13 ideas
| 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 |
| 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 |
| 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. |
| 7630 | Ryle's dichotomy between knowing how and knowing that is too simplistic [Maund] |
| Full Idea: There is a convincing claim that we need to leave behind Ryle's dichotomy between knowing how and knowing that as being too simplistic. | |
| From: Barry Maund (Perception [2003], Ch. 2) | |
| A reaction: [John Campbell is mentioned as source of this idea] I find this proposal immediately appealing. I was taught that riding a bicycle shows the division, as hardly anyone knows the theory, but I am sure children need some propositional information. |
| 7632 | Perception is sensation-then-concept, or direct-concepts, or sensation-saturated-in-concepts [Maund] |
| Full Idea: Three forms of (cognitive) direct realism are: two stages - non-conceptual sensory experience, then a non-sensory conceptual state; directly acquiring non-sensuous conceptual states; and sensuous states saturated with concepts. | |
| From: Barry Maund (Perception [2003], Ch. 3) | |
| A reaction: [First: Reid, Dretske, Evans, Sellars. Second: Armstrong, Heil, Pitcher, Clark. Third: Kant, McDowell, Strawson, McGinn, Searle]. I find the first one plausible, because of the ambiguity in language, and because unusual experiences separate them. |
| 7635 | Sense-data have an epistemological purpose (foundations) and a metaphysical purpose (explanation) [Maund] |
| Full Idea: Sense-data have an epistemological purpose (to serve as foundations on which the edifice of knowledge is to be constructed), and a metaphysical purpose (to provide an accurate account of the phenomenology of perceptual experience). | |
| From: Barry Maund (Perception [2003], Ch. 6) | |
| A reaction: This is very important, because there is a real danger (e.g. in Russell) that the epistemological convenience of sense-data for giving reliability in knowledge means that we are too quick in making the assumption that they actually exist. |
| 7638 | One thesis says we are not aware of qualia, but only of objects and their qualities [Maund] |
| Full Idea: The representationalist/intentionalist thesis about perception is that we are not aware of the intrinsic qualities of experience in normal perception; we are instead aware of those objects and their qualities that are specified in the content. | |
| From: Barry Maund (Perception [2003], Ch. 9) | |
| A reaction: If secondary qualities are in the mind, not in objects, how come people always thought they were in objects? Answer: because this thesis is right? The primary mode of the mind is projected outwards, though we can introspect about colours. [Dretske] |
| 7642 | The Myth of the Given claims that thought is rationally supported by non-conceptual experiences [Maund] |
| Full Idea: The so-called 'myth of the given' is the view that conceptual content can be rationally supported by experiences construed as states with non-conceptual content. | |
| From: Barry Maund (Perception [2003], Ch.10) | |
| A reaction: The myth is attacked by Sellars and McDowell, the latter claiming that concepts must be embedded in the experiences. Maybe only realism is required to make the Given work. The experiences are definitely of something, and off we go... |
| 7640 | Mountains are adverbial modifications of the earth, but still have object-characteristics [Maund] |
| Full Idea: Metaphysically, mountains are only adverbial modifications of the Earth's belt. They have no existence independent of being part of the earth. Yet for all that, they have some rather strong 'object'-characteristics. | |
| From: Barry Maund (Perception [2003], Ch.10) | |
| A reaction: The point being that you don't give up all the advantages of a sense-data view if you switch to adverbialism. I'm not convinced by the analogy, but we can only be aware of adverbial qualities if they have causal powers. |
| 7641 | Adverbialism tries to avoid sense-data and preserve direct realism [Maund] |
| Full Idea: The two primary motivations of the adverbialist analysis are thought to be to avoid commitment to sensory particulars such as sense-data, and to allow us to hold on to a version of direct realism. | |
| From: Barry Maund (Perception [2003], Ch.10) | |
| A reaction: Maund says that the adverbialist's fears about indirect/representative theories are unfounded. My feeling is that neither account will do the job properly once we get a better account of consciousness. Maybe adverbialism is only for secondary qualities. |
| 7637 | Thought content is either satisfaction conditions, or exercise of concepts [Maund, by PG] |
| Full Idea: The content of thought can either be expressed as satisfaction conditions (e.g. truth-conditions for beliefs), or as the exercise of at least two concepts. | |
| From: report of Barry Maund (Perception [2003], Ch. 8) by PG - Db (ideas) | |
| A reaction: I think I favour the first view, because not all conjunctions of concepts would count as thoughts (e.g. rhubarb-plus-contradiction). A bunch of concepts becomes a thought when it connects in some way to reality? |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |