15 ideas
| 6211 | Laughter is a sudden glory in realising the infirmity of others, or our own formerly [Hobbes] |
| Full Idea: The passion of laughter is nothing else but sudden glory arising from some sudden conception of some eminency in ourselves, by comparison with the infirmity of others, or with our own formerly. | |
| From: Thomas Hobbes (Human Nature [1640], Ch.IX.13) | |
| A reaction: Laughter tends to involve something unusual. We don't just burst out with a glory of vanity whenever we meet some inferiority in another person. |
| 14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
| Full Idea: Boolos's conception of plural logic is as a reinterpretation of second-order logic. | |
| From: report of George Boolos (On Second-Order Logic [1975]) by Oliver,A/Smiley,T - What are Sets and What are they For? n5 | |
| A reaction: Oliver and Smiley don't accept this view, and champion plural reference differently (as, I think, some kind of metalinguistic device?). |
| 10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
| Full Idea: The metatheory of second-order logic is hopelessly set-theoretic, and the notion of second-order validity possesses many if not all of the epistemic debilities of the notion of set-theoretic truth. | |
| From: George Boolos (On Second-Order Logic [1975], p.45) | |
| A reaction: Epistemic problems arise when a logic is incomplete, because some of the so-called truths cannot be proved, and hence may be unreachable. This idea indicates Boolos's motivation for developing a theory of plural quantification. |
| 10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
| Full Idea: One may be of the opinion that no sentence ought to be considered as a truth of logic if, no matter how it is interpreted, it asserts that there are sets of certain sorts. | |
| From: George Boolos (On Second-Order Logic [1975], p.44) | |
| A reaction: My intuition is that in no way should any proper logic assert the existence of anything at all. Presumably interpretations can assert the existence of numbers or sets, but we should be able to identify something which is 'pure' logic. Natural deduction? |
| 10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
| Full Idea: One may say that '∀x x=x' means 'everything is identical to itself', but one must realise that one's answer has a determinate sense only if the reference (range) of 'everything' is fixed. | |
| From: George Boolos (On Second-Order Logic [1975], p.46) | |
| A reaction: This is the problem now discussed in the recent book 'Absolute Generality', of whether one can quantify without specifying a fixed or limited domain. |
| 10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
| Full Idea: A weak completeness theorem shows that a sentence is provable whenever it is valid; a strong theorem, that a sentence is provable from a set of sentences whenever it is a logical consequence of the set. | |
| From: George Boolos (On Second-Order Logic [1975], p.52) | |
| A reaction: So the weak version says |- φ → |= φ, and the strong versions says Γ |- φ → Γ |= φ. Presumably it is stronger if it can specify the source of the inference. |
| 13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
| Full Idea: Boolos asks why on earth compactness, whatever its virtues, should be definitive of logic itself. | |
| From: report of George Boolos (On Second-Order Logic [1975]) by Ian Hacking - What is Logic? §13 |
| 10833 | Many concepts can only be expressed by second-order logic [Boolos] |
| Full Idea: The notions of infinity and countability can be characterized by second-order sentences, though not by first-order sentences (as compactness and Skolem-Löwenheim theorems show), .. as well as well-ordering, progression, ancestral and identity. | |
| From: George Boolos (On Second-Order Logic [1975], p.48) |
| 6213 | A man cannot will to will, or will to will to will, so the idea of a voluntary will is absurd [Hobbes] |
| Full Idea: The will is not voluntary: for a man can no more say he will will, than he will will will, and so make an infinite repetition of the word 'will', which is absurd and insignificant. | |
| From: Thomas Hobbes (Human Nature [1640], Ch.XII.5) | |
| A reaction: A nice simple point, allied to Nietzsche's notion that thoughts are uncontrollable (Idea 2291). Even Aquinas, who is quite a fan of free will, spotted the problem (Idea 1854). Personally I agree with Hobbes. Free will is a shibboleth. |
| 6208 | Conceptions and apparitions are just motion in some internal substance of the head [Hobbes] |
| Full Idea: Conceptions and apparitions are nothing really, but motion in some internal substance of the head. | |
| From: Thomas Hobbes (Human Nature [1640], Ch.VII.1) | |
| A reaction: Note that he carefully covers both thought in concepts and thought in images, and also that he is not saying that thought is the substance, but that it is a 'motion'. This strikes me as an excellent word, and I think Hobbes is right. |
| 6209 | There is no absolute good, for even the goodness of God is goodness to us [Hobbes] |
| Full Idea: There is no such thing as absolute goodness, considered without relation: for even the goodness which we apprehend in God Almighty, is his goodness to us. | |
| From: Thomas Hobbes (Human Nature [1640], Ch.VII.3) | |
| A reaction: Plato's view of goodness is much more absolute than that of religion, as he proposes the Good as the eternal underpinning of nature. I agree with Hobbes that if God is the source of goodness, that will prevent goodness from being truly absolute. |
| 6210 | Life has no end (not even happiness), because we have desires, which presuppose a further end [Hobbes] |
| Full Idea: For an utmost end, in which the ancient philosophers have placed felicity, there is no such thing in this world, nor way to it: for while we live, we have desires, and desire presupposeth a further end. | |
| From: Thomas Hobbes (Human Nature [1640], Ch.VII.6) | |
| A reaction: Kant's definition of happiness (Idea 1452) seems to be the underlying idea, and hence with the same implication (of impossibility). However, an alcoholic locked in a brewery would seem to have all that Hobbes requires for happiness. |
| 6212 | Lust involves pleasure, and also the sense of power in pleasing others [Hobbes] |
| Full Idea: Lust consists of two appetites together, to please, and to be pleased, and the delight men take in delighting is not sensual, but a pleasure or joy of the mind consisting in the imagination of the power they have so much to please. | |
| From: Thomas Hobbes (Human Nature [1640], Ch.IX) | |
| A reaction: Hobbes would rather burst a blood-vessel than admit any altruism. If you take pleasure in pleasing someone else, why can't that simply be because of the other person's pleasure, with which we sympathise, rather than relishing our own 'power'? |
| 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 |
| 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. |