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All the ideas for 'fragments/reports', 'The Logic of What Might Have Been' and 'The Rise of Analytic Philosophy 1879-1930'

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45 ideas

2. Reason / D. Definition / 8. Impredicative Definition
Impredicative definitions are circular, but fine for picking out, rather than creating something [Potter]
     Full Idea: The circularity in a definition where the property being defined is used in the definition is now known as 'impredicativity'. ...Some cases ('the tallest man in the room') are unproblematic, as they pick him out, and don't conjure him into existence.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 07 'Impred')
     A reaction: [part summary]
3. Truth / A. Truth Problems / 2. Defining Truth
The Identity Theory says a proposition is true if it coincides with what makes it true [Potter]
     Full Idea: The Identity Theory of truth says a proposition is true just in case it coincides with what makes it true.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 23 'Abs')
     A reaction: The obvious question is how 'there are trees in the wood' can somehow 'coincide with' or 'be identical to' the situation outside my window. The theory is sort of right, but we will never define the relationship, which is no better than 'corresponds'.
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
It has been unfortunate that externalism about truth is equated with correspondence [Potter]
     Full Idea: There has been an unfortunate tendency in the secondary literature to equate externalism about truth with the correspondence theory.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 65 'Truth')
     A reaction: Quite helpful to distinguish internalist from externalist theories of truth. It is certainly the case that robust externalist views of truth have unfortunately been discredited merely because the correspondence account is inadequate.
4. Formal Logic / D. Modal Logic ML / 2. Tools of Modal Logic / b. Terminology of ML
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.
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / d. System T
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.
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / f. System B
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)
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)
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.
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
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]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
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)
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.
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.
4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
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)
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
Frege's sign |--- meant judgements, but the modern |- turnstile means inference, with intecedents [Potter]
     Full Idea: Natural deduction systems generally depend on conditional proof, but for Frege everything is asserted unconditionally. The modern turnstile |- is allowed to have antecedents, and hence to represent inference rather than Frege's judgement sign |---.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 03 'Axioms')
     A reaction: [compressed] Shockingly, Frege's approach seems more psychological than the modern approach. I would say that the whole point of logic is that it has to be conditional, because the truth of the antecedents is irrelevant.
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Deductivism can't explain how the world supports unconditional conclusions [Potter]
     Full Idea: Deductivism is a good account of large parts of mathematics, but stumbles where mathematics is directly applicable to the world. It fails to explain how we detach the antecedent so as to arrive at unconditional conclusions.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 12 'Deduc')
     A reaction: I suppose the reply would be that we have designed deductive structures which fit our understanding of reality - so it is all deductive, but selected pragmatically.
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Modern logical truths are true under all interpretations of the non-logical words [Potter]
     Full Idea: In the modern definition, a 'logical truth' is true under every interpretation of the non-logical words it contains.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 19 'Frege's')
     A reaction: What if the non-logical words are nonsense, or are used inconsistently ('good'), or ambiguously ('bank'), or vaguely ('bald'), or with unsure reference ('the greatest philosopher' becomes 'Bentham')? What qualifies as an 'interpretation'?
6. Mathematics / C. Sources of Mathematics / 7. Formalism
The formalist defence against Gödel is to reject his metalinguistic concept of truth [Potter]
     Full Idea: Gödel's theorem does not refute formalism outright, because the committed formalist need not recognise the metalinguistic notion of truth to which the theorem appeals.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 45 'Log')
     A reaction: The theorem was prior to Tarski's account of truth. Potter says Gödel avoided explicit mention of truth because of this problem. In general Gödel showed that there are truths outside the formal system (which is all provable).
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
Why is fictional arithmetic applicable to the real world? [Potter]
     Full Idea: Fictionalists struggle to explain why arithmetic is applicable to the real world in a way that other stories are not.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 21 'Math')
     A reaction: We know why some novels are realistic and others just the opposite. If a novel aimed to 'model' the real world it would be even closer to it. Fictionalists must explain why some fictions are useful.
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
If 'concrete' is the negative of 'abstract', that means desires and hallucinations are concrete [Potter]
     Full Idea: The word 'concrete' is often used as the negative of 'abstract', with the slightly odd consequence that desires and hallucinations are thereby classified as concrete.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 12 'Numb')
     A reaction: There is also the even more baffling usage of 'abstract' for the most highly generalised mathematics, leaving lower levels as 'concrete'. I favour the use of 'generalised' wherever possible, rather than 'abstract'.
8. Modes of Existence / A. Relations / 4. Formal Relations / c. Ancestral relation
'Greater than', which is the ancestral of 'successor', strictly orders the natural numbers [Potter]
     Full Idea: From the successor function we can deduce its ancestral, the 'greater than' relation, which is a strict total ordering of the natural numbers. (Frege did not mention this, but Dedekind worked it out, when expounding definition by recursion).
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 07 'Def')
     A reaction: [compressed]
9. Objects / D. Essence of Objects / 15. Against Essentialism
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'.
10. Modality / A. Necessity / 3. Types of Necessity
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.
10. Modality / A. Necessity / 5. Metaphysical Necessity
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)
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.
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.
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.
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)
10. Modality / A. Necessity / 6. Logical Necessity
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?
10. Modality / A. Necessity / 7. Natural Necessity
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.
10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals
A material conditional cannot capture counterfactual reasoning [Potter]
     Full Idea: What the material conditional most significantly fails to capture is counterfactual reasoning.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 04 'Sem')
     A reaction: The point is that counterfactuals say 'if P were the case (which it isn't), then Q'. But that means P is false, and in the material conditional everything follows from a falsehood. A reinterpretation of the conditional might embrace counterfactuals.
10. Modality / C. Sources of Modality / 5. Modality from Actuality
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.
10. Modality / E. Possible worlds / 1. Possible Worlds / b. Impossible worlds
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?
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!)
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.
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
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.
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
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)
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.
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / c. Worlds as propositions
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'.
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
Knowledge from a drunken schoolteacher is from a reliable and unreliable process [Potter]
     Full Idea: Knowledge might result from a reliable and an unreliable process. ...Is something knowledge if you were told it by a drunken schoolteacher?
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 66 'Rel')
     A reaction: Nice example. The listener must decide which process to rely on. But how do you decide that, if not by assessing the likely truth of what you are being told? It could be a bad teacher who is inspired by drink.
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
Traditionally there are twelve categories of judgement, in groups of three [Potter]
     Full Idea: The traditional categorisation of judgements (until at least 1800) was as universal, particular or singular; as affirmative, negative or infinite; as categorical, hypothetical or disjunctive; or as problematic, assertoric or apodictic.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 02 'Trans')
     A reaction: Arranging these things in neat groups of three seems to originate with the stoics. Making distinctions like this is very much the job of a philosopher, but arranging them in neat equinumerous groups is intellectual tyranny.
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
The phrase 'the concept "horse"' can't refer to a concept, because it is saturated [Potter]
     Full Idea: Frege's mirroring principle (that the structure of thoughts mirrors that of language) has the uncomfortable consequence that since the phrase 'the concept "horse"' is saturated, it cannot refer to something unsaturated, which includes concepts.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 16 'Conc')
19. Language / C. Assigning Meanings / 4. Compositionality
Compositionality should rely on the parsing tree, which may contain more than sentence components [Potter]
     Full Idea: Compositionality is best seen as saying the semantic value of a string is explained by the strings lower down its parsing tree. It is unimportant whether a string is always parsed in terms of its own substrings.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 05 'Sem')
     A reaction: That is, the analysis must explain the meaning, but the analysis can contain more than the actual ingredients of the sentence (which would be too strict).
'Direct compositonality' says the components wholly explain a sentence meaning [Potter]
     Full Idea: Some authors urge the strong notion of 'direct compositionality', which requires that the content of a sentence be explained in terms of the contents of the component parts of that very sentence.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 05 'Sem')
     A reaction: The alternative is that meaning is fully explained by an analysis, but that may contain more than the actual components of the sentence.
Compositionality is more welcome in logic than in linguistics (which is more contextual) [Potter]
     Full Idea: The principle of compositionality is more popular among philosophers of logic than of language, because the subtle context-sensitivity or ordinary language makes providing a compositional semantics for it a daunting challenge.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 21 'Lang')
     A reaction: Logicians love breaking complex entities down into simple atomic parts. Linguistics tries to pin down something much more elusive.
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]
     Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice.
     From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where?