49 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? |
| 4456 | Epistemological Ockham's Razor demands good reasons, but the ontological version says reality is simple [Moreland] |
| Full Idea: Ockham's Razor has an epistemological version, which says we should not multiply existences or explanations without adequate reason, and an ontological version, which says reality is simple, and so a simpler ontology represents it more accurately. | |
| From: J.P. Moreland (Universals [2001], Ch.2) | |
| A reaction: A nice distinction. Is it reality which is simple, or us? One shouldn't write off the ontological version. If one explanation is simpler than the others, there may be a reason in nature for that. |
| 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? |
| 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. |
| 3425 | Reduction has been defined as deriving one theory from another by logic and maths [Nagel,E, by Kim] |
| Full Idea: Ernest Nagel defines reduction as the possibility of deriving all laws of one theory by logic and mathematics to another theory, with appropriate 'bridging principles' (either definitions, or empirical laws) connecting the expressions of the two theories. | |
| From: report of Ernest Nagel (The Structure of Science [1961]) by Jaegwon Kim - Philosophy of Mind p.213 | |
| A reaction: This has been labelled as 'weak' reduction, where 'strong' reduction would be identity, as when lightning is reduced to electrical discharge. You reduce x by showing that it is y in disguise. |
| 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. |
| 4474 | Existence theories must match experience, possibility, logic and knowledge, and not be self-defeating [Moreland] |
| Full Idea: A theory of existence should 1) be consistent with what actually exists, 2) be consistent with what could exist, 3) not make existence impossible (e.g. in space-time), 4) not violate logic, 5) make knowing the theory possible. | |
| From: J.P. Moreland (Universals [2001], Ch.6) | |
| A reaction: A nice bit of metaphilosophical analysis. I still doubt whether a theory of existence is possible (something has to be 'given' a priori), but this is a good place to start the attempt. |
| 4461 | Tropes are like Hume's 'impressions', conceived as real rather than as ideal [Moreland] |
| Full Idea: Tropes are (says Campbell) substances (in Hume's sense), and indeed resemble his impressions conceived realistically rather than idealistically. | |
| From: J.P. Moreland (Universals [2001], Ch.3) | |
| A reaction: An interesting link. It doesn't get rid of the problem Hume has, of saying when two impressions are the same. Are they types or tokens? Trope-theory claims they are tokens. Hume's ontology includes 'resemblance'. |
| 4462 | A colour-trope cannot be simple (as required), because it is spread in space, and so it is complex [Moreland] |
| Full Idea: A property-instance must be spread out in space, or it is not clear how a colour nature can be present, but then it has to be a complex entity, and tropes are supposed to be simple entities. | |
| From: J.P. Moreland (Universals [2001], Ch.3) | |
| A reaction: Seems a fair point. Nothing else in reality can be sharply distinguished, so why should 'simple' and 'complex'? |
| 4463 | In 'four colours were used in the decoration', colours appear to be universals, not tropes [Moreland] |
| Full Idea: If a decorator says that they used four colours to decorate a house, four tropes is not what was meant, and the statement seems to view colours as universals. | |
| From: J.P. Moreland (Universals [2001], Ch.3) | |
| A reaction: Although I am suspicious of using language to deduce ontology, you have to explain why certain statements (like this) are even possible to make. |
| 4451 | If properties are universals, what distinguishes two things which have identical properties? [Moreland] |
| Full Idea: If properties are universals, what account can be given of the individuation of two entities that have all their pure properties in common? | |
| From: J.P. Moreland (Universals [2001], Ch.1) | |
| A reaction: Is this a big problem? Maybe only a space-time location can do it. Or, in the nice case where the universe is just two identical spheres, it may be impossible. |
| 4453 | One realism is one-over-many, which may be the model/copy view, which has the Third Man problem [Moreland] |
| Full Idea: One version of realism says that the universal does not enter into the being of its instances, and thus is a One-Over-Many. One version of this is the model/copy view, but this is not widely held, because of difficulties such as the Third Man Argument. | |
| From: J.P. Moreland (Universals [2001], Ch.1) | |
| A reaction: This presumably arises if the model is held to have the properties of the copy (self-predication), and looks like a bad theory |
| 4464 | Realists see properties as universals, which are single abstract entities which are multiply exemplifiable [Moreland] |
| Full Idea: Traditional realism is the view that a property is a universal construed as a multiply exemplifiable abstract entity that is a numerically identical constituent in each of its instances. | |
| From: J.P. Moreland (Universals [2001], Ch.4) | |
| A reaction: Put like that, it seems hard to commit oneself fully to realism. How can two red buses contain one abstract object spread out between them. Common sense says there are two 'rednesses' which resemble one another, which is a version of nominalism. |
| 4449 | Evidence for universals can be found in language, communication, natural laws, classification and ideals [Moreland] |
| Full Idea: Those who believe in universals appeal to the meaningfulness of language, the lawlike nature of causation, the inter-subjectivity of thinking, our ability to classify new entities, gradation, and the need for perfect standards or paradigms. | |
| From: J.P. Moreland (Universals [2001], Ch.1) | |
| A reaction: Of these, language and communication ought to be explicable by convention, but classification and natural laws look to me like the best evidence. |
| 4450 | The traditional problem of universals centres on the "One over Many", which is the unity of natural classes [Moreland] |
| Full Idea: Historically the problem of universals has mainly been about the "One over Many", which involves giving an account of the unity of natural classes. | |
| From: J.P. Moreland (Universals [2001], Ch.1) | |
| A reaction: This still strikes me as the main problem (rather than issues of language). If universals are not natural, they must be analysed as properties, which break down into causation, which is seen as a human convention. |
| 4454 | The One-In-Many view says universals have abstract existence, but exist in particulars [Moreland] |
| Full Idea: Another version of realism says is One-In-Many, where the universal is not another particular, but is literally in the instances. The universal is an abstract entity, in the instances by means of a primitive non-spatiotemporal tie of predication. | |
| From: J.P. Moreland (Universals [2001], Ch.1) | |
| A reaction: This sounds like Aristotle (and is Loux's view of properties and relations). If they are abstract, why must they be confined to particulars? |
| 4468 | How could 'being even', or 'being a father', or a musical interval, exist naturally in space? [Moreland] |
| Full Idea: Many properties (being even) and relations (musical intervals, being a father) are such that it is not clear what it would mean to take them as natural things existing in space. | |
| From: J.P. Moreland (Universals [2001], Ch.4) | |
| A reaction: 'Being even' certainly seems to be a property, and it is a struggle to see how it could exist in space, unless it is a set of actual or potential brain states. |
| 4452 | Maybe universals are real, if properties themselves have properties, and relate to other properties [Moreland] |
| Full Idea: Realism about universals is supported by the phenomenon of abstract reference - that is the fact that properties themselves have properties ('red is a colour'), and stand in relation to other properties ('red is more like orange than like blue'). | |
| From: J.P. Moreland (Universals [2001], Ch.1) | |
| A reaction: While a property may be an obviously natural feature, properties of properties seem more likely to be the produce of human perception and convention. It is a good argument, though. |
| 4467 | A naturalist and realist about universals is forced to say redness can be both moving and stationary [Moreland] |
| Full Idea: If a property is held to be at the location of the particular, then if there are two objects having the same property, and one object is stationary and the other is moving, the realist is forced to say that the universal is both moving and at rest. | |
| From: J.P. Moreland (Universals [2001], Ch.4) | |
| A reaction: The target of this comment is D.M.Armstrong. The example nicely illustrates the problem of trying to combine science and metaphysics. It pushes you back to Platonism, but that seems wrong too… |
| 4469 | There are spatial facts about red particulars, but not about redness itself [Moreland] |
| Full Idea: When one attends to something existing in space, one attends to an instance of redness, not to redness itself (which is a colour, which resembles orange). The facts about red itself are not spatial facts, but are traditionally seen as a priori synthetic. | |
| From: J.P. Moreland (Universals [2001], Ch.4) | |
| A reaction: This is the fact that properties can themselves have properties (and so on?), which seems to take us further and further from the natural world. |
| 4472 | Redness is independent of red things, can do without them, has its own properties, and has identity [Moreland] |
| Full Idea: Four arguments for Platonism: 1) there are truths about redness (it's a colour) even if nothing red exists, 2) redness does not depend on particulars, 3) most universals are at some time not exemplified, 4) universals satisfy the criteria of existence. | |
| From: J.P. Moreland (Universals [2001], Ch.6) | |
| A reaction: This adds up to quite a good case, particularly the point that things can be said about redness which are independent of any particular, but the relationships between concepts and the brain seems at the heart of the problem. |
| 4459 | Moderate nominalism attempts to embrace the existence of properties while avoiding universals [Moreland] |
| Full Idea: Moderate nominalism attempts to embrace the existence of properties while avoiding universals. | |
| From: J.P. Moreland (Universals [2001], Ch.2) | |
| A reaction: Clearly there is going to be quite a struggle to make sense of 'exists' here (Russell tries 'subsists). Presumably each property must be a particular? |
| 4458 | Unlike Class Nominalism, Resemblance Nominalism can distinguish natural from unnatural classes [Moreland] |
| Full Idea: Resemblance Nominalism is clearly superior to Class Nominalism, since the former offers a clear ground for distinguishing between natural and unnatural classes. | |
| From: J.P. Moreland (Universals [2001], Ch.2) | |
| A reaction: Important. It seems evident to me that there are natural classes, and the only ground for this claim would be either the resemblance or the identity of properties. |
| 4457 | There can be predicates with no property, and there are properties with no predicate [Moreland] |
| Full Idea: Linguistic predicates are neither sufficient nor necessary for specifying a property. Predicates can be contrived which express no property, properties are far more numerous than linguistic predicates, and properties are what make predicates apply. | |
| From: J.P. Moreland (Universals [2001], Ch.2) | |
| A reaction: This seems to me conclusive, and is a crucial argument against anyone who thinks that our metaphysics can simply be inferred from our language. |
| 4471 | We should abandon the concept of a property since (unlike sets) their identity conditions are unclear [Moreland] |
| Full Idea: Some argue that compared to sets, the identity conditions for properties are obscure, and so properties, including realist depictions of them, should be rejected. | |
| From: J.P. Moreland (Universals [2001], Ch.6) | |
| A reaction: I have never thought that difficulty in precisely identifying something was a good reason for denying its existence. Consider low morale in a work force. 2nd thoughts: I like this! |
| 4476 | Most philosophers think that the identity of indiscernibles is false [Moreland] |
| Full Idea: Most philosophers think that the identity of indiscernibles is false. | |
| From: J.P. Moreland (Universals [2001], Ch.7) | |
| A reaction: This is as opposed to the generally accepted 'indiscernibility of identicals'. 'Discernment' is an epistemological concept, and 'identity' is an ontological concept. |
| 4460 | Abstractions are formed by the mind when it concentrates on some, but not all, the features of a thing [Moreland] |
| Full Idea: If something is 'abstract' it is got before the mind by an act of abstraction, that is, by concentrating attention on some (but not all) of what is presented. | |
| From: J.P. Moreland (Universals [2001], Ch.3) | |
| A reaction: Presumably it usually involves picking out the behavioural or causal features, and leaving out the physical features - though I suppose it works for physical properties too… |
| 4455 | It is always open to a philosopher to claim that some entity or other is unanalysable [Moreland] |
| Full Idea: It is always open to a philosopher to claim that some entity or other is unanalysable. | |
| From: J.P. Moreland (Universals [2001], Ch.2) | |
| A reaction: For example, Davidson on truth. There is an onus to demonstrate why all attempted analyses fail. |
| 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) |
| 4473 | 'Presentism' is the view that only the present moment exists [Moreland] |
| Full Idea: 'Presentism' is the view that only the present moment exists. | |
| From: J.P. Moreland (Universals [2001], Ch.6) | |
| A reaction: And Greek scepticism doubted even the present, since there is no space between past and future. It is a delightfully vertigo-inducing idea. |
| 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) |