21 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? |
| 17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
| Full Idea: The facts of geometry order themselves into a geometry, the facts of arithmetic into a theory of numbers, the facts of statics, electrodynamics into a theory of statics, electrodynamics, or the facts of the physics of gases into a theory of gases. | |
| From: David Hilbert (Axiomatic Thought [1918], [03]) | |
| A reaction: This is the confident (I would say 'essentialist') view of axioms, which received a bit of a setback with Gödel's Theorems. I certainly agree that the world proposes an order to us - we don't just randomly invent one that suits us. |
| 17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
| Full Idea: If a theory is to serve its purpose of orienting and ordering, it must first give us an overview of the independence and dependence of its propositions, and second give a guarantee of the consistency of all of the propositions. | |
| From: David Hilbert (Axiomatic Thought [1918], [09]) | |
| A reaction: Gödel's Second theorem showed that the theory can never prove its own consistency, which made the second Hilbert requirement more difficult. It is generally assumed that each of the axioms must be independent of the others. |
| 17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
| Full Idea: It is necessary to study the essence of mathematical proof itself if one wishes to answer such questions as the one about decidability in a finite number of operations. | |
| From: David Hilbert (Axiomatic Thought [1918], [53]) |
| 17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
| Full Idea: The linearity of the equation of the plane and of the orthogonal transformation of point-coordinates is completely adequate to produce the whole broad science of spatial Euclidean geometry purely by means of analysis. | |
| From: David Hilbert (Axiomatic Thought [1918], [05]) | |
| A reaction: This remark comes from the man who succeeded in producing modern axioms for geometry (in 1897), so he knows what he is talking about. We should not be wholly pessimistic about Hilbert's ambitious projects. He had to dig deeper than this idea... |
| 17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
| Full Idea: The laws of calculation and the rules of integers suffice for the construction of number theory. | |
| From: David Hilbert (Axiomatic Thought [1918], [05]) | |
| A reaction: This is the confident Hilbert view that the whole system can be fully spelled out. Gödel made this optimism more difficult. |
| 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. |
| 21513 | We can no more expect a precise definition of coherence than we can of the moral ideal [Ewing] |
| Full Idea: I think it is wrong to tie down the advocates of the coherence theory to a precise definition. ...It would be altogether unreasonable to demand that the moral ideal should be exhaustively defined, and the same may be true of the ideal of thought. | |
| From: A.C. Ewing (Idealism: a critical survey [1934], p.231), quoted by Erik J. Olsson - Against Coherence 7.6 | |
| A reaction: I strongly agree. It is not a council of despair. I think the criteria of coherence can be articulated quite well (e.g by Thagard), and the virtues of enquiry can also be quite well specified (e.g. by Zagzebski). Very dissimilar evidence must cohere. |
| 21497 | If undetailed, 'coherence' is just a vague words that covers all possible arguments [Ewing] |
| Full Idea: Without a detailed account, coherence is reduced to the mere muttering of the word 'coherence', which can be interpreted so as to cover all arguments, but only by making its meaning so wide as to rob it of almost all significance. | |
| From: A.C. Ewing (Idealism: a critical survey [1934], p.246), quoted by Erik J. Olsson - Against Coherence 2.2 | |
| A reaction: I'm a fan of coherence, but it is a placeholder, involving no intrinsic or detailed theory. I just think it points to the reality of how we make judgements, especially practical ones. We can categorise the inputs, and explain the required virtues. |
| 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. |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
| Full Idea: By pushing ahead to ever deeper layers of axioms ...we also win ever-deeper insights into the essence of scientific thought itself, and become ever more conscious of the unity of our knowledge. | |
| From: David Hilbert (Axiomatic Thought [1918], [56]) | |
| A reaction: This is the less fashionable idea that scientific essentialism can also be applicable in the mathematic sciences, centring on the project of axiomatisation for logic, arithmetic, sets etc. |