26 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. |
| 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. |
| 23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
| Full Idea: Naïve set theory is based on the principles that any formula defines a set, and that coextensive sets are identical. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 4.2) | |
| A reaction: The second principle is a standard axiom of ZFC. The first principle causes the trouble. |
| 23447 | In classical semantics singular terms refer, and quantifiers range over domains [Linnebo] |
| Full Idea: In classical semantics the function of singular terms is to refer, and that of quantifiers, to range over appropriate domains of entities. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 7.1) |
| 23443 | The axioms of group theory are not assertions, but a definition of a structure [Linnebo] |
| Full Idea: Considered in isolation, the axioms of group theory are not assertions but comprise an implicit definition of some abstract structure, | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 3.5) | |
| A reaction: The traditional Euclidean approach is that axioms are plausible assertions with which to start. The present idea sums up the modern approach. In the modern version you can work backwards from a structure to a set of axioms. |
| 23444 | To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo] |
| Full Idea: Mathematics investigates the deductive consequences of axiomatic theories, but it also needs its own foundational axioms in order to provide models for its various axiomatic theories. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 4.1) | |
| A reaction: This is a problem which faces the deductivist (if-then) approach. The deductive process needs its own grounds. |
| 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! |
| 23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
| Full Idea: If the 2nd Incompleteness Theorem undermines Hilbert's attempt to use a weak theory to prove the consistency of a strong one, it is still possible to prove the consistency of one theory, assuming the consistency of another theory. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 4.6) | |
| A reaction: Note that this concerns consistency, not completeness. |
| 23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo] |
| Full Idea: Philosophical structuralism holds that mathematics is the study of abstract structures, or 'patterns'. If mathematics is the study of all possible patterns, then it is inevitable that the world is described by mathematics. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 11.1) | |
| A reaction: [He cites the physicist John Barrow (2010) for this] For me this is a major idea, because the concept of a pattern gives a link between the natural physical world and the abstract world of mathematics. No platonism is needed. |
| 23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
| Full Idea: Modern logic requires that logical truths be true in all models, including ones devoid of any mathematical objects. It follows immediately that the existence of mathematical objects can never be a matter of logic alone. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 2) | |
| A reaction: Hm. Could there not be a complete set of models for a theory which all included mathematical objects? (I can't answer that). |
| 23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
| Full Idea: Game Formalism seeks to banish all semantics from mathematics, and Term Formalism seeks to reduce any such notions to purely syntactic ones. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 3.3) | |
| A reaction: This approach was stimulated by the need to justify the existence of the imaginary number i. Just say it is a letter! |
| 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]) |
| 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. |
| 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]) |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 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. |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |
| 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]) |