22 ideas
17266 | Using modal logic, philosophers tried to handle all metaphysics in modal terms [Correia/Schnieder] |
Full Idea: In the heyday of modal logic, philosophers typically tried to account for any metaphysical notions in modal terms. | |
From: Correia,F/Schnieder,B (Grounding: an opinionated introduction [2012], 2.4) | |
A reaction: Lewisian realism about possible worlds actually gets rid of purely 'modal' terms, but I suppose they include possible worlds in their remark. Annoying for modal logicians to be told they had a 'heyday' - a nice example of the rhetoric of philosophy. |
17263 | Why do rationalists accept Sufficient Reason, when it denies the existence of fundamental facts? [Correia/Schnieder] |
Full Idea: What is most puzzling about the rationalist tradition is the steadfast certainty with which the Principle of Sufficient Reason was often accepted, since it in effect denies that there are fundamental facts. | |
From: Correia,F/Schnieder,B (Grounding: an opinionated introduction [2012], 2.2) | |
A reaction: A very simple and interesting observation. The principle implies either a circle of reasons, or an infinite regress of reasons. Nothing can be labelled as 'primitive' or 'foundational' or 'given'. The principle is irrational! |
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... |
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. |
17270 | Is existential dependence by grounding, or do grounding claims arise from existential dependence? [Correia/Schnieder] |
Full Idea: We may take existential dependence to be a relation induced by certain cases of grounding, but one may also think that facts about existential dependence are prior to corresponding ground claims, and in fact ground those claims. | |
From: Correia,F/Schnieder,B (Grounding: an opinionated introduction [2012], 4.3) | |
A reaction: I would vote for grounding, since dependence seems more abstract, and seems to demand explanation, whereas grounding seems more like a feature of reality, and to resist further intrinsic explanation (on the whole). |
17268 | Grounding is metaphysical and explanation epistemic, so keep them apart [Correia/Schnieder] |
Full Idea: To us it seems advisable to separate the objective notion of grounding, which belongs to the field of metaphysics, from the epistemically loaded notion of explanation. | |
From: Correia,F/Schnieder,B (Grounding: an opinionated introduction [2012], 4.2) | |
A reaction: Paul Audi is the defender of the opposite view. I'm with Audi. The 'epistemically loaded' pragmatic aspect is just contextual - that we have different interests in different aspects of the grounding on different occasions. |
17267 | The identity of two facts may depend on how 'fine-grained' we think facts are [Correia/Schnieder] |
Full Idea: There is a disagreement on the issue of factual identity, concerning the 'granularity' of facts, the question of how fine-grained they are. | |
From: Correia,F/Schnieder,B (Grounding: an opinionated introduction [2012], 3.3) | |
A reaction: If they are very fine-grained, then no two descriptions of a supposed fact will capture the same details. If we go broadbrush, facts become fuzzy and less helpful. 'Fact' was never going to be a clear term. |
23681 | The first motion or effect cannot be produced necessarily, so the First Cause must be a free agent [Reid] |
Full Idea: That the first motion, or the first effect, whatever it be, cannot be produced necessarily, and, consequently, that the First Cause must be a free agent, has been demonstrated clearly and unanswerably. | |
From: Thomas Reid (Essays on Active Powers 4: Liberty of Agents [1788], 8) | |
A reaction: He has said that the First Cause can only be conceived by us as an 'agent'. If there is an agential First Cause, then he must be right. It is this need for God to be free which makes scepticism about free will unacceptable to many. |
23676 | A willed action needs reasonable understanding of what is to be done [Reid] |
Full Idea: There can be no will without such a degree of understanding, at least, as gives the conception of that which we will. | |
From: Thomas Reid (Essays on Active Powers 4: Liberty of Agents [1788], 1) | |
A reaction: Presumably this 'conception' includes an understanding of the probable consequences, but they are of infinite complexity. I see this as an objection to 'ultimate' free will and responsibility, because there are only ever degrees of understanding. |
23680 | We are morally free, because we experience it, we are accountable, and we pursue projects [Reid] |
Full Idea: I believe in moral liberty first because we have a natural conviction of belief that in many cases we act freely, second because we are accountable, and third because we can prosecute an end by a long series of means adapted. | |
From: Thomas Reid (Essays on Active Powers 4: Liberty of Agents [1788], 5) | |
A reaction: This is his final summary of why he believes in free will. Why didn't Plato and Aristotle have this natural belief? He could only believe we are 'accountable' because he believes in free will. Ants and bees pursue lengthy projects. Hm. |
23678 | A motive is merely an idea, like advice, and not a force for action [Reid] |
Full Idea: A motive is equally incapable of action and of passion; because it is not a thing that exists, but a thing that is conceived. …Motives may be compared to advice or exhortation. | |
From: Thomas Reid (Essays on Active Powers 4: Liberty of Agents [1788], 4) | |
A reaction: We say people are motivated by greed or anger or love, which seems a bit stronger than mere advice. |
23677 | We all know that mere priority or constant conjunction do not have to imply causation [Reid] |
Full Idea: Every man who understands the language knows that neither priority, nor constant conjunction, nor both taken together, imply efficiency. | |
From: Thomas Reid (Essays on Active Powers 4: Liberty of Agents [1788], 2) | |
A reaction: This invites the question of how we do know causal events, if none of our experiences are enough to prove it. Reid says we have an innate knowledge that all events are caused, but that isn't much help. The presence of power? |
23679 | The principle of the law of nature is that matter is passive, and is acted upon [Reid] |
Full Idea: The law of nature respecting matter is grounded upon this principle: That matter is an inert, inactive substance, which does not act, but is acted upon. | |
From: Thomas Reid (Essays on Active Powers 4: Liberty of Agents [1788], 5) | |
A reaction: A clear statement (alongside Euler's) of the 18th century view, still with us, but strikes me as entirely wrong. Their view needs the active power of God to drive the laws. Matter has intrinsic primitive powers, and laws describe patterns of behaviour. |