinions about what is right and honourable? [Plato] |
| Full Idea: Do the gods too hold different opinions about what is right, and similarly about what is honourable and dishonourable, good and bad? | |
| From: Plato (Euthyphro [c.398 BCE], 07e) |
| 7734 | Maybe a mollusc's brain events for pain ARE of the same type (broadly) as a human's [PG] |
| Full Idea: To defend type-type identity against the multiple realisability objection, we might say that a molluscs's brain events that register pain ARE of the same type as humans, given that being 'of the same type' is a fairly flexible concept. | |
| From: PG (Db (ideas) [2031]) | |
| A reaction: But this reduces 'of the same type' to such vagueness that it may become vacuous. You would be left with token-token identity, where the mental event is just identical to some brain event, with its 'type' being irrelevant. |
| 7735 | Maybe a frog's brain events for fear are functionally like ours, but not phenomenally [PG] |
| Full Idea: To defend type-type identity against the multiple realisability objection, we might (also) say that while a frog's brain events for fear are functionally identical to a human's (it runs away), that doesn't mean they are phenomenally identical. | |
| From: PG (Db (ideas) [2031]) | |
| A reaction: I take this to be the key reply to the multiple realisability problem. If a frog flees from a loud noise, it is 'frightened' in a functional sense, but that still leaves the question 'What's it like to be a frightened frog?', which may differ from humans. |
| 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. |
| 3877 | Utilitarianism seems to justify the discreet murder of unhappy people [PG] |
| Full Idea: If I discreetly murdered a gloomy and solitary tramp who was upsetting people in my village, if is hard to see how utilitarianism could demonstrate that I had done something wrong. | |
| From: PG (Db (ideas) [2031]) |
| 6126 | Life is Movement, Respiration, Sensation, Nutrition, Excretion, Reproduction, Growth (MRS NERG) [PG] |
| Full Idea: The biologists' acronym for the necessary conditions of life is MRS NERG: that is, Movement, Respiration, Sensation, Nutrition, Excretion, Reproduction, Growth. | |
| From: PG (Db (ideas) [2031]) | |
| A reaction: How strictly necessary are each of these is a point for discussion. A notorious problem case is fire, which (at a stretch) may pass all seven tests. |
| 3873 | An omniscient being couldn't know it was omniscient, as that requires information from beyond its scope of knowledge [PG] |
| Full Idea: God seems to be in the paradoxical situation that He may be omniscient, but can never know that He is, because that involves knowing that there is nothing outside his scope of knowledge (e.g. another God) | |
| From: PG (Db (ideas) [2031]) |
| 3874 | How could God know there wasn't an unknown force controlling his 'free' will? [PG] |
| Full Idea: How could God be certain that he has free will (if He has), if He couldn't be sure that there wasn't an unknown force controlling his will? | |
| From: PG (Db (ideas) [2031]) |
| 336 | Is what is pious loved by the gods because it is pious, or is it pious because they love it? (the 'Euthyphro Question') [Plato] |
| Full Idea: Is what is pious loved by the gods because it is pious, or is it pious because they love it? | |
| From: Plato (Euthyphro [c.398 BCE], 10a) | |
| A reaction: The famous Euthyphro Question, the key question about the supposed religious basis of morality. The answer of Socrates is Idea 337. |
| 337 | It seems that the gods love things because they are pious, rather than making them pious by loving them [Plato] |
| Full Idea: So things are loved by the gods because they are pious, and not pious because they are loved? It seems so. | |
| From: Plato (Euthyphro [c.398 BCE], 10e) | |
| A reaction: Socrates' answer to the Euthyphro Question (see Idea 336). The form of piety precedes the gods. |
| 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. |