39 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? |
| 3340 | Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn] |
| Full Idea: Von Neumann defines each number as the set of all smaller numbers. | |
| From: report of John von Neumann (works [1935]) by Simon Blackburn - Oxford Dictionary of Philosophy p.280 |
| 15943 | Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann] |
| Full Idea: Von Neumann's Limitation of Size axiom is not self-evident, and he himself admitted that it seemed too strong. | |
| From: comment on John von Neumann (An Axiomatization of Set Theory [1925]) by Shaughan Lavine - Understanding the Infinite VII.1 |
| 3355 | Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA] |
| Full Idea: Von Neumann suggested that functions be pressed into service to replace sets. | |
| From: report of John von Neumann (works [1935]) by José A. Benardete - Metaphysics: the logical approach Ch.23 |
| 13489 | Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD] |
| Full Idea: Von Neumann's decision was to start with the ordinals and to treat cardinals as a special sort of ordinal. | |
| From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by William D. Hart - The Evolution of Logic 3 | |
| A reaction: [see Hart 73-74 for an explication of this] |
| 22716 | Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone] |
| Full Idea: At age twenty, Von Neumann devised the formal definition of ordinal numbers that is used today: an ordinal number is the set of all smaller ordinal numbers. | |
| From: report of John von Neumann (works [1935]) by William Poundstone - Prisoner's Dilemma 02 'Sturm' | |
| A reaction: I take this to be an example of an impredicative definition (not predicating something new), because it uses 'ordinal number' in the definition of ordinal number. I'm guessing the null set gets us started. |
| 12336 | A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou] |
| Full Idea: In Von Neumann's definition an ordinal is a transitive set in which all of the elements are transitive. | |
| From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Alain Badiou - Briefings on Existence 11 |
| 18179 | For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy] |
| Full Idea: For Von Neumann the successor of n is n U {n} (rather than Zermelo's successor, which is {n}). | |
| From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Penelope Maddy - Naturalism in Mathematics I.2 n8 |
| 18180 | Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann] |
| Full Idea: Von Neumann's version of the natural numbers is in fact preferred because it carries over directly to the transfinite ordinals. | |
| From: comment on John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Penelope Maddy - Naturalism in Mathematics I.2 n9 |
| 15925 | Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine] |
| Full Idea: Each Von Neumann ordinal number is the set of its predecessors. ...He had shown how to introduce ordinal numbers as sets, making it possible to use them without leaving the domain of sets. | |
| From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Shaughan Lavine - Understanding the Infinite V.3 |
| 13672 | All the axioms for mathematics presuppose set theory [Neumann] |
| Full Idea: There is no axiom system for mathematics, geometry, and so forth that does not presuppose set theory. | |
| From: John von Neumann (An Axiomatization of Set Theory [1925]), quoted by Stewart Shapiro - Foundations without Foundationalism 8.2 | |
| A reaction: Von Neumann was doubting whether set theory could have axioms, and hence the whole project is doomed, and we face relativism about such things. His ally was Skolem in this. |
| 21812 | Being is the product of pure intellect [Plotinus] |
| Full Idea: Intellectual-Principle [Nous] by its intellective act establishes Being. | |
| From: Plotinus (The Enneads [c.245], 5.1.04) | |
| A reaction: This is a surprising view - that there is something which is prior to Being - but I take it to be Plotinus giving primacy to Plato's Form of the Good (a pure ideal), ahead of the One of Parmenides (which is Being). |
| 21817 | The One does not exist, but is the source of all existence [Plotinus] |
| Full Idea: The First is no member of existence, but can be the source of all. | |
| From: Plotinus (The Enneads [c.245], 5.1.07) | |
| A reaction: The First is the One, and this explicitly denies that it has Being. This answers the self-predication problem of Forms. Plato thought the Form of the Beautiful was beautiful, but it can't be (because of the regress). The source of existence can't exist. |
| 21824 | The One is a principle which transcends Being [Plotinus] |
| Full Idea: There exists a principle which transcends Being; this the One. | |
| From: Plotinus (The Enneads [c.245], 5.1.10) | |
| A reaction: The idea that the One transcends Being is the distinctive Plotinus doctrine. He defends the view that this was also the view of Anaxagoras, Empedocles and Plato. |
| 21813 | Number determines individual being [Plotinus] |
| Full Idea: Number is the determinant of individual being. | |
| From: Plotinus (The Enneads [c.245], 5.1.05) | |
| A reaction: You might have thought that number was the consequence of the individualities (or units) within being, but not so. You can't get more platonic than saying that the idealised numbers are the source of the particular units. |
| 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. |
| 5506 | If soul was like body, its parts would be separate, without communication [Plotinus] |
| Full Idea: If the soul had the nature of the body, it would have isolated members each unaware of the condition of the other;..there would be a particular soul as a distinct entity to each local experience, so a multiplicity of souls would administer an individual. | |
| From: Plotinus (The Enneads [c.245], 4.2.2), quoted by R Martin / J Barresi - Introduction to 'Personal Identity' p.15 | |
| A reaction: Of course, the modern 'modularity of mind' theory does suggest that we are run by a team, but a central co-ordinator is required, with a full communication network across the modules. |
| 21827 | The movement of Soul is continuous, but we are only aware of the parts of it that are sensed [Plotinus] |
| Full Idea: The Soul maintains its unfailing movement; for not all that passes in the soul is, by that fact, perceptible; we know just as much as impinges on the faculty of the sense. | |
| From: Plotinus (The Enneads [c.245], 5.1.12) | |
| A reaction: This is a straightforward argument in favour of an unconscious aspect to the mind - and a rather good argument too. No one thinks that our minds ever stop working, even in sleep. |
| 21828 | A person is the whole of their soul [Plotinus] |
| Full Idea: Man is not merely a part (the higher part) of the Soul but the total. | |
| From: Plotinus (The Enneads [c.245], 5.1.12) | |
| A reaction: The soul is psuche, which includes the vegetative soul. The higher part is normally taken to be reason. This seems pretty close to John Locke's view of the matter. |
| 21809 | Our soul has the same ideal nature as the oldest god, and is honourable above the body [Plotinus] |
| Full Idea: Our own soul is of that same ideal nature [as the oldest god of them all], so that to consider it, purified, freed from all accruement, is to recognise in ourselves which we have found soul to be, honourable above the body. For what is body but earth? | |
| From: Plotinus (The Enneads [c.245], 5.1.02) | |
| A reaction: The strongest versions of substance dualism are religious in character, because the separateness of the mind elevates us above the grubby physical character of the world. I'm with Nietzsche on this one - this view is actually harmful to us. |
| 21825 | The soul is outside of all of space, and has no connection to the bodily order [Plotinus] |
| Full Idea: We may not seek any point in space in which to seat the soul; it must be set outside of all space; its distinct quality, its separateness, its immateriality, demand that it be a thing alone, untouched by all of the bodily order. | |
| From: Plotinus (The Enneads [c.245], 5.1.10) | |
| A reaction: You can't get more dualist than that. He doesn't seem bothered about the interaction problem. He likens such influence to the radiation of the sun, rather than to physical movement. |
| 21826 | The Soul reasons about the Right, so there must be some permanent Right about which it reasons [Plotinus] |
| Full Idea: Since there is a Soul which reasons upon the right and good - for reasoning is an enquiry into the rightness and goodness of this rather than that - there must exist some pemanent Right, the source and foundation of this reasoning in our soul. | |
| From: Plotinus (The Enneads [c.245], 5.1.11) | |
| A reaction: This is pretty close the Kant's concept of 'the moral order within me', and Plotinus even sees it as rational. Presumably this right is 'permanent' because the revelatlons of reason about it are necessary truths. |
| 6922 | Ecstasy is for the neo-Platonist the highest psychological state of man [Plotinus, by Feuerbach] |
| Full Idea: Ecstasy or rapture is for the neo-Platonist the highest psychological state of man. | |
| From: report of Plotinus (The Enneads [c.245]) by Ludwig Feuerbach - Principles of Philosophy of the Future §29 | |
| A reaction: See Bernini's statue of St Theresa. Personally I find this very unappealing because of its utter irrationality, but what is the 'highest' human psychological state? Doing mental arithmetic? Doing what is morally right? Dignity under pressure? |
| 21814 | How can multiple existence arise from the unified One? [Plotinus] |
| Full Idea: The problem endlessly debated is how, from such a unity as we have declared the One to be, does anything at all come into substantial existence, any multiplicity, dyad or number? | |
| From: Plotinus (The Enneads [c.245], 5.1.06) | |
| A reaction: This was precisely Aristotle's objection to the One of Parmenides, and especially the problem of the source of movement (which Plotinus also notices). |
| 21816 | Soul is the logos of Nous, just as Nous is the logos of the One [Plotinus] |
| Full Idea: The soul is an utterance [logos] and act of the Intellectual-Principle [Nous], as that is an utterance and act of the One. | |
| From: Plotinus (The Enneads [c.245], 5.1.06) | |
| A reaction: Being only comes into the picture at the secondary Nous stage. Nous is the closest to the modern concept of God. |
| 21815 | Because the One is immobile, it must create by radiation, light the sun producing light [Plotinus] |
| Full Idea: Given this immobility of the Supreme ...what happened then? It must be a circumradiation, which may be compared to the brilliant light encircling the sun and ceaselessly generating from that unchanging substance, | |
| From: Plotinus (The Enneads [c.245], 5.1.06) | |
| A reaction: This is the answer given to the problem raised in Idea 21814. The sun produces energy, without apparent movement. Not an answer that will satisfy a physicist, but an interesting answer. |
| 21808 | Soul is author of all of life, and of the stars, and it gives them law and movement [Plotinus] |
| Full Idea: Soul is the author of all living things, ...it has breathed life into them all, whatever is nourished by earth and sea, the divine stars in the sky; ...it is the principle distinct from all of these to which it gives law and movement and life. | |
| From: Plotinus (The Enneads [c.245], 5.1.02) | |
| A reaction: This seems to derive from Anaxagoras, who is mentioned by Plotinus. The soul he refers to his not the same as our concept of God. Note the word 'law', which I am guessing is nomos. Not, I think, modern laws of nature, but closer to guidelines. |
| 21811 | Even the soul is secondary to the Intellectual-Principle [Nous], of which soul is an utterance [Plotinus] |
| Full Idea: Soul, for all the worth we have shown to belong to it, is yet a secondary, an image of the Intellectual-Principle [Nous]; reason uttered is an image of reason stored within the soul, and similarly soul is an utterance of the Intellectual-Principle. | |
| From: Plotinus (The Enneads [c.245], 5.1.03) | |
| A reaction: It then turns out that Nous is secondary to the One, so there is a hierarchy of Being (which only enters at the Nous stage). |