19 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? |
| 8921 | Structuralism is now common, studying relations, with no regard for what the objects might be [Hellman] |
| Full Idea: With developments in modern mathematics, structuralist ideas have become commonplace. We study 'abstract structures', having relations without regard to the objects. As Hilbert famously said, items of furniture would do. | |
| From: Geoffrey Hellman (Structuralism [2007], §1) | |
| A reaction: Hilbert is known as a Formalist, which suggests that modern Structuralism is a refined and more naturalist version of the rather austere formalist view. Presumably the sofa can't stand for six, so a structural definition of numbers is needed. |
| 8698 | Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend] |
| Full Idea: The modal structuralist thinks of mathematical structures as possibilities. The application of mathematics is just the realisation that a possible structure is actualised. As structures are possibilities, realist ontological problems are avoided. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Michèle Friend - Introducing the Philosophy of Mathematics 4.3 | |
| A reaction: Friend criticises this and rejects it, but it is appealing. Mathematics should aim to be applicable to any possible world, and not just the actual one. However, does the actual world 'actualise a mathematical structure'? |
| 9557 | Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara] |
| Full Idea: Hellman represents statements of pure mathematics as elliptical for modal conditionals of a certain sort. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Charles Chihara - A Structural Account of Mathematics 5.3 | |
| A reaction: It's a pity there is such difficulty in understanding conditionals (see Graham Priest on the subject). I intuit a grain of truth in this, though I take maths to reflect the structure of the actual world (with possibilities being part of that world). |
| 10263 | Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman] |
| Full Idea: The usual way to show that a sentence is possible is to show that it has a model, but for Hellman presumably a sentence is possible if it might have a model (or if, possibly, it has a model). It is not clear what this move brings us. | |
| From: comment on Geoffrey Hellman (Mathematics without Numbers [1989]) by Stewart Shapiro - Philosophy of Mathematics 7.3 | |
| A reaction: I can't assess this, but presumably the possibility of the model must be demonstrated in some way. Aren't all models merely possible, because they are based on axioms, which seem to be no more than possibilities? |
| 8922 | Maybe mathematical objects only have structural roles, and no intrinsic nature [Hellman] |
| Full Idea: There is the tantalizing possibility that perhaps mathematical objects 'have no nature' at all, beyond their 'structural role'. | |
| From: Geoffrey Hellman (Structuralism [2007], §1) | |
| A reaction: This would fit with a number being a function rather than an object. We are interested in what cars do, not the bolts that hold them together? But the ontology of mathematics is quite separate from how you do mathematics. |
| 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. |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
| Full Idea: Anaxarchus said that he was not even sure that he knew nothing. | |
| From: report of Anaxarchus (fragments/reports [c.340 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.10.1 |
| 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. |