22 ideas
| 5893 | A wise man has integrity, firmness of will, nobility, consistency, sobriety, patience [Cicero] |
| Full Idea: The wise man does nothing of which he can repent, nothing against his will, does everything nobly, consistently, soberly, rightly, not looking forward to anything as bound to come, is not astonished at any novel occurrence, abides by his own decisions. | |
| From: M. Tullius Cicero (Tusculan Disputations [c.44 BCE], V.xxviii) | |
| A reaction: Notice that the wise man never exhibits weakness of will (an Aristotelian virtue), and is consistent (as Kant proposed), and is patient (as the Stoics proposed). But Cicero doesn't think he should busy himself maximising happiness. |
| 5891 | Philosophy is the collection of rational arguments [Cicero] |
| Full Idea: Philosophy consists in the collection of rational arguments. [Philosophia ex rationum collatione constet] | |
| From: M. Tullius Cicero (Tusculan Disputations [c.44 BCE], IV.xxxviii.84) | |
| A reaction: A nice epigraph for this database. Philosophy is, I trust, a little more than that, because you don't just hide them away in a drawer. But if you arrange them nicely in a museum (a website, for example), not a lot more can be done. |
| 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. |
| 5879 | The soul is the heart, or blood in the heart, or part of the brain, of something living in heart or brain, or breath [Cicero] |
| Full Idea: Some think the soul is the heart; Empedocles holds that the soul is blood in the heart; others said one part of the brain claimed the primacy of soul; others say the heart or brain are habitations of the soul; while others identify soul and breath. | |
| From: M. Tullius Cicero (Tusculan Disputations [c.44 BCE], I.ix.17-19) | |
| A reaction: A nice survey of views. Note that many of them identify the psuché/anima with physical parts of the body; only the fourth option seems to be dualist. This is despite the contemptuous response to Democritus' atomist theory of soul. |
| 5884 | How can one mind perceive so many dissimilar sensations? [Cicero] |
| Full Idea: Why is it that, using the same mind, we have perception of things so utterly unlike as colour, taste, heat, smell and sound? | |
| From: M. Tullius Cicero (Tusculan Disputations [c.44 BCE], I.xx.47) | |
| A reaction: This leaves us with the 'binding problem', of how the dissimilar sensations are pulled together into one field of experience. It is a nice simple objection, though, to anyone who simplistically claims that the mind is self-evidently unified. |
| 5887 | The soul has a single nature, so it cannot be divided, and hence it cannot perish [Cicero] |
| Full Idea: In souls there is no mingling of ingredients, nothing of two-fold nature, so it is impossible for the soul to be divided; impossible, therefore, for it to perish either; for perishing is like the separation of parts which were maintained in union. | |
| From: M. Tullius Cicero (Tusculan Disputations [c.44 BCE], I.xxix.71) | |
| A reaction: Cicero knows he is pushing his luck in asserting that perishing is a sort of division. Why can't something be there one moment and gone the next? He appears to be in close agreement with Descartes about being a 'thinking thing'. |
| 5886 | Like the eye, the soul has no power to see itself, but sees other things [Cicero] |
| Full Idea: The soul has not the power of itself to see itself, but, like the eye, the soul, though it does not see itself, yet discerns other things. | |
| From: M. Tullius Cicero (Tusculan Disputations [c.44 BCE], I.xxvii) | |
| A reaction: The soul is a complex item which contributes many layers of interpretation to what it sees, so there is scope for parts of the soul seeing other parts. Somewhere in the middle Cicero seems to be right - there is an elusive something we can't get at. |
| 5885 | Souls contain no properties of elements, and elements contain no properties of souls [Cicero] |
| Full Idea: No beginnings of souls can be found on earth; there is no combination in souls that could be born from earth, nothing that partakes of moist or airy or fiery; for in those elements there is nothing to possess the power of memory, thought, or reflection. | |
| From: M. Tullius Cicero (Tusculan Disputations [c.44 BCE], I.xxvi.66) | |
| A reaction: Interesting, but I think magnetism is an instructive analogy, which has weird properties which we never perceive in elements (though it is there, buried deep - suggesting panpsychism). Cicero would be disconcerted to find that fire isn't an element. |
| 5890 | We should not share the distress of others, but simply try to relieve it [Cicero] |
| Full Idea: We ought not to share distresses ourselves for the sake of others, but we ought to relieve others of their distress if we can. | |
| From: M. Tullius Cicero (Tusculan Disputations [c.44 BCE], IV.xxvi.56) | |
| A reaction: This strikes me as a sensible and balanced attitude. Some people, particularly in a Christian culture, urge that feeling strong and painful compassion for others is an intrinsic good, but the commonsense view is that that just increases human suffering. |
| 5894 | All men except philosophers fear poverty [Cicero] |
| Full Idea: All men are afraid of poverty, but not a single philosopher is so. | |
| From: M. Tullius Cicero (Tusculan Disputations [c.44 BCE], V.xxxi.88) | |
| A reaction: Not a thought which is encountered very often in modern philosophy journals. If a person is to be 'philosophical' in the way they live, calm endurance of the vicissitudes and hardships of life has to be a key prerequisite. |
| 5895 | If one despises illiterate mechanics individually, they are not worth more collectively [Cicero] |
| Full Idea: Can anything be more foolish than to suppose that those, whom individually one despises as illiterate mechanics, are worth anything collectively? | |
| From: M. Tullius Cicero (Tusculan Disputations [c.44 BCE], V.xxxvi.104) | |
| A reaction: Aristotle disagrees (Idea 2823). In 1906 a huge number of people guessed the weight of a cow at a fair, and the average was within one pound of the truth. In our world the healthy workings of the group are warped by the mass media. |
| 14014 | Space alone, and time alone, will fade away, and only their union has an independent reality [Minkowski] |
| Full Idea: Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality. | |
| From: Hermann Minkowski (Space and Time [1908], Intro) | |
| A reaction: Notice the qualification that it is a 'kind of' union. Deep confusion arises from exaggerating the analogy between space and time. Craig Bourne remarks (2006:157) that this shows independence of measurement, not of reality |