37 ideas
| 19504 | My modus ponens might be your modus tollens [Pritchard,D] |
| Full Idea: One philosopher's modus ponens is another philosopher's modus tollens. | |
| From: Duncan Pritchard (Epistemological Disjunctivism [2012], 3.§2) | |
| A reaction: [Anyone know the originator of this nice thought?] You say A is true, and A proves B, so B is true. I reply that if A proves something as daft as B, then so much the worse for A. Ain't it the truth? |
| 9470 | Modal logic is not an extensional language [Parsons,C] |
| Full Idea: Modal logic is not an extensional language. | |
| From: Charles Parsons (A Plea for Substitutional Quantification [1971], p.159 n8) | |
| A reaction: [I record this for investigation. Possible worlds seem to contain objects] |
| 10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
| Full Idea: The main objection to the axiom of choice was that it had to be given by some law or definition, but since sets are arbitrary this seems irrelevant. Formalists consider it meaningless, but set-theorists consider it as true, and practically obvious. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §3) |
| 13418 | The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C] |
| Full Idea: The difficulties historically attributed to the axiom of choice are probably better ascribed to the law of excluded middle. | |
| From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2) | |
| A reaction: The law of excluded middle was a target for the intuitionists, so presumably the debate went off in that direction. |
| 10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
| Full Idea: One can distinguish at least two quite different senses of logic: as an instrument of demonstration, and perhaps as an instrument for the characterization of structures. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: This is trying to capture the proof-theory and semantic aspects, but merely 'characterizing' something sounds like a rather feeble aspiration for the semantic side of things. Isn't it to do with truth, rather than just rule-following? |
| 10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
| Full Idea: Elementary logic cannot characterize the usual mathematical structures, but seems to be distinguished by its completeness. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
| Full Idea: The expressive power of second-order logic is too great to admit a proof procedure, but is adequate to express set-theoretical statements, and open questions such as the continuum hypothesis or the existence of big cardinals are easily stated. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
| Full Idea: In sentential logic there is a simple proof that all truth functions, of any number of arguments, are definable from (say) 'not' and 'and'. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §0) | |
| A reaction: The point of 'say' is that it can be got down to two connectives, and these are just the usual preferred pair. |
| 10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
| Full Idea: The symbols ∀ and ∃ may, to start with, be regarded as extrapolations of the truth functional connectives ∧ ('and') and ∨ ('or') to infinite domains. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §5) |
| 9469 | Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C] |
| Full Idea: I argue (against Quine) that the existential quantifier substitutionally interpreted has a genuine claim to express a concept of existence, which may give the best account of linguistic abstract entities such as propositions, attributes, and classes. | |
| From: Charles Parsons (A Plea for Substitutional Quantification [1971], p.156) | |
| A reaction: Intuitively I have my doubts about this, since the whole thing sounds like a verbal and conventional game, rather than anything with a proper ontology. Ruth Marcus and Quine disagree over this one. |
| 9468 | On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C] |
| Full Idea: For the substitutional interpretation of quantifiers, a sentence of the form '(∃x) Fx' is true iff there is some closed term 't' of the language such that 'Ft' is true. For the objectual interpretation some object x must exist such that Fx is true. | |
| From: Charles Parsons (A Plea for Substitutional Quantification [1971], p.156) | |
| A reaction: How could you decide if it was true for 't' if you didn't know what object 't' referred to? |
| 10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
| Full Idea: One might add to one's logic an 'uncountable quantifier', or a 'Chang quantifier', or a 'two-argument quantifier', or 'Shelah's quantifier', or 'branching quantifiers'. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §3) | |
| A reaction: [compressed - just listed for reference, if you collect quantifiers, like collecting butterflies] |
| 10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
| Full Idea: Skolem deduced from the Löwenheim-Skolem theorem that 'the absolutist conceptions of Cantor's theory' are 'illusory'. I think it is clear that this conclusion would not follow even if elementary logic were in some sense the true logic, as Skolem assumed. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §7) | |
| A reaction: [Tharp cites Skolem 1962 p.47] Kit Fine refers to accepters of this scepticism about the arithmetic of infinities as 'Skolemites'. |
| 10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
| Full Idea: The Löwenheim-Skolem property seems to be undesirable, in that it states a limitation concerning the distinctions the logic is capable of making, such as saying there are uncountably many reals ('Skolem's Paradox'). | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
| Full Idea: Soundness would seem to be an essential requirement of a proof procedure, since there is little point in proving formulas which may turn out to be false under some interpretation. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10763 | Completeness and compactness together give axiomatizability [Tharp] |
| Full Idea: Putting completeness and compactness together, one has axiomatizability. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §1) |
| 10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
| Full Idea: In general, if completeness fails there is no algorithm to list the valid formulas. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: I.e. the theory is not effectively enumerable. |
| 10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
| Full Idea: It is strange that compactness is often ignored in discussions of philosophy of logic, since the most important theories have infinitely many axioms. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: An example of infinite axioms is the induction schema in first-order Peano Arithmetic. |
| 10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
| Full Idea: The compactness condition seems to state some weakness of the logic (as if it were futile to add infinitely many hypotheses). To look at it another way, formalizations of (say) arithmetic will admit of non-standard models. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
| Full Idea: A complete logic has an effective enumeration of the valid formulas. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
| Full Idea: Despite completeness, the mere existence of an effective enumeration of the valid formulas will not, by itself, provide knowledge. For example, one might be able to prove that there is an effective enumeration, without being able to specify one. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: The point is that completeness is supposed to ensure knowledge (of what is valid but unprovable), and completeness entails effective enumerability, but more than the latter is needed to do the key job. |
| 17447 | Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck] |
| Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal. | |
| From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3 | |
| A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'. |
| 18201 | General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C] |
| Full Idea: The existence of very general principles in mathematics are universally regarded as obvious, where on an empiricist view one would expect them to be bold hypotheses, about which a prudent scientist would maintain reserve. | |
| From: Charles Parsons (Mathematical Intuition [1980], p.152), quoted by Penelope Maddy - Naturalism in Mathematics | |
| A reaction: This is mainly aimed at Quine's and Putnam's indispensability (to science) argument about mathematics. |
| 13419 | If functions are transfinite objects, finitists can have no conception of them [Parsons,C] |
| Full Idea: The finitist may have no conception of function, because functions are transfinite objects. | |
| From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §4) | |
| A reaction: He is offering a view of Tait's. Above my pay scale, but it sounds like a powerful objection to the finitist view. Maybe there is a finitist account of functions that could be given? |
| 13417 | If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C] |
| Full Idea: If experience shows that some aspect of the physical world fails to instantiate a certain mathematical structure, one will modify the theory by sustituting a different structure, while the original structure doesn't lose its status as part of mathematics. | |
| From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2) | |
| A reaction: This seems to be a beautifully simple and powerful objection to the Quinean idea that mathematics somehow only gets its authority from physics. It looked like a daft view to begin with, of course. |
| 19503 | An improbable lottery win can occur in a nearby possible world [Pritchard,D] |
| Full Idea: Low probability events such as lottery wins can occur in nearby possible worlds. | |
| From: Duncan Pritchard (Epistemological Disjunctivism [2012], 2.n2) | |
| A reaction: This seems to ruin any chance of mapping probabilities and counterfactuals in the neat model of nested possible worlds (like an onion). [Lewis must have thought of this, surely? - postcards, please] |
| 19505 | Moore begs the question, or just offers another view, or uses 'know' wrongly [Pritchard,D, by PG] |
| Full Idea: The three main objections to Moore's common-sense refutation of scepticism is that it either begs the question, or it just offers a rival view instead of a refutation, or it uses 'know' in a conversationally inappropriate way. | |
| From: report of Duncan Pritchard (Epistemological Disjunctivism [2012], 3.§2) by PG - Db (ideas) | |
| A reaction: [I deserve applause for summarising two pages of Pritchard's wordy stuff so neatly] |
| 19499 | We can have evidence for seeing a zebra, but no evidence for what is entailed by that [Pritchard,D] |
| Full Idea: The closure principle forces us to regard Zula as knowing that what she is looking at is not a cleverly disguised mule, and yet she doesn't appear to have any supporting evidence for this knowledge. | |
| From: Duncan Pritchard (Epistemological Disjunctivism [2012], 2.§3) | |
| A reaction: [Zula observes a zebra in the zoo] Entailment is a different type of justification from perception. If we add fallibilism to the mix, then fallibility can increase as we pursue a string of entailments. But proper logic, of course, should not be fallible. |
| 19500 | Favouring: an entailment will give better support for the first belief than reason to deny the second [Pritchard,D] |
| Full Idea: The Favouring Principle says that if S knows two things, and that the first entails the second, then S has better evidence in support of her belief in the first than she has for denying the second. | |
| From: Duncan Pritchard (Epistemological Disjunctivism [2012], 2.§3) | |
| A reaction: [his version is full of Greek letters, but who wants that stuff?] Pritchard concludes that if you believe in the closure principle then you should deny the favouring principle. |
| 19502 | Maybe knowledge just needs relevant discriminations among contrasting cases [Pritchard,D] |
| Full Idea: According to the 'contrastivist' proposal knowledge is to be understood as essentially involving discrimination, such that knowing a proposition boils down to having the relevant discriminatory capacities. | |
| From: Duncan Pritchard (Epistemological Disjunctivism [2012], 2.§6) | |
| A reaction: Pritchard says this isn't enough, and we must also to be aware of supporting favouring evidence. I would focus on the concept of coherence, even for simple perceptual knowledge. If I see a hawk in England, that's fine. What if I 'see' a vulture? |
| 19498 | Epistemic internalism usually says justification must be accessible by reflection [Pritchard,D] |
| Full Idea: Typically, internal epistemic conditions are characterised in terms of a reflective access requirement. | |
| From: Duncan Pritchard (Epistemological Disjunctivism [2012], 1.§6) | |
| A reaction: If your justification is straightforwardly visual, it is unclear what the difference would be between seeing the thing and having reflective access to the seeing. |
| 19506 | Externalism is better than internalism in dealing with radical scepticism [Pritchard,D] |
| Full Idea: Standard epistemic internalism faces an uphill struggle when it comes to dealing with radical scepticism, which points in favour of epistemic externalist neo-Mooreanism. | |
| From: Duncan Pritchard (Epistemological Disjunctivism [2012], 3.§3) | |
| A reaction: I incline towards internalism. I deal with scepticism by being a fallibilist, and adding 'but you never know' to every knowledge claim, and then getting on with life. |
| 19496 | Disjunctivism says perceptual justification must be both factual and known by the agent [Pritchard,D] |
| Full Idea: Slogan for disjunctivism: perceptual knowledge is paradigmatically constituted by a true belief whose epistemic support is both factive (i.e. it entails the truth of the propositions believed) and reflectively accessible to the agent. | |
| From: Duncan Pritchard (Epistemological Disjunctivism [2012], Intro) | |
| A reaction: I'm not a fan of externalism, but it could be that the factive bit achieves the knowledge, and then being able to use and answer for that knowledge may just be a bonus, and not an essential ingredient. |
| 19497 | Metaphysical disjunctivism says normal perceptions and hallucinations are different experiences [Pritchard,D] |
| Full Idea: Metaphysical disjunctivists hold that veridical perceptual experiences are not essentially the same as the experiences involved in corresponding cases involving illusion and (especially) hallucination. | |
| From: Duncan Pritchard (Epistemological Disjunctivism [2012], 1.§4) | |
| A reaction: Metaphysical disjunctivism concerns what the experiences are; epistemological justification concerns the criteria of justification. I think. I wish Pritchard would spell things out more clearly. Indeed, I wish all philosophers would. |
| 19495 | Epistemic externalism struggles to capture the idea of epistemic responsibility [Pritchard,D] |
| Full Idea: A fundamental difficulty for epistemic externalist positions is that it is hard on this view to capture any adequate notion of epistemic responsibility. | |
| From: Duncan Pritchard (Epistemological Disjunctivism [2012], Intro) | |
| A reaction: He never explains the 'responsibility', but I presume that would be like an expert witness in court, vouching for their knowledge. |
| 19501 | We assess error against background knowledge, but that is just what radical scepticism challenges [Pritchard,D] |
| Full Idea: When faced with an error-possibility we can appeal to background knowledge, as long as the error-possibility does not call into question this background knowledge. The same is not true when we focus on the radical sceptical hypothesis. | |
| From: Duncan Pritchard (Epistemological Disjunctivism [2012], 2.§5) | |
| A reaction: [reworded] Doubting everything simultaneously just looks like a mad project. If you doubt linguistic meaning, you can't even express your doubts. |
| 19507 | Radical scepticism is merely raised, and is not a response to worrying evidence [Pritchard,D] |
| Full Idea: Crucially, radical sceptical error-possibilities are never epistemically motivated, but are instead merely raised. | |
| From: Duncan Pritchard (Epistemological Disjunctivism [2012], 3.§5) | |
| A reaction: In 'The Matrix' someone sees a glitch in the software (a cat crossing a passageway), and that would have to be taken seriously. Otherwise it is a nice strategy to ask why the sceptic is raising this bizzare possibility, without evidence. |