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All the ideas for 'True Method in Philosophy and Theology', 'comedies (frags)' and 'Logical Necessity'

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19 ideas

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
The logic of metaphysical necessity is S5 [Rumfitt]
     Full Idea: It is a widely accepted thesis that the logic of metaphysical necessity is S5.
     From: Ian Rumfitt (Logical Necessity [2010], §5)
     A reaction: Rumfitt goes on to defend this standard view (against Dummett's defence of S4). The point, I take it, is that one can only assert that something is 'true in all possible worlds' only when the worlds are all accessible to one another.
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
Soundness in argument varies with context, and may be achieved very informally indeed [Rumfitt]
     Full Idea: Our ordinary standards for deeming arguments to be sound vary greatly from context to context. Even the package tourist's syllogism ('It's Tuesday, so this is Belgium') may meet the operative standards for soundness.
     From: Ian Rumfitt (Logical Necessity [2010], Intro)
     A reaction: No doubt one could spell out the preconceptions of package tourist reasoning, and arrive at the logical form of the implication which is being offered.
There is a modal element in consequence, in assessing reasoning from suppositions [Rumfitt]
     Full Idea: There is a modal element in consequence, in its applicability to assessing reasoning from suppositions.
     From: Ian Rumfitt (Logical Necessity [2010], §2)
We reject deductions by bad consequence, so logical consequence can't be deduction [Rumfitt]
     Full Idea: A rule is to be rejected if it enables us to deduce from some premisses a purported conclusion that does not follow from them in the broad sense. The idea that deductions answer to consequence is incomprehensible if consequence consists in deducibility.
     From: Ian Rumfitt (Logical Necessity [2010], §2)
5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B' [Rumfitt]
     Full Idea: Overt contradictions include formal contradictions of form 'B and not B', but I also take them to include 'This is red all over and green all over' and 'This is red and not coloured'.
     From: Ian Rumfitt (Logical Necessity [2010], Intro)
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths) [Rumfitt]
     Full Idea: The geometrical style of formalization of logic is now little more than a quaint anachronism, largely because it fails to show logical truths for what they are: simply by-products of rules of inference that are applicable to suppositions.
     From: Ian Rumfitt (Logical Necessity [2010], §1)
     A reaction: This is the rejection of Russell-style axiom systems in favour of Gentzen-style natural deduction systems (starting from rules). Rumfitt quotes Dummett in support.
7. Existence / A. Nature of Existence / 6. Criterion for Existence
What is not active is nothing [Leibniz]
     Full Idea: We can now show from the inner truths of metaphysics that what is not active is nothing.
     From: Gottfried Leibniz (True Method in Philosophy and Theology [1686], p.64)
     A reaction: This is Leibniz's rebellion against the Cartesian idea that all that matters for natural existence is spatial extension. I agree (tentatively) with Leibniz's vision of nature here. Modern physics reveals a seething turmoil beneath the placid exterior.
9. Objects / C. Structure of Objects / 6. Constitution of an Object
Additional or removal of any part changes a thing, so people are never the same person [Epicharmus]
     Full Idea: If you add or take away a pebble, the same number does not remain. If you add to a length or cut off from it, the former measure does not remain. So human beings grow or waste away. Both you and I were, and shall be, other men.
     From: Epicharmus (comedies (frags) [c.470 BCE], B02), quoted by Diogenes Laertius - Lives of Eminent Philosophers 03.12
     A reaction: [The original is in dialogue form from a play. The context is a joke about not paying a debt.] Note the early date for this metaphysical puzzle. My new favourite reply is Chrysippus's Idea 16059; identity actually requires change.
10. Modality / A. Necessity / 3. Types of Necessity
A distinctive type of necessity is found in logical consequence [Rumfitt, by Hale/Hoffmann,A]
     Full Idea: Rumfitt argues that there is a distinctive notion of necessity implicated in the notion of logical consequence.
     From: report of Ian Rumfitt (Logical Necessity [2010]) by Bob Hale/ Aviv Hoffmann - Introduction to 'Modality' 2
10. Modality / A. Necessity / 6. Logical Necessity
Logical necessity is when 'necessarily A' implies 'not-A is contradictory' [Rumfitt]
     Full Idea: By the notion of 'logical necessity' I mean that there is a sense of 'necessary' for which 'It is necessary that A' implies and is implied by 'It is logically contradictory that not A'. ...From this, logical necessity is implicated in logical consequence.
     From: Ian Rumfitt (Logical Necessity [2010], Intro)
     A reaction: Rumfitt expresses a commitment to classical logic at this point. We will need to be quite sure what we mean by 'contradiction', which will need a clear notion of 'truth'....
A logically necessary statement need not be a priori, as it could be unknowable [Rumfitt]
     Full Idea: There is no reason to suppose that any statement that is logically necessary (in the present sense) is knowable a priori. ..If a statement is logically necessary, its negation will yield a contradiction, but that does not imply that someone could know it.
     From: Ian Rumfitt (Logical Necessity [2010], §2)
     A reaction: This remark is aimed at Dorothy Edgington, who holds the opposite view. Rumfitt largely defends McFetridge's view (q.v.).
Narrow non-modal logical necessity may be metaphysical, but real logical necessity is not [Rumfitt]
     Full Idea: While Fine suggests defining a narrow notion of logical necessity in terms of metaphysical necessity by 'restriction' (to logical truths that can be defined in non-modal terms), this seems unpromising for broad logical necessity, which is modal.
     From: Ian Rumfitt (Logical Necessity [2010], §2)
     A reaction: [compressed] He cites Kit Fine 2002. Rumfitt glosses the non-modal definitions as purely formal. The metaphysics lurks somewhere in the proof.
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
If a world is a fully determinate way things could have been, can anyone consider such a thing? [Rumfitt]
     Full Idea: A world is usually taken to be a fully determinate way that things could have been; but then one might seriously wonder whether anyone is capable of 'considering' such a thing at all.
     From: Ian Rumfitt (Logical Necessity [2010], §4)
     A reaction: This has always worried me. If I say 'maybe my coat is in the car', I would hate to think that I had to be contemplating some entire possible world (including all the implications of my coat not being on the hat stand).
13. Knowledge Criteria / E. Relativism / 1. Relativism
A dog seems handsome to another a dog, and even a pig to another pig [Epicharmus]
     Full Idea: Dog seems very handsome to dog, and ox to ox, and donkey very handsome to donkey, and even pig to pig.
     From: Epicharmus (comedies (frags) [c.470 BCE], B05), quoted by (who?) - where?
22. Metaethics / C. The Good / 3. Pleasure / f. Dangers of pleasure
Pleasures are like pirates - if you are caught they drown you in a sea of pleasures [Epicharmus]
     Full Idea: Pleasures for mortals are like impious pirates, for the man who is caught by pleasures is immediately drowned in a sea of them.
     From: Epicharmus (comedies (frags) [c.470 BCE], B44), quoted by (who?) - where?
     A reaction: Not all slopes are slippery. Plenty of people hold themselves to strict rules about alcohol or gambling. People have occasional treats.
23. Ethics / B. Contract Ethics / 1. Contractarianism
Hands wash hands; give that you may get [Epicharmus]
     Full Idea: The hand washes the hand; give something and you may get something.
     From: Epicharmus (comedies (frags) [c.470 BCE], B30), quoted by (who?) - where?
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
Against a villain, villainy is not a useless weapon [Epicharmus]
     Full Idea: Against a villain, villainy is not a useless weapon.
     From: Epicharmus (comedies (frags) [c.470 BCE], B32), quoted by (who?) - where?
28. God / A. Divine Nature / 3. Divine Perfections
God knows everything, and nothing is impossible for him [Epicharmus]
     Full Idea: Nothing escapes the divine, this you must realise. God himself is our overseer, and nothing is impossible for him.
     From: Epicharmus (comedies (frags) [c.470 BCE], B23), quoted by (who?) - where?
29. Religion / D. Religious Issues / 3. Problem of Evil / c. Human Error
Human logos is an aspect of divine logos, and is sufficient for successful living [Epicharmus]
     Full Idea: Man has calculation, but there is also the divine logos. But human logos is sprung from the divine logos, and it brings to each man his means of life, and his maintenance.
     From: Epicharmus (comedies (frags) [c.470 BCE], B57), quoted by (who?) - where?