39 ideas
| 12330 | In ontology, logic dominated language, until logic was mathematized [Badiou] |
| Full Idea: From Aristotle to Hegel, logic was the philosophical category of ontology's dominion over language. The mathematization of logic has authorized language to become that which seizes philosophy for itself. | |
| From: Alain Badiou (Briefings on Existence [1998], 8) |
| 12318 | The female body, when taken in its entirety, is the Phallus itself [Badiou] |
| Full Idea: The female body, when taken in its entirety, is the Phallus itself. | |
| From: Alain Badiou (Briefings on Existence [1998]) | |
| A reaction: Too good to pass over, too crazy to file sensibly, too creepy to have been filed under humour, my candidate for the weirdest remark I have ever read in a serious philosopher, but no doubt if you read Lacan etc for long enough it looks deeply wise. |
| 12325 | Philosophy has been relieved of physics, cosmology, politics, and now must give up ontology [Badiou] |
| Full Idea: Philosophy has been released from, even relieved of, physics, cosmology, and politics, as well as many other things. It is important for it to be released from ontology per se. | |
| From: Alain Badiou (Briefings on Existence [1998], 3) | |
| A reaction: A startling proposal, for anyone who thought that ontology was First Philosophy. Badiou wants to hand ontology over to mathematicians, but I am unclear what remains for the philosophers to do. |
| 12324 | Consensus is the enemy of thought [Badiou] |
| Full Idea: Consensus is the enemy of thought. | |
| From: Alain Badiou (Briefings on Existence [1998], 2) | |
| A reaction: A nice slogan for bringing Enlightenment optimists to a halt. I am struck. Do I allow my own thinking to always be diverted towards something which might result in a consensus? Do I actually (horror!) prefer consensus to truth? |
| 4901 | Truth has to be correspondence to facts, and a match between relations of ideas and relations in the world [Perry] |
| Full Idea: I think knowledge and truth are a matter of correspondence to facts, despite all the energy spent showing the naïveté of this view. The connections of our ideas in our heads correspond to relations in the outside world. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §8.1) | |
| A reaction: Yes. Modern books offer the difficulties of defining 'correspondence', and finding an independent account of 'facts', as conclusive objections, but I say a brain is a truth machine, and it had better be useful. Indefinability doesn't nullify concepts. |
| 12337 | There is 'transivity' iff membership ∈ also means inclusion ⊆ [Badiou] |
| Full Idea: 'Transitivity' signifies that all of the elements of the set are also parts of the set. If you have α∈Β, you also have α⊆Β. This correlation of membership and inclusion gives a stability which is the sets' natural being. | |
| From: Alain Badiou (Briefings on Existence [1998], 11) |
| 12321 | The axiom of choice must accept an indeterminate, indefinable, unconstructible set [Badiou] |
| Full Idea: The axiom of choice actually amounts to admitting an absolutely indeterminate infinite set whose existence is asserted albeit remaining linguistically indefinable. On the other hand, as a process, it is unconstructible. | |
| From: Alain Badiou (Briefings on Existence [1998], 2) | |
| A reaction: If only constructible sets are admitted (see 'V = L') then there is a contradiction. |
| 12342 | Topos theory explains the plurality of possible logics [Badiou] |
| Full Idea: Topos theory explains the plurality of possible logics. | |
| From: Alain Badiou (Briefings on Existence [1998], 14) | |
| A reaction: This will because logic will have a distinct theory within each 'topos'. |
| 12341 | Logic is a mathematical account of a universe of relations [Badiou] |
| Full Idea: Logic should first and foremost be a mathematical thought of what a universe of relations is. | |
| From: Alain Badiou (Briefings on Existence [1998], 14) |
| 12335 | Numbers are for measuring and for calculating (and the two must be consistent) [Badiou] |
| Full Idea: Number is an instance of measuring (distinguishing the more from the less, and calibrating data), ..and a figure for calculating (one counts with numbers), ..and it ought to be a figure of consistency (the compatibility of order and calculation). | |
| From: Alain Badiou (Briefings on Existence [1998], 11) |
| 12334 | There is no single unified definition of number [Badiou] |
| Full Idea: Apparently - and this is quite unlike old Greek times - there is no single unified definition of number. | |
| From: Alain Badiou (Briefings on Existence [1998], 11) |
| 12333 | Each type of number has its own characteristic procedure of introduction [Badiou] |
| Full Idea: There is a heterogeneity of introductory procedures of different classical number types: axiomatic for natural numbers, structural for ordinals, algebraic for negative and rational numbers, topological for reals, mainly geometric for complex numbers. | |
| From: Alain Badiou (Briefings on Existence [1998], 11) |
| 12322 | Must we accept numbers as existing when they no longer consist of units? [Badiou] |
| Full Idea: Do we have to confer existence on numbers whose principle is to no longer consist of units? | |
| From: Alain Badiou (Briefings on Existence [1998], 2) | |
| A reaction: This very nicely expresses what seems to me perhaps the most important question in the philosophy of mathematics. I am reluctant to accept such 'unitless' numbers, but I then feel hopelessly old-fashioned and naïve. What to do? |
| 12327 | The undecidability of the Continuum Hypothesis may have ruined or fragmented set theory [Badiou] |
| Full Idea: As we have known since Paul Cohen's theorem, the Continuum Hypothesis is intrinsically undecidable. Many believe Cohen's discovery has driven the set-theoretic project into ruin, or 'pluralized' what was once presented as a unified construct. | |
| From: Alain Badiou (Briefings on Existence [1998], 6) | |
| A reaction: Badiou thinks the theorem completes set theory, by (roughly) finalising its map. |
| 12329 | If mathematics is a logic of the possible, then questions of existence are not intrinsic to it [Badiou] |
| Full Idea: If mathematics is a logic of the possible, then questions of existence are not intrinsic to it (as they are for the Platonist). | |
| From: Alain Badiou (Briefings on Existence [1998], 7) | |
| A reaction: See also Idea 12328. I file this to connect it with Hellman's modal (and nominalist) version of structuralism. Could it be that mathematics and modal logic are identical? |
| 12328 | Platonists like axioms and decisions, Aristotelians like definitions, possibilities and logic [Badiou] |
| Full Idea: A Platonist's interest focuses on axioms in which the decision of thought is played out, where an Aristotelian or Leibnizian interest focuses on definitions laying out the representation of possibilities (...and the essence of mathematics is logic). | |
| From: Alain Badiou (Briefings on Existence [1998], 7) | |
| A reaction: See Idea 12323 for the significance of the Platonist approach. So logicism is an Aristotelian project? Frege is not a true platonist? I like the notion of 'the representation of possibilities', so will vote for the Aristotelians, against Badiou. |
| 12331 | Logic is definitional, but real mathematics is axiomatic [Badiou] |
| Full Idea: Logic is definitional, whereas real mathematics is axiomatic. | |
| From: Alain Badiou (Briefings on Existence [1998], 10) |
| 12340 | There is no Being as a whole, because there is no set of all sets [Badiou] |
| Full Idea: The fundamental theorem that 'there does not exist a set of all sets' designates the inexistence of Being as a whole. ...A crucial consequence of this property is that any ontological investigation is irremediably local. | |
| From: Alain Badiou (Briefings on Existence [1998], 14) | |
| A reaction: The second thought pushes Badiou into Topos Theory, where the real numbers (for example) have a separate theory in each 'topos'. |
| 12323 | Existence is Being itself, but only as our thought decides it [Badiou] |
| Full Idea: Existence is precisely Being itself in as much as thought decides it. And that decision orients thought essentially. ...It is when you decide upon what exists that you bind your thought to Being. | |
| From: Alain Badiou (Briefings on Existence [1998], 2) | |
| A reaction: [2nd half p.57] Helpful for us non-Heideggerians to see what is going on. Does this mean that Being is Kant's noumenon? |
| 21982 | I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L] |
| Full Idea: "I see nobody on the road," said Alice. - "I only wish I had such eyes," the King remarked. ..."To be able to see Nobody! ...Why, it's as much as I can do to see real people." | |
| From: Lewis Carroll (C.Dodgson) (Through the Looking Glass [1886], p.189), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.7 | |
| A reaction: [Moore quotes this, inevitably, in a chapter on Hegel] This may be a better candidate for the birth of philosophy of language than Frege's Groundwork. |
| 12332 | The modern view of Being comes when we reject numbers as merely successions of One [Badiou] |
| Full Idea: The saturation and collapse of the Euclidean idea of the being of number as One's procession signs the entry of the thought of Being into modern times. | |
| From: Alain Badiou (Briefings on Existence [1998], 11) | |
| A reaction: That is, by allowing that not all numbers are built of units, numbers expand widely enough to embrace everything we think of as Being. The landmark event is the acceptance of the infinite as a number. |
| 12326 | The primitive name of Being is the empty set; in a sense, only the empty set 'is' [Badiou] |
| Full Idea: In Set Theory, the primitive name of Being is the void, the empty set. The whole hierarchy takes root in it. In a certain sense, it alone 'is'. | |
| From: Alain Badiou (Briefings on Existence [1998], 6) | |
| A reaction: This is the key to Badiou's view that ontology is mathematics. David Lewis pursued interesting enquiries in this area. |
| 12320 | Ontology is (and always has been) Cantorian mathematics [Badiou] |
| Full Idea: Enlightened by the Cantorian grounding of mathematics, we can assert ontology to be nothing other than mathematics itself. This has been the case ever since its Greek origin. | |
| From: Alain Badiou (Briefings on Existence [1998], 1) | |
| A reaction: There seems to be quite a strong feeling among mathematicians that new 'realms of being' are emerging from their researches. Only a Platonist, of course, is likely to find this idea sympathetic. |
| 4885 | Identity is a very weak relation, which doesn't require interdefinability, or shared properties [Perry] |
| Full Idea: The truth of "a=b" doesn't require much of 'a' and 'b' other than that there is a single thing to which they both refer. They needn't be interdefinable, or have supervenient properties. In this sense, identity is a very weak relation. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §1.2) | |
| A reaction: Interesting. This is seeing the epistemological aspects of identity. Ontologically, identity must invoke Leibniz's Law, and is the ultimately powerful 'relation'. A given student, and the cause of a crop circle, may APPEAR to be quite different. |
| 4899 | Possible worlds thinking has clarified the logic of modality, but is problematic in epistemology [Perry] |
| Full Idea: Using possible worlds to model truth-conditions of statements has led to considerable clarity about the logic of modality. Attempts to use the system for epistemic purposes, however, have been plagued by problems. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §8.1) | |
| A reaction: Presumably what lurks behind this is a distinction between what is logically or naturally possible, and what appears to be possible from the perspective of a conscious mind. Is there a possible world in which I can fly? |
| 4898 | Possible worlds are indices for a language, or concrete realities, or abstract possibilities [Perry] |
| Full Idea: Possible worlds can be thought of as indices for models of the language in question, or as concrete realities (David Lewis), or as abstract ways the world might be (Robert Stalnaker), or in various other ways. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §8.1) | |
| A reaction: I strongly favour the Stalnaker route here. Reducing great metaphysics to mere language I find abhorrent, and I suspect that Lewis was trapped by his commitment to strong empiricism. We must embrace abstractions into our ontology. |
| 4887 | We try to cause other things to occur by causing mental events to occur [Perry] |
| Full Idea: We try to cause other things to occur by causing mental events to occur. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §2.4) | |
| A reaction: A small and obvious, but important, point. Mental causation isn't just thoughts leading to physical happenings. Here Perry means that events can be designed to cause thoughts, such as a threatening letter. Not much room for epiphenomenalism here. |
| 4884 | Brain states must be in my head, and yet the pain seems to be in my hand [Perry] |
| Full Idea: The brain state will involve certain parts of the brain, whereas my feeling of pain seems to be located in my hand insofar as it has a bodily location. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §1.2) | |
| A reaction: This seems important to me. The brain is a ventriloquist. Perry implies that pain is quasi-disembodied, but it isn't, it is just experienced as IN the hand. Perhaps it is in the hand? Cutting the nerves loses contact with the pain. |
| 4888 | It seems plausible that many animals have experiences without knowing about them [Perry] |
| Full Idea: It seems quite plausible to me that many animals have experiences without knowing about them. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §3.1) | |
| A reaction: I agree, which makes us acknowledge levels of consciousness, which probably applies to human experience as well. The simplest idea is to distinguish between experiences which involve concepts, and those which don't. Animals sometimes appear surprised. |
| 4891 | If epiphenomenalism just says mental events are effects but not causes, it is consistent with physicalism [Perry] |
| Full Idea: Epiphenomenalism is usually considered to be a form of dualism, but if we define it as the doctrine that conscious events are effects but not causes, it appears to be consistent with physicalism. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §4.2) | |
| A reaction: Interesting. The theory was invented to put mind outside physics, and make the closure of physics possible. However, being capable of causing things seems to be a necessary condition for physical objects. An effect in one domain is a cause in another. |
| 4900 | Prior to Kripke, the mind-brain identity theory usually claimed that the identity was contingent [Perry] |
| Full Idea: Advocates of the mind-body identity theory typically claimed that identity between particular mental states and brain states was contingent, until Kripke argued persuasively that identity is always necessary. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §8.1) | |
| A reaction: Kripke wanted to argue against the identity theory, but what he seems to have done is reformulate it into a much more powerful version (involving necessary identity). |
| 4892 | If physicalists stick with identity (not supervenience), Martian pain will not be like ours [Perry] |
| Full Idea: The physicalist should not retreat to causal supervenience but should stick with identity. This means we will have to accept that a Martian and I (when in pain) are not in the same phenomenal state. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §4.3) | |
| A reaction: We naturally presume that frogs feel pain as we do, but many different phenomenal states could lead to the same behavioural end. Only an unpleasant feeling is required. A foul smell would do. Frogs could function with inverted qualia, too. |
| 4889 | Although we may classify ideas by content, we individuate them differently, as their content can change [Perry] |
| Full Idea: Although we classify ideas by content for many purposes, we do not individuate them by content. The content of an idea can change. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §3.2) | |
| A reaction: As the compiler of this database, I find this very appealing. The mind works exactly like a database. I have a 'file' (Perry's word) marked "London", the content of which undergoes continual change. I am a database management system. |
| 4896 | The intension of an expression is a function from possible worlds to an appropriate extension [Perry] |
| Full Idea: In possible-worlds semantics, expressions have intensions, which are functions from possible worlds to appropriate extensions (names to individuals, n-place predicates to n-tuples, and sentences to truth values, built from parts). | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §8.1) | |
| A reaction: Interesting. Perry distinguishes 'referential' (or 'subject matter') content, which is prior to the link to extensions - a link which creates 'reflexive' content. He is keen that they should not become confused. True knowledge is 'situated'. |
| 4897 | A proposition is a set of possible worlds for which its intension delivers truth [Perry] |
| Full Idea: The proposition expressed by a sentence can be thought of as a set of possible worlds, the worlds for which its intension delivers truth. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §8.1) | |
| A reaction: It has always struck me as important to hang on to the concept of a 'proposition' (over and above sentences). This idea gives a metaphysics for the concept, and the 'language of thought' offers appropriate brain structures. A neat picture. |
| 4890 | A sharp analytic/synthetic line can rarely be drawn, but some concepts are central to thought [Perry] |
| Full Idea: Although there is seldom a sharp analytic/synthetic distinction to be drawn in the case of our concepts, there are clearly things that are more and less central. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §3.2) | |
| A reaction: Most Americans seem enslaved to Quine on this one, so it is nice to see the obvious being stated for once. Human thought is an organic offshoot of the natural world. To think it is all arbitrary and changeable is human arrogance. |
| 12338 | We must either assert or deny any single predicate of any single subject [Badiou] |
| Full Idea: There can be nothing intermediate to an assertion and a denial. We must either assert or deny any single predicate of any single subject. | |
| From: Alain Badiou (Briefings on Existence [1998], 1011b24) | |
| A reaction: The first sentence seems to be bivalence, and the second sentence excluded middle. |
| 12316 | For Enlightenment philosophers, God was no longer involved in politics [Badiou] |
| Full Idea: For the philosophers of the Enlightenment politics is strictly the affair of humankind, an immanent practice from which recourse to the All Mighty's providential organization had to be discarded. | |
| From: Alain Badiou (Briefings on Existence [1998], Prol) |
| 12317 | The God of religion results from an encounter, not from a proof [Badiou] |
| Full Idea: The God of metaphysics makes sense of existing according to a proof, while the God of religion makes sense of living according to an encounter | |
| From: Alain Badiou (Briefings on Existence [1998], Prol) |