43 ideas
18261 | A simplification which is complete constitutes a definition [Kant] |
Full Idea: By dissection I can make the concept distinct only by making the marks it contains clear. That is what analysis does. If this analysis is complete ...and in addition there are not so many marks, then it is precise and so constitutes a definition. | |
From: Immanuel Kant (Wiener Logik [1795], p.455), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 1 'Conc' | |
A reaction: I think Aristotle would approve of this. We need to grasp that a philosophical definition is quite different from a lexicographical definition. 'Completeness' may involve quite a lot. |
9376 | A sentence may simultaneously define a term, and also assert a fact [Boghossian] |
Full Idea: It doesn't follow from the fact that a given sentence is being used to implicitly define one of its ingredient terms, that it is not a factual statement. 'This stick is a meter long at t' may define an ingredient terms and express something factual. | |
From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
A reaction: This looks like a rather good point, but it is tied in with a difficulty about definition, which is deciding which sentences are using a term, and which ones are defining it. If I say 'this stick in Paris is a meter long', I'm not defining it. |
14684 | A world is 'accessible' to another iff the first is possible according to the second [Salmon,N] |
Full Idea: A world w' is accessible to a consistent world w if and only if w' is possible in w. Being 'inaccessible to' or 'possible relative to' a consistent world is simply being possible according to that world, nothing more and nothing less. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], IV) | |
A reaction: More illuminating than just saying that w can 'see' w'. Accessibility is internal to worIds. It gives some connection to why we spend time examining modal logic. There is no more important metaphysical notion than what is possible according to actuality. |
14669 | For metaphysics, T may be the only correct system of modal logic [Salmon,N] |
Full Idea: Insofar as modal logic is concerned exclusively with the logic of metaphysical modality, ..T may well be the one and only (strongest) correct system of (first-order) propositional logic. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], Intro) | |
A reaction: This contrasts sharply with the orthodox view, that S5 (or at the very least S4) is the correct system for metaphysics. |
14692 | System B implies that possibly-being-realized is an essential property of the world [Salmon,N] |
Full Idea: Friends of B modal logic commit themselves to the loaded claim that it is logically true that the property of possibly being realized (or being a way things might have been) is an essential property of the world. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], V) | |
A reaction: I think this 'loaded' formulation captures quite nicely the dispositional view I favour, that the possibilities of the actual world are built into the actual world, and define its nature just as much as the 'categorial' facts do. |
14667 | System B has not been justified as fallacy-free for reasoning on what might have been [Salmon,N] |
Full Idea: Even the conventionally accepted system B, which is weaker than S5 and independent of S4, has not been adequately justified as a fallacy-free system of reasoning about what might have been. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], Intro) |
14668 | In B it seems logically possible to have both p true and p is necessarily possibly false [Salmon,N] |
Full Idea: The characteristic of B has the form φ⊃□◊φ. ...Even if these axioms are necessarily true, it seems logically possible for p to be true while the proposition that p is necessarily possible is at the same time false. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], Intro) |
14671 | What is necessary is not always necessarily necessary, so S4 is fallacious [Salmon,N] |
Full Idea: We can say of a wooden table that it would have been possible for it to have originated from some different matter, even though it is not actually possible. So what is necessary fails to be necessarily necessary, and S4 modal logic is fallacious. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], I) | |
A reaction: [compressed] |
14686 | S5 modal logic ignores accessibility altogether [Salmon,N] |
Full Idea: When we ignore accessibility altogether, we have finally zeroed in on S5 modal logic. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], IV) |
14691 | S5 believers say that-things-might-have-been-that-way is essential to ways things might have been [Salmon,N] |
Full Idea: Believers in S5 as a correct system of propositional reasoning about what might have been must claim that it is an essential property of any way things might have been that things might have been that way. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], V) | |
A reaction: Salmon is working in a view where you are probably safe to substitute 'necessary' for 'essential' without loss of meaning. |
14693 | The unsatisfactory counterpart-theory allows the retention of S5 [Salmon,N] |
Full Idea: Counterpart-theoretic modal semantics allows for the retention of S5 modal propositional logic, at a considerable cost. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], V n18) | |
A reaction: See the other ideas in this paper by Salmon for his general attack on S5 as the appropriate system for metaphysical necessity. He favours the very modest System T. |
14670 | Metaphysical (alethic) modal logic concerns simple necessity and possibility (not physical, epistemic..) [Salmon,N] |
Full Idea: Metaphysical modal logic concerns metaphysical (or alethic) necessity and metaphysical (alethic) possibility, or necessity and possibility tout court - as opposed to such other types of modality as physical necessity, epistemic necessity etc. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], Intro n2) |
22275 | Logic gives us the necessary rules which show us how we ought to think [Kant] |
Full Idea: In logic the question is not one of contingent but of necessary rules, not how to think, but how we ought to think. | |
From: Immanuel Kant (Wiener Logik [1795], p.16), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 02 'Trans' | |
A reaction: Presumably it aspires to the objectivity of a single correct account of how we all ought to think. I'm sympathetic to that, rather than modern cultural relativism about reason. Logic is rooted in nature, not in arbitrary convention. |
9375 | Conventionalism agrees with realists that logic has truth values, but not over the source [Boghossian] |
Full Idea: Conventualism is a factualist view: it presupposes that sentences of logic have truth values. It differs from a realist view in its conception of the source of those truth values, not on their existence. I call the denial of truths Non-Factualism. | |
From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
A reaction: It barely seems to count as truth is we say 'p is true because we say so'. It is a truth about an agreement, not a truth about logic. Driving on the left isn't a truth about which side of the road is best. |
14678 | Any property is attached to anything in some possible world, so I am a radical anti-essentialist [Salmon,N] |
Full Idea: By admitting possible worlds of unlimited variation and recombination, I simply abandon true metaphysical essentialism. By my lights, any property is attached to anything in some possible world or other. I am a closet radical anti-essentialist. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], II) | |
A reaction: Salmon includes impossible worlds within his scheme of understanding. It strikes me that this is metaphysical system which tells us nothing about how things are: it is sort of 'logical idealist'. Later he talks of 'we essentialists'. |
14680 | Logical possibility contains metaphysical possibility, which contains nomological possibility [Salmon,N] |
Full Idea: Just as nomological possibility is a special kind of metaphysical possibility, so metaphysical possibility is a special kind of logical possibility. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], III) | |
A reaction: This is the standard view of how the three types of necessity are nested. He gives a possible counterexample in footnote 7. |
14685 | Metaphysical necessity is NOT truth in all (unrestricted) worlds; necessity comes first, and is restricted [Salmon,N] |
Full Idea: A mythology gave us the idea that metaphysical necessity is truth in every world whatsoever, without restriction. But the notion of metaphysical modality comes first, and, like every notion of modality, it is restricted. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], IV) |
14690 | In the S5 account, nested modalities may be unseen, but they are still there [Salmon,N] |
Full Idea: The S5 theorist's miscontrual of English (in the meaning of 'possibly possible') makes nested modality unseen, but it does not make nested modality vanish. Inaccessible worlds are still worlds. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], IV) |
14688 | Without impossible worlds, the unrestricted modality that is metaphysical has S5 logic [Salmon,N] |
Full Idea: If one confines one's sights to genuinely possible worlds, disavowing the impossible worlds, then metaphysical modality emerges as the limiting case - the 'unrestricted' modality that takes account of 'every' world - and S5 emerges as its proper logic. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], IV) | |
A reaction: He observes that this makes metaphysical modality 'restricted' simply because you have restricted what 'all worlds' means. Could there be non-maximal worlds? Are logical and metaphysical modality coextensive? I think I like the S5 view. |
14677 | Metaphysical necessity is said to be unrestricted necessity, true in every world whatsoever [Salmon,N] |
Full Idea: It is held that it is the hallmark of metaphysical necessity is that it is completely unrestricted, the limiting case of restricted necessity, with no restrictions whatever. A proposition is necessary only if it is true in absolutely every world whatever. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], II) | |
A reaction: This is the standard picture which leads to the claim that S5 modal logic is appropriate for metaphysical necessity, because there are no restrictions on accessibility. Salmon raises objections to this conventional view. |
14679 | Bizarre identities are logically but not metaphysically possible, so metaphysical modality is restricted [Salmon,N] |
Full Idea: Though there is a way things logically could be according to which I am a credit card account, there is no way things metaphysically might be according to which I am a credit card account. This illustrates the restricted nature of metaphysical modality. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], III) | |
A reaction: His drift is that metaphyical modality is restricted, but expressing it in S5 modal logic (where all worlds see one another) makes it unrestricted, so S5 logic is wrong for metaphysics. I'm impressed by his arguments. |
14681 | Logical necessity is free of constraints, and may accommodate all of S5 logic [Salmon,N] |
Full Idea: With its freedom from the constraint of metaphysical possibility, logical necessity may be construed as accommodating all the axioms and rules of S5. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], III) | |
A reaction: He goes on to raise problems for this simple thought. The big question: what are the limits of what is actually possible? Compare: what are the limits of what is imaginable? what are the limits of what is meaningfully sayable? |
14676 | Nomological necessity is expressed with intransitive relations in modal semantics [Salmon,N] |
Full Idea: Intransitive relations are introduced into modal semantics for the purposes of interpreting various 'real' or restricted types of modalities, such as nomological necessity. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], II) | |
A reaction: The point here is that the (so-called) 'laws of nature' are held to change from world to world, so necessity in one could peter out in some more remote world, rather than being carried over everywhere. A very Humean view of such things. |
14689 | Necessity and possibility are not just necessity and possibility according to the actual world [Salmon,N] |
Full Idea: The real meanings of the simple modal terms 'necessary' and 'possible' are not the same as the concepts of actual necessity and actual possibility, necessity and possibility according to the actual world. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], IV) | |
A reaction: If you were an 'actualist' (who denies everything except the actual world) then you are unlikely to agree with this. In unrestricted possible worlds, being true in one world makes it possible in all worlds. So actual necessity is possible everywhere. |
14674 | Impossible worlds are also ways for things to be [Salmon,N] |
Full Idea: Total ways things cannot be are also 'worlds', or maximal ways for things to be. They are impossible worlds. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], I) | |
A reaction: This unorthodox view doesn't sound too plausible to me. To think of a circular square as a 'way things could be' sounds pretty empty, and mere playing with words. The number 7 could be the Emperor of China? |
14682 | Denial of impossible worlds involves two different confusions [Salmon,N] |
Full Idea: Every argument I am aware of against impossible worlds confuses ways for things to be with ways things might have been, or worse, confuses ways things cannot be with ways for things to be that cannot exist - or worse yet, commits both errors. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], III) | |
A reaction: He is claiming that 'ways for things to be' allows impossible worlds, whereas 'ways things might have been' appears not to. (I think! Read the paragraph yourself!) |
14687 | Without impossible worlds, how things might have been is the only way for things to be [Salmon,N] |
Full Idea: If one ignores impossible worlds, then ways things might have been are the only ways for things to be that are left. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], IV) | |
A reaction: Impossible worlds are included in 'ways for things to be', but excluded from 'ways things might have been'. I struggle with a circle being square as a 'way for circles to be'. I suppose being the greatest philosopher is a way for me to be. |
14683 | Possible worlds rely on what might have been, so they can' be used to define or analyse modality [Salmon,N] |
Full Idea: On my conception, the notions of metaphysical necessity and possibility are not defined or analyzed in terms of the apparatus of possible worlds. The order of analysis is just the reverse: possible worlds rely on the notion of what might have been. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], IV) | |
A reaction: This view seems to be becoming the new orthodoxy, and I certainly agree with it. I have no idea how you can begin to talk about possible worlds if you don't already have some idea of what 'possible' means. |
14675 | Possible worlds just have to be 'maximal', but they don't have to be consistent [Salmon,N] |
Full Idea: As far as I can tell, worlds need not be logically consistent. The only restriction on worlds is that they must be (in some sense) 'maximal' ways for things to be. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], I) | |
A reaction: The normal idea of a maximal model is that it must contain either p or ¬p, and not both, so I don't think I understand this thought, but I pass it on. |
14672 | Possible worlds are maximal abstract ways that things might have been [Salmon,N] |
Full Idea: I conceive of possible worlds as certain sorts of maximal abstract entities according to which certain things (facts, states of affairs) obtain and certain other things do not obtain. They are total ways things might have been. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], I) |
14673 | You can't define worlds as sets of propositions, and then define propositions using worlds [Salmon,N] |
Full Idea: It is not a good idea to think of possible worlds as sets of propositions, and at the same time to think of propositions as sets of possible worlds. | |
From: Nathan Salmon (The Logic of What Might Have Been [1989], I n3) | |
A reaction: Salmon favours thinking of worlds as sets of propositions, and hence rejects the account of propositions as sets of worlds. He favours the 'Russellian' view of propositions, which seem to me to be the same as 'facts'. |
9369 | 'Snow is white or it isn't' is just true, not made true by stipulation [Boghossian] |
Full Idea: Isn't it overwhelmingly obvious that 'Either snow is white or it isn't' was true before anyone stipulated a meaning for it, and that it would have been true even if no one had thought about it, or chosen it to be expressed by one of our sentences? | |
From: Paul Boghossian (Analyticity Reconsidered [1996], §I) | |
A reaction: Boghossian would have to believe in propositions (unexpressed truths) to hold this - which he does. I take the notion of truth to only have relevance when there are minds around. Otherwise the so-called 'truths' are just the facts. |
9367 | The a priori is explained as analytic to avoid a dubious faculty of intuition [Boghossian] |
Full Idea: The central impetus behind the analytic explanation of the a priori is a desire to explain the possibility of a priori knowledge without having to postulate a special evidence-gathering faculty of intuition. | |
From: Paul Boghossian (Analyticity Reconsidered [1996], §I) | |
A reaction: I don't see at all why one has to postulate a 'faculty' in order to talk about intuition. I take an intuition to be an apprehension of a probable truth, combined with an inability to articulate how the conclusion was arrived at. |
9373 | That logic is a priori because it is analytic resulted from explaining the meaning of logical constants [Boghossian] |
Full Idea: The analytic theory of the apriority of logic arose indirectly, as a by-product of the attempt to explain in what a grasp of the meaning of the logical constants consists. | |
From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
A reaction: Preumably he is referring to Wittgenstein's anguish over the meaning of the word 'not' in his World War I notebooks. He first defined the constants by truth tables, then asserted that they were purely conventional - so logic is conventional. |
9380 | We can't hold a sentence true without evidence if we can't agree which sentence is definitive of it [Boghossian] |
Full Idea: If there is no sentence I must hold true if it is to mean what it does, then there is no basis on which to argue that I am entitled to hold it true without evidence. | |
From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
A reaction: He is exploring Quine's view. Truth by convention depends on agreeing which part of the usage of a term constitutes its defining sentence(s), and that may be rather tricky. Boghossian says this slides into the 'dreaded indeterminacy of meaning'. |
9384 | We may have strong a priori beliefs which we pragmatically drop from our best theory [Boghossian] |
Full Idea: It is consistent with a belief's being a priori in the strong sense that we should have pragmatic reasons for dropping it from our best overall theory. | |
From: Paul Boghossian (Analyticity Reconsidered [1996], n 6) | |
A reaction: Does 'dropping it' from the theory mean just ignoring it, or actually denying it? C.I. Lewis is the ancestor of this view. Could it be our 'best' theory, while conflicting with beliefs that were strongly a priori? Pragmatism can embrace falsehoods. |
9374 | If we learn geometry by intuition, how could this faculty have misled us for so long? [Boghossian] |
Full Idea: If we learn geometrical truths by intuition, how could this faculty have misled us for so long? | |
From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
A reaction: This refers to the development of non-Euclidean geometries, though the main misleading concerns parallels, which involves infinity. Boghossian cites 'distance' as a concept the Euclideans had misunderstood. Why shouldn't intuitions be wrong? |
18260 | If we knew what we know, we would be astonished [Kant] |
Full Idea: If we only know what we know ...we would be astonished by the treasures contained in our knowledge. | |
From: Immanuel Kant (Wiener Logik [1795], p.843), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 1 'Conc' | |
A reaction: Nice remark. He doesn't require immediat recall of knowledge. You can't be required to know that you know something. That doesn't imply externalism, though. I believe in securely founded internal knowledge which is hard to recall. |
9378 | If meaning depends on conceptual role, what properties are needed to do the job? [Boghossian] |
Full Idea: Conceptual Role Semantics must explain what properties an inference or sentence involving a logical constant must have, if that inference or sentence is to be constitutive of its meaning. | |
From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
A reaction: This is my perennial request that if something is to be defined by its function (or role), we must try to explain what properties it has that make its function possible, and those properties will be the more basic explanation. |
9377 | 'Conceptual role semantics' says terms have meaning from sentences and/or inferences [Boghossian] |
Full Idea: 'Conceptual role semantics' says the logical constants mean what they do by virtue of figuring in certain inferences and/or sentences involving them and not others, ..so some inferences and sentences are constitutive of an expression's meaning. | |
From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
A reaction: If the meaning of the terms derives from the sentences in which they figure, that seems to be meaning-as-use. The view that it depends on the inferences seems very different, and is a more interesting but more risky claim. |
9372 | Could expressions have meaning, without two expressions possibly meaning the same? [Boghossian] |
Full Idea: Could there be a fact of the matter about what each expression means, but no fact of the matter about whether they mean the same? | |
From: Paul Boghossian (Analyticity Reconsidered [1996], §II) | |
A reaction: He is discussing Quine's attack on synonymy, and his scepticism about meaning. Boghossian and I believe in propositions, so we have no trouble with two statements having the same meaning. Denial of propositions breeds trouble. |
17721 | There are no truths in virtue of meaning, but there is knowability in virtue of understanding [Boghossian, by Jenkins] |
Full Idea: Boghossian distinguishes metaphysical analyticity (truth purely in virtue of meaning, debunked by Quine, he says) from epistemic analyticity (knowability purely in virtue of understanding - a notion in good standing). | |
From: report of Paul Boghossian (Analyticity Reconsidered [1996]) by Carrie Jenkins - Grounding Concepts 2.4 | |
A reaction: [compressed] This fits with Jenkins's claim that we have a priori knowledge just through understanding and relating our concepts. She, however, rejects that idea that a priori is analytic. |
9368 | Epistemological analyticity: grasp of meaning is justification; metaphysical: truth depends on meaning [Boghossian] |
Full Idea: The epistemological notion of analyticity: a statement is 'true by virtue of meaning' provided that grasp of its meaning alone suffices for justified belief in its truth; the metaphysical reading is that it owes its truth to its meaning, not to facts. | |
From: Paul Boghossian (Analyticity Reconsidered [1996], §I) | |
A reaction: Kripke thinks it is neither, but is a purely semantic notion. How could grasp of meaning alone be a good justification if it wasn't meaning which was the sole cause of the statement's truth? I'm not convinced by his distinction. |