31 ideas
4187 | 'There is nothing without a reason why it should be rather than not be' (a generalisation of 'Why?') [Schopenhauer] |
Full Idea: The Principle may be stated as 'There is nothing without a reason why it should be rather than not be', which is a generalisation of the assumption which justifies the question 'Why?', which is the mother of all science. | |
From: Arthur Schopenhauer (Abstract of 'The Fourfold Root' [1813], Ch.I) | |
A reaction: This faith is the core of philosophy, to be maintained against all defeatists like Wittgenstein and Colin McGinn. Reality must be rational, or we wouldn't be here to think about it. (Maybe!) |
13838 | A decent modern definition should always imply a semantics [Hacking] |
Full Idea: Today we expect that anything worth calling a definition should imply a semantics. | |
From: Ian Hacking (What is Logic? [1979], §10) | |
A reaction: He compares this with Gentzen 1935, who was attempting purely syntactic definitions of the logical connectives. |
13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
Full Idea: 'Dilution' (or 'Thinning') provides an essential contrast between deductive and inductive reasoning; for the introduction of new premises may spoil an inductive inference. | |
From: Ian Hacking (What is Logic? [1979], §06.2) | |
A reaction: That is, inductive logic (if there is such a thing) is clearly non-monotonic, whereas classical inductive logic is monotonic. |
13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
Full Idea: If A |- B and B |- C, then A |- C. This generalises to: If Γ|-A,Θ and Γ,A |- Θ, then Γ |- Θ. Gentzen called this 'cut'. It is the transitivity of a deduction. | |
From: Ian Hacking (What is Logic? [1979], §06.3) | |
A reaction: I read the generalisation as 'If A can be either a premise or a conclusion, you can bypass it'. The first version is just transitivity (which by-passes the middle step). |
13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
Full Idea: Only the cut rule can have a conclusion that is less complex than its premises. Hence when cut is not used, a derivation is quite literally constructive, building up from components. Any theorem obtained by cut can be obtained without it. | |
From: Ian Hacking (What is Logic? [1979], §08) |
13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
Full Idea: I don't believe English is by nature classical or intuitionistic etc. These are abstractions made by logicians. Logicians attend to numerous different objects that might be served by 'If...then', like material conditional, strict or relevant implication. | |
From: Ian Hacking (What is Logic? [1979], §15) | |
A reaction: The idea that they are 'abstractions' is close to my heart. Abstractions from what? Surely 'if...then' has a standard character when employed in normal conversation? |
13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
Full Idea: First-order logic is the strongest complete compact theory with a Löwenheim-Skolem theorem. | |
From: Ian Hacking (What is Logic? [1979], §13) |
13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
Full Idea: Henkin proved that there is no first-order treatment of branching quantifiers, which do not seem to involve any idea that is fundamentally different from ordinary quantification. | |
From: Ian Hacking (What is Logic? [1979], §13) | |
A reaction: See Hacking for an example of branching quantifiers. Hacking is impressed by this as a real limitation of the first-order logic which he generally favours. |
13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
Full Idea: Second-order logic has no chance of a completeness theorem unless one ventures into intensional entities and possible worlds. | |
From: Ian Hacking (What is Logic? [1979], §13) |
13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
Full Idea: My doctrine is that the peculiarity of the logical constants resides precisely in that given a certain pure notion of truth and consequence, all the desirable semantic properties of the constants are determined by their syntactic properties. | |
From: Ian Hacking (What is Logic? [1979], §09) | |
A reaction: He opposes this to Peacocke 1976, who claims that the logical connectives are essentially semantic in character, concerned with the preservation of truth. |
13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
Full Idea: For some purposes the variables of first-order logic can be regarded as prepositions and place-holders that could in principle be dispensed with, say by a system of arrows indicating what places fall in the scope of which quantifier. | |
From: Ian Hacking (What is Logic? [1979], §11) | |
A reaction: I tend to think of variables as either pronouns, or as definite descriptions, or as temporary names, but not as prepositions. Must address this new idea... |
11115 | 'All horses' either picks out the horses, or the things which are horses [Jubien] |
Full Idea: Two ways to see 'all horses are animals' are as picking out all the horses (so that it is a 'horse-quantifier'), ..or as ranging over lots of things in addition to horses, with 'horses' then restricting the things to those that satisfy 'is a horse'. | |
From: Michael Jubien (Analyzing Modality [2007], 2) | |
A reaction: Jubien says this gives you two different metaphysical views, of a world of horses etc., or a world of things which 'are horses'. I vote for the first one, as the second seems to invoke an implausible categorical property ('being a horse'). Cf Idea 11116. |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
Full Idea: A Löwenheim-Skolem theorem holds for anything which, on my delineation, is a logic. | |
From: Ian Hacking (What is Logic? [1979], §13) | |
A reaction: I take this to be an unusually conservative view. Shapiro is the chap who can give you an alternative view of these things, or Boolos. |
11116 | Being a physical object is our most fundamental category [Jubien] |
Full Idea: Being a physical object (as opposed to being a horse or a statue) really is our most fundamental category for dealing with the external world. | |
From: Michael Jubien (Analyzing Modality [2007], 2) | |
A reaction: This raises the interesting question of why any categories should be considered to be more 'fundamental' than others. I can only think that we perceive something to be an object fractionally before we (usually) manage to identify it. |
11117 | Haecceities implausibly have no qualities [Jubien] |
Full Idea: Properties of 'being such and such specific entity' are often called 'haecceities', but this term carries the connotation of non-qualitativeness which I don't favour. | |
From: Michael Jubien (Analyzing Modality [2007], 2) | |
A reaction: The way he defines it makes it sound as if it was a category, but I take it to be more like a bare individual essence. If it has not qualities then it has no causal powers, so there could be no evidence for its existence. |
11119 | De re necessity is just de dicto necessity about object-essences [Jubien] |
Full Idea: I suggest that the de re is to be analyzed in terms of the de dicto. ...We have a case of modality de re when (and only when) the appropriate property in the de dicto formulation is an object-essence. | |
From: Michael Jubien (Analyzing Modality [2007], 5) |
4192 | All necessity arises from causation, which is conditioned; there is no absolute or unconditioned necessity [Schopenhauer] |
Full Idea: Necessity has no meaning other than the irresistible sequence of the effect where the cause is given. All necessity is thus conditioned, and absolute or unconditioned necessity is a contradiction in terms. | |
From: Arthur Schopenhauer (Abstract of 'The Fourfold Root' [1813], Ch.VIII) | |
A reaction: I.e. there is only natural necessity, and no such thing as metaphysical necessity. But what about logical necessity(e.g. 2+3=5)? I think there may be metaphysical necessity, but we can't know much about it, and we are over-confident in assessing it. |
11118 | Modal propositions transcend the concrete, but not the actual [Jubien] |
Full Idea: Where modal propositions may once have seemed to transcend the actual, they now seem only to transcend the concrete. | |
From: Michael Jubien (Analyzing Modality [2007], 4) | |
A reaction: This is because Jubien has defended a form of platonism. Personally I take modal propositions to be perceptible in the concrete world, by recognising the processes involved, not the mere static stuff. |
11108 | Your properties, not some other world, decide your possibilities [Jubien] |
Full Idea: The possibility of your having been a playwright has nothing to do with how people are on other planets, whether in our own or in some other realm. It is only to do with you and the relevant property. | |
From: Michael Jubien (Analyzing Modality [2007], 1) | |
A reaction: I'm inclined to think that this simple point is conclusive disproof of possible worlds as an explanation of modality (apart from Jubien's other nice points). What we need to understand are modal properties, not other worlds. |
11111 | Modal truths are facts about parts of this world, not about remote maximal entities [Jubien] |
Full Idea: Typical modal truths are just facts about our world, and generally facts about very small parts of it, not facts about some infinitude of complex, maximal entities. | |
From: Michael Jubien (Analyzing Modality [2007], 1) | |
A reaction: I think we should embrace this simple fact immediately, and drop all this nonsense about possible worlds, even if they are useful for the semantics of modal logic. |
11105 | We have no idea how many 'possible worlds' there might be [Jubien] |
Full Idea: As soon as we start talking about 'possible world', we beg the question of their relevance to our prior notion of possibility. For all we know, there are just two such realms, or twenty-seven, or uncountably many, or even set-many. | |
From: Michael Jubien (Analyzing Modality [2007], 1) |
11107 | If there are no other possible worlds, do we then exist necessarily? [Jubien] |
Full Idea: Suppose there happen to be no other concrete realms. Would we happily accept the consequence that we exist necessarily? | |
From: Michael Jubien (Analyzing Modality [2007], 1) |
11106 | If all possible worlds just happened to include stars, their existence would be necessary [Jubien] |
Full Idea: If all of the possible worlds happened to include stars, how plausible is it to think that if this is how things really are, then we've just been wrong to regard the existence of stars as contingent? | |
From: Michael Jubien (Analyzing Modality [2007], 1) |
11112 | Possible worlds just give parallel contingencies, with no explanation at all of necessity [Jubien] |
Full Idea: In the world theory, what passes for 'necessity' is just a bunch of parallel 'contingencies'. The theory provides no basis for understanding why these contingencies repeat unremittingly across the board (while others do not). | |
From: Michael Jubien (Analyzing Modality [2007], 1) |
11109 | If other worlds exist, then they are scattered parts of the actual world [Jubien] |
Full Idea: Any other realms that happened to exist would just be scattered parts of the actual world, not entire worlds at all. It would just happen that physical reality was fragmented in this remarkable but modally inconsequential way. | |
From: Michael Jubien (Analyzing Modality [2007], 1) | |
A reaction: This is aimed explicitly at Lewis's modal realism, and strikes me as correct. Jubien's key point here is that they are irrelevant to modality, just as foreign countries are irrelevant to the modality of this one. |
11113 | Worlds don't explain necessity; we use necessity to decide on possible worlds [Jubien] |
Full Idea: The suspicion is that the necessity doesn't arise from how worlds are, but rather that the worlds are taken to be as they are in order to capture the intuitive necessity. | |
From: Michael Jubien (Analyzing Modality [2007], 1) | |
A reaction: It has always seemed to me rather glaring that you need a prior notion of 'possible' before you can start to talk about 'possible worlds', but I have always been too timid to disagree with the combination of Saul Kripke and David Lewis. Thank you, Jubien! |
11110 | We mustn't confuse a similar person with the same person [Jubien] |
Full Idea: If someone similar to Humphrey won the election, that nicely establishes the possibility of someone's winning who is similar to Humphrey. But we mustn't confuse this possibility with the intuitively different possibility of Humphrey himself winning. | |
From: Michael Jubien (Analyzing Modality [2007], 1) |
4190 | All understanding is an immediate apprehension of the causal relation [Schopenhauer] |
Full Idea: All understanding is an immediate apprehension of the causal relation. | |
From: Arthur Schopenhauer (Abstract of 'The Fourfold Root' [1813], Ch.IV) | |
A reaction: Based, I take it, on Hume. Presumably he means a posteriori understanding, as it hardly fits an understanding of arithmetic. Understanding needs more than just causation. What aspects of causation? |
4191 | What we know in ourselves is not a knower but a will [Schopenhauer] |
Full Idea: What we know in ourselves is never what knows, but what wills, the will. | |
From: Arthur Schopenhauer (Abstract of 'The Fourfold Root' [1813], Ch.VII) | |
A reaction: An interesting slant on Hume's scepticism about personal identity. Hume was hunting for a thing-which-experiences. If he had sought his will, he might have spotted it. |
21368 | The knot of the world is the use of 'I' to refer to both willing and knowing [Schopenhauer] |
Full Idea: The identity of the subject of willing with that of knowing by virtue whereof ...the word 'I' includes and indicates both, is the knot of the world, and hence inexplicable. | |
From: Arthur Schopenhauer (Abstract of 'The Fourfold Root' [1813], p.211-2), quoted by Christopher Janaway - Schopenhauer 4 'Self' | |
A reaction: I'm struggling to see this as a deep mystery. If we look objectively at animals and ask 'what is their brain for?' the answer seems obvious. This may be a case of everything looking mysterious after a philosopher has stared at it for a while. |
4189 | Time may be defined as the possibility of mutually exclusive conditions of the same thing [Schopenhauer] |
Full Idea: Time may be defined as the possibility of mutually exclusive conditions of the same thing. | |
From: Arthur Schopenhauer (Abstract of 'The Fourfold Root' [1813], Ch.IV) | |
A reaction: An off-beat philosophical view of the question. Sounds more like a consequence of time than its essential nature. |