23 ideas
| 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. |
| 18928 | If maximalism is necessary, then that nothing exists has a truthmaker, which it can't have [Cameron] |
| Full Idea: I think truthmaker theory is contingently true. [n24] If there could have been nothing, what makes that true? But if truthmaker maximalism is a necessary truth, there's necessarily something. | |
| From: Ross P. Cameron (Truthmaking for Presentists [2011], 4 n24) | |
| A reaction: Truthmaking is beginning to feel like Gödel's Theorems. You can 'make' lots and lots of truths ('prove' in Gödel), but there will be truths that elude the making. Truthmaker theory itself will be one example. So is Maximalism another one? |
| 18931 | Determinate truths don't need extra truthmakers, just truthmakers that are themselves determinate [Cameron] |
| Full Idea: I reject saying there must be an additional truthmaker for 'Determinately, p': rather, I say that the truthmaker for p must simply be a determinate existent rather than a mere existent. | |
| From: Ross P. Cameron (Truthmaking for Presentists [2011], 6) | |
| A reaction: As he puts it (quite persuasively), God doesn't need to add an extra truthmaker for a determinate truth. Cameron rejects Necessitarianism. He uses 'determinate' fairly uncritically. What makes the truth of the truthmaker's determinacy? |
| 18932 | The facts about the existence of truthmakers can't have a further explanation [Cameron] |
| Full Idea: The orthodox truthmaker theorist thinks the facts concerning the existence of the truthmakers do not admit of further explanation. | |
| From: Ross P. Cameron (Truthmaking for Presentists [2011], 6) | |
| A reaction: It is fairly obvious, I suppose, that not every truth can have a truthmaker, just as the verification principle could not be verified, and you can't perceive your perception in order to check it. Could God withdraw the power of truthmaking? |
| 18923 | The present property 'having been F' says nothing about a thing's intrinsic nature [Cameron] |
| Full Idea: The property 'being such as to have been a child' is suspicious because it points beyond its instances in the sense that a thing's presently having that property tells us nothing about the present intrinsic nature of the thing. | |
| From: Ross P. Cameron (Truthmaking for Presentists [2011], 2) | |
| A reaction: This is his objection to what he calls the 'Lucretian' strategy, which tries to make history into a property of present reality. That is implausible, I think, because there is no test for the property, apart from knowledge of the past. Reality is tensed? |
| 18926 | One temporal distibution property grounds our present and past truths [Cameron] |
| Full Idea: Temporal distributional properties are fundamental - it is exactly the same property that is grounding the truth about how the bearer now is that is grounding truths about how the bearer was. | |
| From: Ross P. Cameron (Truthmaking for Presentists [2011], 4) | |
| A reaction: Some kind of slight of hand is going on here, though he does a nice job of confronting all possible objections. This is the sort of metaphysics you come up with when you stake everything on the dubious notion of a 'property'. |
| 18929 | We don't want present truthmakers for the past, if they are about to cease to exist! [Cameron] |
| Full Idea: Whilst not logically inconsistent, it would be bad if it could now be true that ten years ago there was a sea battle, but that five years ago it wasn't true that five years before that there was a sea battle. | |
| From: Ross P. Cameron (Truthmaking for Presentists [2011], 4) | |
| A reaction: Nicely makes the point that you can't let the past rely on truthmakers in the present, if those truthmakers are about to go out of existence. So you need a sustained truthmaker, without giving up presentism. Enter 'temporally distributed properties'? |
| 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... |
| 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. |
| 18924 | Being polka-dotted is a 'spatial distribution' property [Cameron] |
| Full Idea: Spatial distribution properties say how things are across a region of space, such as being polka-dotted. | |
| From: Ross P. Cameron (Truthmaking for Presentists [2011], 3) | |
| A reaction: I think the routine fallacy of inferring properties from predicates is buried here. We truthfully describe it as 'polka-dotted', but that doesn't mean we must reify polka-dottedness, and see it as a feature of the world. What is a 'jumbled' space? |
| 14979 | Being alone doesn't guarantee intrinsic properties; 'being alone' is itself extrinsic [Lewis, by Sider] |
| Full Idea: The property of 'being alone in the world' is an extrinsic property, even though it has had by an object that is alone in the world. | |
| From: report of David Lewis (Extrinsic Properties [1983]) by Theodore Sider - Writing the Book of the World 01.2 | |
| A reaction: I always choke on my cornflakes whenever anyone cites a true predicate as if it were a genuine property. This is a counterexample to Idea 14978. Sider offers another more elaborate example from Lewis. |
| 15454 | Extrinsic properties come in degrees, with 'brother' less extrinsic than 'sibling' [Lewis] |
| Full Idea: Properties may be more or less intrinsic; being a brother has more of an admixture of intrinsic structure than being a sibling does, yet both are extrinsic. | |
| From: David Lewis (Extrinsic Properties [1983], I) | |
| A reaction: I suppose the point is that a brother is intrinsically male - but then a sibling is intrinsically human. A totally extrinsic relation would be one between entities which shared virtually no categories of existence. |
| 15455 | Total intrinsic properties give us what a thing is [Lewis] |
| Full Idea: The way something is is given by the totality of its intrinsic properties. | |
| From: David Lewis (Extrinsic Properties [1983], I) | |
| A reaction: No. Some properties are intrinsic but trivial. The 'important' ones fix the identity (if the identity is indeed 'fixed'). |
| 18930 | Change is instantiation of a non-uniform distributional property, like 'being red-then-orange' [Cameron] |
| Full Idea: What change is on the account being offered is to instantiate a non-uniform distributional property. Being red at one time and orange at a later time is to be analysed as instantiating the distributional property 'being red-then-orange'. | |
| From: Ross P. Cameron (Truthmaking for Presentists [2011], 4) | |
| A reaction: One of those moments when you begin to doubt whether 'being analysed' successfully actually adds much to our wisdom. His property sounds suspiciously 'gruesome' - i.e. subject to the vagaries of how we chose to describe the thing. |
| 18927 | Surely if things extend over time, then time itself must be extended? [Cameron] |
| Full Idea: If there are temporally extended entities - and there are - then there must be extended regions of time for those entities to extend in. Hence presentism is false. | |
| From: Ross P. Cameron (Truthmaking for Presentists [2011], 4) | |
| A reaction: [Cameron is playing devil's advocate] Something has to be weird here, and I take it to be the fact that the past no longer exists, and yet it is fixed and supports truths. Get over it. My childhood has gone. Totally. Irrevocably. |