12 ideas
13342 | Carnap defined consequence by contradiction, but this is unintuitive and changes with substitution [Tarski on Carnap] |
Full Idea: Carnap proposed to define consequence as 'sentence X follows from the sentences K iff the sentences K and the negation of X are contradictory', but 1) this is intuitively impossible, and 2) consequence would be changed by substituting objects. | |
From: comment on Rudolph Carnap (The Logical Syntax of Language [1934], p.88-) by Alfred Tarski - The Concept of Logical Consequence p.414 | |
A reaction: This seems to be the first step in the ongoing explicit discussion of the nature of logical consequence, which is now seen by many as the central concept of logic. Tarski brings his new tool of 'satisfaction' to bear. |
13251 | Each person is free to build their own logic, just by specifying a syntax [Carnap] |
Full Idea: In logic, there are no morals. Everyone is at liberty to build his own logic, i.e. his own form of language. All that is required is that he must state his methods clearly, and give syntactical rules instead of philosophical arguments. | |
From: Rudolph Carnap (The Logical Syntax of Language [1934], §17), quoted by JC Beall / G Restall - Logical Pluralism 7.3 | |
A reaction: This is understandable, but strikes me as close to daft relativism. If I specify a silly logic, I presume its silliness will be obvious. By what criteria? I say the world dictates the true logic, but this is a minority view. |
15086 | Absolute necessity might be achievable either logically or metaphysically [Hale] |
Full Idea: Maybe peaceful co-existence between absolute logical necessity and absolute metaphysical necessity can be secured, ..and absolute necessity is their union. ...However, a truth would then qualify as absolutely necessary in two quite different ways. | |
From: Bob Hale (Absolute Necessities [1996], 4) | |
A reaction: Hale is addressing a really big question for metaphysic (absolute necessity) which others avoid. In the end he votes for rejecting 'metaphysical' necessity. I am tempted to vote for rejecting logical necessity (as being relative). 'Absolute' is an ideal. |
8261 | Maybe not-p is logically possible, but p is metaphysically necessary, so the latter is not absolute [Hale] |
Full Idea: It might be metaphysically necessary that p but logically possible that not-p, so that metaphysical necessity is not, after all, absolute. | |
From: Bob Hale (Absolute Necessities [1996]), quoted by E.J. Lowe - The Possibility of Metaphysics 1.5 | |
A reaction: Lowe presents this as dilemma, but it sounds fine to me. Flying pigs etc. have no apparent logical problems, but I can't conceive of a possible world where pigs like ours fly in a world like ours. Earthbound pigs may be metaphysically necessary. |
15081 | A strong necessity entails a weaker one, but not conversely; possibilities go the other way [Hale] |
Full Idea: One type of necessity may be said to be 'stronger' than another when the first always entails the second, but not conversely. This will obtain only if the possibility of the first is weaker than the possibility of the second. | |
From: Bob Hale (Absolute Necessities [1996], 1) | |
A reaction: Thus we would normally say that if something is logically necessary (a very strong claim) then it will have to be naturally necessary. If something is naturally possible, then clearly it will have to be logically possible. Sounds OK. |
15080 | 'Relative' necessity is just a logical consequence of some statements ('strong' if they are all true) [Hale] |
Full Idea: Necessity is 'relative' if a claim of φ-necessary that p just claims that it is a logical consequence of some statements Φ that p. We have a 'strong' version if we add that the statements in Φ are all true, and a 'weak' version if not. | |
From: Bob Hale (Absolute Necessities [1996], 1) | |
A reaction: I'm not sure about 'logical' consequence here. It may be necessary that a thing be a certain way in order to qualify for some category (which would be 'relative'), but that seems like 'sortal' necessity rather than logical. |
15082 | Metaphysical necessity says there is no possibility of falsehood [Hale] |
Full Idea: Friends of metaphysical necessity would want to hold that when it is metaphysically necessary that p, there is no good sense of 'possible' (except, perhaps, an epistemic one) in which it is possible that not-p. | |
From: Bob Hale (Absolute Necessities [1996], 2) | |
A reaction: We might want to say which possible worlds this refers to (and presumably it won't just be in the actual world). The normal claim would refer to all possible worlds. Adding a '...provided that' clause moves it from absolute to relative necessity. |
15085 | 'Broadly' logical necessities are derived (in a structure) entirely from the concepts [Hale] |
Full Idea: 'Broadly' logical necessities are propositions whose truth derives entirely from the concepts involved in them (together, of course, with relevant structure). | |
From: Bob Hale (Absolute Necessities [1996], 3) | |
A reaction: Is the 'logical' part of this necessity bestowed by the concepts, or by the 'structure' (which I take to be a logical structure)? |
15088 | Logical necessities are true in virtue of the nature of all logical concepts [Hale] |
Full Idea: The logical necessities can be taken to be the propositions which are true in virtue of the nature of all logical concepts. | |
From: Bob Hale (Absolute Necessities [1996], p.10) | |
A reaction: This is part of his story of essences giving rise to necessities. His proposal sounds narrow, but logical concepts may have the highest degree of generality which it is possible to have. It must be how the concepts connect that causes the necessities. |
15087 | Conceptual necessities are made true by all concepts [Hale] |
Full Idea: Conceptual necessities can be taken to be propositions which are true in virtue of the nature of all concepts. | |
From: Bob Hale (Absolute Necessities [1996], p.9) | |
A reaction: Fine endorse essences for these concepts. Could we then come up with a new concept which contradicted all the others, and destroyed the necessity? Yes, presumably. Presumably witchcraft and astrology are full of 'conceptual necessities'. |
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. |