27 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. |
| 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. |
| 19730 | Epistemic virtues: love of knowledge, courage, caution, autonomy, practical wisdom... [Kvanvig] |
| Full Idea: Virtue theorists may focus on the particular habits or virtues of successful cognizers, such as love of knowledge, firmness, courage and caution, humility, autonomy, generosity, and practical wisdom. | |
| From: Jonathan Kvanvig (Virtue Epistemology [2011], III) | |
| A reaction: [He cites Roberts and Wood 2007] It is interesting that most of these virtues do not merely concern cognition. How about diligence, self-criticism, flexibility...? |
| 19731 | If epistemic virtues are faculties or powers, that doesn't explain propositional knowledge [Kvanvig] |
| Full Idea: Conceiving of the virtues in terms of faculties or powers doesn't help at all with the problem of accounting for propositional knowledge. | |
| From: Jonathan Kvanvig (Virtue Epistemology [2011], IV B) | |
| A reaction: It always looks as if epistemic virtues are a little peripheral to the main business of knowledge, which is getting beliefs to be correct and well-founded. Given that epistemic saints make occasional mistakes, talk of virtues can't be enough. |
| 19732 | The value of good means of attaining truth are swamped by the value of the truth itself [Kvanvig] |
| Full Idea: The Swamping Problem is that the value of truth swamps the value of additional features of true beliefs which are only instrumentally related to them. True belief is no more valuable if one adds a feature valuable for getting one to the truth. | |
| From: Jonathan Kvanvig (Virtue Epistemology [2011], IV B) | |
| A reaction: His targets here are reliabilism and epistemic virtues. Kvanvig's implication is that the key to understanding the nature of knowledge is to pinpoint why we value it so much. |
| 20712 | God is 'eternal' either by being non-temporal, or by enduring forever [Davies,B] |
| Full Idea: Saying 'God is eternal' means either that God is non-temporal or timeless, or that God has no beginning and no end. The first ('classical') view is found in Anselm, Augustine, Boethius, Aquinas, Calvin and Descartes. | |
| From: Brian Davies (Introduction to the Philosophy of Religion [1982], 8 'Meaning') | |
| A reaction: A God who is outside of time but performs actions is a bit of a puzzle. It seems that Augustine started the idea of a timeless God. |
| 20701 | Can God be good, if he has not maximised goodness? [Davies,B] |
| Full Idea: We may wonder whether God can be good since he has not produced more moral goodness than he has. We may wonder whether God is guilty by neglect. | |
| From: Brian Davies (Introduction to the Philosophy of Religion [1982], 3 'Freedom') | |
| A reaction: The orthodox response is that we cannot possibly know what the maximum of moral goodness would look like, so we can't make this judgement. Atheists say that God fails by human standards, which are not particularly high. |
| 20702 | The goodness of God may be a higher form than the goodness of moral agents [Davies,B] |
| Full Idea: If we can know that God exists and if God's goodness is not moral goodness, then moral goodness is not the highest form of goodness we know. There is the goodness of God to be reckoned with. | |
| From: Brian Davies (Introduction to the Philosophy of Religion [1982], 3 'Goodness') | |
| A reaction: This idea is to counter the charge that God fails to meet human standards for an ideal moral agent. But it sounds hand-wavy, since we presumably cannot comprehend the sort of goodness that is postulated here. |
| 20703 | How could God have obligations? What law could possibly impose them? [Davies,B] |
| Full Idea: We have good reason for resisting the suggestion that God has any duties or obligations. …What can oblige God in relation to his creatures? Could there be a law saying God has such obligations? Where does such a law come from? | |
| From: Brian Davies (Introduction to the Philosophy of Religion [1982], 3 'Goodness') | |
| A reaction: Plato can answer this question. Greek gods are not so supreme that nothing could put them under an obligation, but 'God' has to be supreme in every respect. |
| 20694 | 'Natural theology' aims to prove God to anyone (not just believers) by reason or argument [Davies,B] |
| Full Idea: 'Natural theology' is the attempt to show that belief in God's existence can be defended with reference to reason or argument which ought to be acceptable to anyone, not simply to those who believe in God's existence. | |
| From: Brian Davies (Introduction to the Philosophy of Religion [1982], 1 'Other') | |
| A reaction: I assume by 'reason or argument' he primarily means evidence (plus the ontological argument). He cites Karl Barth as objecting to the assumption of natural theology (preferring revelation). Presumably Kierkegaard offers a rival view too. |
| 20706 | A distinct cause of the universe can't be material (which would be part of the universe) [Davies,B] |
| Full Idea: If the universe was caused to come into being, it presumably could not have been caused to do so by anything material. For a material object would be part of the universe, and we are now asking for a cause distinct from the universe. | |
| From: Brian Davies (Introduction to the Philosophy of Religion [1982], 5 'God') | |
| A reaction: We're out of our depth here. We only have two modes of existence to offer, material and spiritual, and 'spiritual' means little more than non-material. |
| 20707 | The universe exhibits design either in its sense of purpose, or in its regularity [Davies,B] |
| Full Idea: The design argument offers two lines: the first states that the universe displays design in the sense of purpose; the second that it displays design in the sense of regularity. | |
| From: Brian Davies (Introduction to the Philosophy of Religion [1982], 6 'Versions') | |
| A reaction: I would have thought that you would infer the purpose from the regularity. How could you see purpose in a totally chaotic universe? |
| 20708 | If God is an orderly being, he cannot be the explanation of order [Davies,B] |
| Full Idea: If God is an instance of something orderly, how can he serve to account for the order of orderly things? | |
| From: Brian Davies (Introduction to the Philosophy of Religion [1982], 6 'b Has') | |
| A reaction: You can at least explain the tidiness of a house by the tidiness of its owner, but obviously that won't explain the phenomenon of tidiness. |
| 20710 | Maybe an abnormal state of mind is needed to experience God? [Davies,B] |
| Full Idea: Might it not be possible that experience of God requires an unusual state or psychological abnormality, just as an aerial view of Paris requires that one be in the unusual state of being abnormally elevated? | |
| From: Brian Davies (Introduction to the Philosophy of Religion [1982], 7 'Are the') | |
| A reaction: That would make sense if it were analogous to great mathematical or musical ability, but it sounds more like ouija boards in darkened rooms. Talent has a wonderful output, but people in mystical states don't return with proofs. |
| 20711 | A believer can experience the world as infused with God [Davies,B] |
| Full Idea: Maybe someone who believes in God can be regarded as experiencing everything as something behind which God lies. Believers see the world as a world in which God is present. | |
| From: Brian Davies (Introduction to the Philosophy of Religion [1982], 7 'Experiencing') | |
| A reaction: [Attributed to John Hick] This would count as supporting evidence for God, perhaps, if seeing reality as infused with God produces a consistent and plausible picture. But seeing reality as infused with other things might pass the same test. |
| 20709 | The experiences of God are inconsistent, not universal, and untestable [Davies,B] |
| Full Idea: A proclaimed experience of God must be rejected because a) there is no agreed test that it is such an experience, b) some people experience God's absence, and c) there is no uniformity of testimony about the experience. | |
| From: Brian Davies (Introduction to the Philosophy of Religion [1982], 7 'Objections') | |
| A reaction: [compressed] I'm not sure that absence of an experience is experience of an absence. Compare it with experiencing the greatness of Beethoven's Ninth. |
| 20697 | One does not need a full understanding of God in order to speak of God [Davies,B] |
| Full Idea: In order to speak meaningfully about God, it is not necessary that one should understand exactly the import of one's statements about him. | |
| From: Brian Davies (Introduction to the Philosophy of Religion [1982], 2 'Sayng') | |
| A reaction: Perfectly reasonable. To insist that all discussion of a thing requires exact understanding of the thing is ridiculous. Equally, though, to discuss God while denying all understanding of God is just as ridiculous. |
| 20699 | Paradise would not contain some virtues, such as courage [Davies,B] |
| Full Idea: There are virtues (such as courage) that would not be present in a paradise. | |
| From: Brian Davies (Introduction to the Philosophy of Religion [1982], 3 'Evil') | |
| A reaction: Part of a suggestion that morality would be entirely inapplicable in paradise, and so we need dangers etc in the world. |