13 ideas
| 14970 | Normal system K has five axioms and rules [Cresswell] |
| Full Idea: Normal propositional modal logics derive from the minimal system K: wffs of PC are axioms; □(p⊃q)⊃(□p⊃□q); uniform substitution; modus ponens; necessitation (α→□α). | |
| From: Max J. Cresswell (Modal Logic [2001], 7.1) |
| 14971 | D is valid on every serial frame, but not where there are dead ends [Cresswell] |
| Full Idea: If a frame contains any dead end or blind world, then D is not valid on that frame, ...but D is valid on every serial frame. | |
| From: Max J. Cresswell (Modal Logic [2001], 7.1.1) |
| 14972 | S4 has 14 modalities, and always reduces to a maximum of three modal operators [Cresswell] |
| Full Idea: In S4 there are exactly 14 distinct modalities, and any modality may be reduced to one containing no more than three modal operators in sequence. | |
| From: Max J. Cresswell (Modal Logic [2001], 7.1.2) | |
| A reaction: The significance of this may be unclear, but it illustrates one of the rewards of using formal systems to think about modal problems. There is at least an appearance of precision, even if it is only conditional precision. |
| 14973 | In S5 all the long complex modalities reduce to just three, and their negations [Cresswell] |
| Full Idea: S5 contains the four main reduction laws, so the first of any pair of operators may be deleted. Hence all but the last modal operator may be deleted. This leaves six modalities: p, ◊p, □p, and their negations. | |
| From: Max J. Cresswell (Modal Logic [2001], 7.1.2) |
| 14976 | Reject the Barcan if quantifiers are confined to worlds, and different things exist in other worlds [Cresswell] |
| Full Idea: If one wants the quantifiers in each world to range only over the things that exist in that world, and one doesn't believe that the same things exist in every world, one would probably not want the Barcan formula. | |
| From: Max J. Cresswell (Modal Logic [2001], 7.2.2) | |
| A reaction: I haven't quite got this, but it sounds to me like I should reject the Barcan formula (but Idea 9449!). I like a metaphysics to rest on the actual world (with modal properties). I assume different things could have existed, but don't. |
| 14974 | A relation is 'Euclidean' if aRb and aRc imply bRc [Cresswell] |
| Full Idea: A relation is 'Euclidean' if aRb and aRc imply bRc. | |
| From: Max J. Cresswell (Modal Logic [2001], 7.1.2) | |
| A reaction: If a thing has a relation to two separate things, then those two things will also have that relation between them. If I am in the same family as Jim and as Jill, then Jim and Jill are in the same family. |
| 14975 | A de dicto necessity is true in all worlds, but not necessarily of the same thing in each world [Cresswell] |
| Full Idea: A de dicto necessary truth says that something is φ, that this proposition is a necessary truth, i.e. that in every accessible world something (but not necessarily the same thing in each world) is φ. | |
| From: Max J. Cresswell (Modal Logic [2001], 7.2.1) | |
| A reaction: At last, a really clear and illuminating account of this term! The question is then invited of what is the truthmaker for a de dicto truth, assuming that the objects themselves are truthmakers for de re truths. |
| 2170 | Homer does not distinguish between soul and body [Homer, by Williams,B] |
| Full Idea: Homer's descriptions of people did without a dualistic distinction between soul and body. | |
| From: report of Homer (The Iliad [c.850 BCE]) by Bernard Williams - Shame and Necessity II - p.23 |
| 2171 | The 'will' doesn't exist; there is just conclusion, then action [Homer, by Williams,B] |
| Full Idea: Homer left out another mental action lying between coming to a conclusion and acting on it; and he did well, since there is no such action, and the idea is the invention of bad philosophy. | |
| From: report of Homer (The Iliad [c.850 BCE]) by Bernard Williams - Shame and Necessity II - p.37 | |
| A reaction: This is a characteristically empiricist view, which is found in Hobbes. The 'will' seems to have a useful role in folk psychology. We can at least say that coming to a conclusion that I should act, and then actually acting, are not the same thing. |
| 15998 | Perfect love is not in spite of imperfections; the imperfections must be loved as well [Kierkegaard] |
| Full Idea: To love another in spite of his weaknesses and errors and imperfections is not perfect love. No, to love is to find him lovable in spite of, and together with, his weaknesses and errors and imperfections. | |
| From: Søren Kierkegaard (Works of Love [1847], p.158) | |
| A reaction: A true romantic at heart, Kierkegaard ideally posits perfect love as unconditional love, and not just of good attributes, predicates and conditions. However, the real question for both me and Kierkegaard is, is perfect love desirable or even possible?[SY] |
| 21819 | Plato says the Good produces the Intellectual-Principle, which in turn produces the Soul [Homer, by Plotinus] |
| Full Idea: In Plato the order of generation is from the Good, the Intellectual-Principle; from the Intellectual-Principle, the Soul. | |
| From: report of Homer (The Iliad [c.850 BCE], 509b) by Plotinus - The Enneads 5.1.08 | |
| A reaction: The doctrine of Plotinus merely echoes Plato, in that case, except that the One replaces the Form of the Good. Does this mean that what is first in Plotinus is less morally significant, and more concerned with reason and being? |
| 11388 | Let there be one ruler [Homer] |
| Full Idea: The rule of many is not good; let there be one ruler. | |
| From: Homer (The Iliad [c.850 BCE], 2.204), quoted by Vassilis Politis - Aristotle and the Metaphysics 8.9 | |
| A reaction: [Quoted by Aristotle at Metaphysics 1076a04] |
| 14829 | Homer so enjoys the company of the gods that he must have been deeply irreligious [Homer, by Nietzsche] |
| Full Idea: Homer is so at home among his gods, and takes such delight in them as a poet, that he surely must have been deeply irreligious. | |
| From: report of Homer (The Iliad [c.850 BCE]) by Friedrich Nietzsche - Human, All Too Human 125 | |
| A reaction: Blake made a similar remark about where the true allegiance of Milton lay in 'Paradise Lost'. |