37 ideas
| 501 | Reason is a more powerful persuader than gold [Democritus (attr)] |
| Full Idea: In power of persuasion, reasoning is far stronger than gold. | |
| From: Democritus (attrib) (reports [c.250 BCE], B051), quoted by John Stobaeus - Anthology 2.04.12 |
| 10751 | Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg] |
| Full Idea: Second-order logic raises doubts because of its ontological commitment to the set-theoretic hierarchy, and the allegedly problematic epistemic status of the second-order consequence relation. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §1) | |
| A reaction: The 'epistemic' problem is whether you can know the truths, given that the logic is incomplete, and so they cannot all be proved. Rossberg defends second-order logic against the second problem. A third problem is that it may be mathematics. |
| 10757 | Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg] |
| Full Idea: Henkin semantics (for second-order logic) specifies a second domain of predicates and relations for the upper case constants and variables. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: This second domain is restricted to predicates and relations which are actually instantiated in the model. Second-order logic is complete with this semantics. Cf. Idea 10756. |
| 10759 | There are at least seven possible systems of semantics for second-order logic [Rossberg] |
| Full Idea: In addition to standard and Henkin semantics for second-order logic, one might also employ substitutional or game-theoretical or topological semantics, or Boolos's plural interpretation, or even a semantics inspired by Lesniewski. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: This is helpful in seeing the full picture of what is going on in these logical systems. |
| 10753 | Logical consequence is intuitively semantic, and captured by model theory [Rossberg] |
| Full Idea: Logical consequence is intuitively taken to be a semantic notion, ...and it is therefore the formal semantics, i.e. the model theory, that captures logical consequence. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2) | |
| A reaction: If you come at the issue from normal speech, this seems right, but if you start thinking about the necessity of logical consequence, that formal rules and proof-theory seem to be the foundation. |
| 10752 | Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg] |
| Full Idea: Deductive consequence, written Γ|-S, is loosely read as 'the sentence S can be deduced from the sentences Γ', and semantic consequence Γ|=S says 'all models that make Γ true make S true as well'. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2) | |
| A reaction: We might read |= as 'true in the same model as'. What is the relation, though, between the LHS and the RHS? They seem to be mutually related to some model, but not directly to one another. |
| 10754 | In proof-theory, logical form is shown by the logical constants [Rossberg] |
| Full Idea: A proof-theorist could insist that the logical form of a sentence is exhibited by the logical constants that it contains. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §2) | |
| A reaction: You have to first get to the formal logical constants, rather than the natural language ones. E.g. what is the truth table for 'but'? There is also the matter of the quantifiers and the domain, and distinguishing real objects and predicates from bogus. |
| 10756 | A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg] |
| Full Idea: A standard model is a set of objects called the 'domain', and an interpretation function, assigning objects in the domain to names, subsets to predicate letters, subsets of the Cartesian product of the domain with itself to binary relation symbols etc. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: The model actually specifies which objects have which predicates, and which objects are in which relations. Tarski's account of truth in terms of 'satisfaction' seems to be just a description of those pre-decided facts. |
| 10758 | If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg] |
| Full Idea: A mathematical theory is 'categorical' if, and only if, all of its models are isomorphic. Such a theory then essentially has just one model, the standard one. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: So the term 'categorical' is gradually replacing the much-used phrase 'up to isomorphism'. |
| 10761 | Completeness can always be achieved by cunning model-design [Rossberg] |
| Full Idea: All that should be required to get a semantics relative to which a given deductive system is complete is a sufficiently cunning model-theorist. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §5) |
| 10755 | A deductive system is only incomplete with respect to a formal semantics [Rossberg] |
| Full Idea: No deductive system is semantically incomplete in and of itself; rather a deductive system is incomplete with respect to a specified formal semantics. | |
| From: Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3) | |
| A reaction: This important point indicates that a system might be complete with one semantics and incomplete with another. E.g. second-order logic can be made complete by employing a 'Henkin semantics'. |
| 7522 | A full neural account of qualia will give new epistemic access to them, beyond private experience [Churchlands] |
| Full Idea: When the hidden neurophysiological structure of qualia (if there is any) gets revealed by unfolding research, then we will automatically gain a new epistemic access to qualia, beyond each person's native and exclusive capacity for internal discrimination. | |
| From: Churchland / Churchland (Recent Work on Consciousness [1997]) | |
| A reaction: Carefully phrased and hard to deny, but something is impenetrable. What experience does an insect have when it encounters ultra-violet light? Nothing remotely interesting about their qualia is likely to emerge from the study of insect brains. |
| 7521 | It is question-begging to assume that qualia are totally simple, hence irreducible [Churchlands] |
| Full Idea: One of the crucial premises of the antireductionists - concerning the intrinsic, nonrelational, metaphysical simplicity of our sensory qualia - is a question-begging and unsupported assumption. | |
| From: Churchland / Churchland (Recent Work on Consciousness [1997]) | |
| A reaction: This is a key point for reductionists, with emphasis on the sheer numbers of connections involved in a simple quale (I estimate a billion involved in one small patch of red). |
| 7523 | The qualia Hard Problem is easy, in comparison with the co-ordination of mental states [Churchlands] |
| Full Idea: The so-called Hard Problem (of qualia) appears to be one of the easiest, in comparison with the problems of short-term memory, fluid and directable attention, the awake state vs sleep, and the unity of consciousness. | |
| From: Churchland / Churchland (Recent Work on Consciousness [1997]) | |
| A reaction: Most of their version of the Hard Problems centre on personal identity, and the centralised co-ordination of mental events. I am inclined to agree with them. Worriers about qualia should think more about the complexity of systems of neurons. |
| 514 | Beauty is merely animal without intelligence [Democritus (attr)] |
| Full Idea: Physical beauty is merely animal unless intelligence be present. | |
| From: Democritus (attrib) (reports [c.250 BCE], B105) |
| 525 | Behave well when alone, and feel shame in you own eyes [Democritus (attr)] |
| Full Idea: Do not say or do what is base, even when you are alone. Learn to feel shame in your own eyes much more than before others. | |
| From: Democritus (attrib) (reports [c.250 BCE], B244), quoted by John Stobaeus - Anthology 3.31.7 | |
| A reaction: I like this. How you think and behave when unobserved is the true test of who you are. Feeling shame at a very private failing is an interesting phenomenon. |
| 502 | Good breeding in men means having a good character [Democritus (attr)] |
| Full Idea: Good breeding in cattle depends on physical health, but in men on a well-formed character. | |
| From: Democritus (attrib) (reports [c.250 BCE], B057), quoted by John Stobaeus - Anthology 4.29.18 | |
| A reaction: In our ultra-democratic age (supposedly) it is heresy to talk about good breeding, or some people being superior to others. But surely people should aim to improve their characters? |
| 507 | Virtuous love consists of decorous desire for the beautiful [Democritus (attr)] |
| Full Idea: Virtuous love consists of decorous desire for the beautiful. | |
| From: Democritus (attrib) (reports [c.250 BCE], B073), quoted by John Stobaeus - Anthology 3.5.23 | |
| A reaction: Is it possible to love something without seeing it as beautiful? A badly crippled dog, for example. If not, that seems to reveal something about beauty. |
| 521 | We should only choose pleasures which are concerned with the beautiful [Democritus (attr)] |
| Full Idea: One should choose not every pleasure, but only that concerned with the beautiful. | |
| From: Democritus (attrib) (reports [c.250 BCE], B207), quoted by John Stobaeus - Anthology 3.05.22 | |
| A reaction: The pleasures we should prefer are those which involve the whole person, rather than the mere stimulation of one sense. Sez me. |
| 505 | Good and true are the same for everyone, but pleasures differ [Democritus (attr)] |
| Full Idea: For all men, good and true are the same; but pleasant differs for different men. | |
| From: Democritus (attrib) (reports [c.250 BCE], B069) | |
| A reaction: Truth is not 'for' anyone, but there's good-in-itself, and good-for-me. Are there some pleasures we should all enjoy (such as watching our children flourish)? |
| 508 | Only accept beneficial pleasures [Democritus (attr)] |
| Full Idea: Accept no pleasure unless it is beneficial. | |
| From: Democritus (attrib) (reports [c.250 BCE], B074) | |
| A reaction: Maybe all pleasures bestow some benefit - even if they are linked to harm. I struggle to see what is wrong with a harmless and non-beneficial pleasure, and I doubt if anyone could explain it to me. |
| 520 | The great pleasures come from the contemplation of noble works [Democritus (attr)] |
| Full Idea: The great pleasures come from the contemplation of noble works. | |
| From: Democritus (attrib) (reports [c.250 BCE], B194), quoted by John Stobaeus - Anthology 3.03.46 | |
| A reaction: Only, of course, for those able to perceive the nobility. In what does the 'nobility' consist, other than in the morally acceptable pleasure? Hard to explain 'noble'. Just 'wow!'? |
| 522 | Moderation brings more pleasures, and so increases pleasure [Democritus (attr)] |
| Full Idea: Moderation multiplies pleasures, and increases pleasure. | |
| From: Democritus (attrib) (reports [c.250 BCE], B211), quoted by John Stobaeus - Anthology 3.05.27 | |
| A reaction: So moderation is a sneaky trick to avoid moderation? I presume the most intense pleasures are mostly unfamiliar, and so add novelty to the mix. Apart from eating chocolate, of course. |
| 506 | Immoderate desire is the mark of a child, not an adult [Democritus (attr)] |
| Full Idea: Immoderate desire is the mark of a child, not a man. | |
| From: Democritus (attrib) (reports [c.250 BCE], B070) | |
| A reaction: Not factually correct, since the world is full of adults who have immoderate desires (notably for money). However, there are plenty of grown ups who don't seem very adult. |
| 523 | It is as brave to master pleasure as to overcome the enemy [Democritus (attr)] |
| Full Idea: The brave man is not only he who overcomes the enemy, but he who is stronger than pleasures. Some men are masters of cities, but are enslaved by women. | |
| From: Democritus (attrib) (reports [c.250 BCE], B214), quoted by John Stobaeus - Anthology 3.07.25 | |
| A reaction: I'm not sure if 'bravery' is the relevant virtue here.Sounds like self-control or temperance. I suspect that mastering a city is quite pleasurable, if that's your thing. |
| 503 | Virtue doesn't just avoid evil, but also doesn't desire it [Democritus (attr)] |
| Full Idea: Virtue consists, not in avoiding wrong-doing, but in having no wish thereto. | |
| From: Democritus (attrib) (reports [c.250 BCE], B062), quoted by John Stobaeus - Anthology 3.17.37 |
| 518 | A bad life is just a drawn-out death [Democritus (attr)] |
| Full Idea: To live badly is not just to live badly, but to spend a long time dying. | |
| From: Democritus (attrib) (reports [c.250 BCE], B160), quoted by (who?) - where? |
| 497 | Be virtuous from duty, not from fear [Democritus (attr)] |
| Full Idea: Refrain from crimes not through fear but through duty [deon]. | |
| From: Democritus (attrib) (reports [c.250 BCE], B041), quoted by John Stobaeus - Anthology 3.01.95 | |
| A reaction: [not sure about the translation here] |
| 499 | Repentance of shameful deeds is salvation [Democritus (attr)] |
| Full Idea: Repentance for shameful deeds is salvation in life. | |
| From: Democritus (attrib) (reports [c.250 BCE], B043) |
| 524 | Virtue comes more from practice than from nature [Democritus (attr)] |
| Full Idea: More men become good through practice than by nature. | |
| From: Democritus (attrib) (reports [c.250 BCE], B242), quoted by John Stobaeus - Anthology 3.29.66 |
| 519 | One must avoid even speaking of evil deeds [Democritus (attr)] |
| Full Idea: One must avoid even speaking of evil deeds. | |
| From: Democritus (attrib) (reports [c.250 BCE], B190), quoted by John Stobaeus - Anthology 3.01.91 |
| 500 | The wrongdoer is more unfortunate than the person wronged [Democritus (attr)] |
| Full Idea: The wrongdoer is more unfortunate than the man wronged. | |
| From: Democritus (attrib) (reports [c.250 BCE], B045) |
| 1539 | The endless desire for money is a crueller slavery than poverty [Democritus (attr)] |
| Full Idea: Unless a point of satiety is reached, the desire for money is far more cruel than the utmost poverty, because the greater the desire, the greater the need | |
| From: Democritus (attrib) (reports [c.250 BCE], B219), quoted by John Stobaeus - Anthology 3.10.43 |
| 526 | Small appetite makes poverty equal to wealth [Democritus (attr)] |
| Full Idea: Small appetite makes poverty equivalent to wealth. | |
| From: Democritus (attrib) (reports [c.250 BCE], B284), quoted by John Stobaeus - Anthology 4.33.24 |
| 511 | It is better to have one intelligent friend than many unintelligent [Democritus (attr)] |
| Full Idea: The friendship of one intelligent man is better than that of all the unintelligent. | |
| From: Democritus (attrib) (reports [c.250 BCE], B098) |
| 498 | It is a great thing, when one is in adversity, to think of duty [Democritus (attr)] |
| Full Idea: It is a great thing, when one is in adversity, to think of duty. | |
| From: Democritus (attrib) (reports [c.250 BCE], B042), quoted by John Stobaeus - Anthology 4.44.68 | |
| A reaction: Something wrong with the translation here, if there is no Greek word for 'duty'. |
| 1541 | It is better to be poor in a democracy than be rich without freedom [Democritus (attr)] |
| Full Idea: Poverty in a democracy is as preferable to what is called prosperity under autocracy as freedom is to slavery. | |
| From: Democritus (attrib) (reports [c.250 BCE], B251), quoted by John Stobaeus - Anthology 3.40.42 |