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) |
| 9808 | Philosophy aims to reveal the grandeur of mathematics [Badiou] |
| Full Idea: Philosophy's role consists in informing mathematics of its own speculative grandeur. | |
| From: Alain Badiou (Mathematics and Philosophy: grand and little [2004], p.11) | |
| A reaction: Revealing the grandeur of something sounds more like a rhetorical than a rational exercise. How would you reveal the grandeur of a sunset to someone? |
| 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? |
| 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) |
| 9812 | In mathematics, if a problem can be formulated, it will eventually be solved [Badiou] |
| Full Idea: Only in mathematics can one unequivocally maintain that if thought can formulate a problem, it can and will solve it, regardless of how long it takes. | |
| From: Alain Badiou (Mathematics and Philosophy: grand and little [2004], p.17) | |
| A reaction: I hope this includes proving the Continuum Hypothesis, and Goldbach's Conjecture. It doesn't seem quite true, but it shows why philosophers of a rationalist persuasion are drawn to mathematics. |
| 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? |
| 9813 | Mathematics shows that thinking is not confined to the finite [Badiou] |
| Full Idea: Mathematics teaches us that there is no reason whatsoever to confne thinking within the ambit of finitude. | |
| From: Alain Badiou (Mathematics and Philosophy: grand and little [2004], p.19) | |
| A reaction: This would perhaps make Cantor the greatest thinker who ever lived. It is an exhilarating idea, but we should ward the reader against romping of into unrestrained philosophical thought about infinities. You may be jumping without your Cantorian parachute. |
| 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'. |
| 9809 | Mathematics inscribes being as such [Badiou] |
| Full Idea: Mathematics inscribes being as such. | |
| From: Alain Badiou (Mathematics and Philosophy: grand and little [2004], p.12) | |
| A reaction: I don't pretend to understand that, but there is something about the purity and certainty of mathematics that makes us feel we are grappling with the core of existence. Perhaps. The same might be said of stubbing your toe on a bedpost. |
| 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. |
| 9811 | It is of the essence of being to appear [Badiou] |
| Full Idea: It is of the essence of being to appear. | |
| From: Alain Badiou (Mathematics and Philosophy: grand and little [2004], p.16) | |
| A reaction: Nice slogan. In my humble opinion 'continental' philosophy is well worth reading because, despite the fluffy rhetoric and the shameless egotism and the desire to shock the bourgeoisie, they occasionally make wonderfully thought-provoking remarks. |
| 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. |
| 11897 | A principle of individuation may pinpoint identity and distinctness, now and over time [Mackie,P] |
| Full Idea: One view of a principle of individuation is what is called a 'criterion of identity', determining answers to questions about identity and distinctness at a time and over time - a principle of distinction and persistence. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 8.2) | |
| A reaction: Since the term 'Prime Minister' might do this job, presumably there could be a de dicto as well as a de re version of individuation. The distinctness consists of chairing cabinet meetings, rather than being of a particular sex. |
| 11898 | Individuation may include counterfactual possibilities, as well as identity and persistence [Mackie,P] |
| Full Idea: A second view of the principle of individuation includes criteria of distinction and persistence, but also determines the counterfactual possibilities for a thing. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 8.5) | |
| A reaction: It would be a pretty comprehensive individuation which defined all the counterfactual truths about a thing, as well as its actual truths. This is where powers come in. We need to know a thing's powers, but not how they cash out counterfactually. |
| 11883 | A haecceity is the essential, simple, unanalysable property of being-this-thing [Mackie,P] |
| Full Idea: Socrates can be assigned a haecceity: an essential property of 'being Socrates' which (unlike the property of 'being identical with Socrates') may be regarded as what 'makes' its possessor Socrates in a non-trivial sense, but is simple and unanalysable. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 2.2) | |
| A reaction: I don't accept that there is any such property as 'being Socrates' (or even 'being identical with Socrates'), except as empty locutions or logical devices. A haecceity seems to be the 'ultimate subject of predication', with no predicates of its own. |
| 11889 | Essentialism must avoid both reduplication of essences, and multiple occupancy by essences [Mackie,P] |
| Full Idea: The argument for unshareable properties (the Reduplication Argument) suggests the danger of reduplication of Berkeley; the argument for incompatible properties (Multiple Occupancy) says Berkeley and Hume could be in the same possible object. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 2.8) | |
| A reaction: These are her arguments in favour of essential properties being necessarily incompatible between objects. Whatever the answer, it must allow essences for indistinguishables like electrons. 'Incompatible' points towards a haecceity. |
| 11877 | An individual essence is the properties the object could not exist without [Mackie,P] |
| Full Idea: By essentialism about individuals I simply mean the view that individual things have essential properties, where an essential property of an object is a property that the object could not have existed without. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 1.1) | |
| A reaction: This presumably means I could exist without a large part of my reason and consciousness, but could not exist without one of my heart valves. This seems to miss the real point of essence. I couldn't exist without oxygen - not one of my properties. |
| 11882 | No other object can possibly have the same individual essence as some object [Mackie,P] |
| Full Idea: Individual essences are essential properties that are unique to them alone. ...If a set of properties is an individual essence of A, then A has the properties essentially, and no other actual or possible object actually or possibly has them. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 2.1/2) | |
| A reaction: I'm unconvinced about this. Tigers have an essence, but individual tigers have individual essences over and above their tigerish qualities, yet the perfect identity of two tigers still seems to be possible. |
| 11886 | There are problems both with individual essences and without them [Mackie,P] |
| Full Idea: If all objects had individual essences, there would be no numerical difference without an essential difference. But if there aren't individual essences, there could be two things sharing all essential properties, differing only in accidental properties. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 2.5) | |
| A reaction: Depends how you define individual essence. Why can't two electrons have the same individual essence. To postulate a 'kind essence' which bestows the properties on each electron is to get things the wrong way round. |
| 11909 | Unlike Hesperus=Phosophorus, water=H2O needs further premisses before it is necessary [Mackie,P] |
| Full Idea: There is a disanalogy between 'necessarily water=H2O' and 'necessarily Hesperus=Phosphorus'. The second just needs the necessity of identity, but the first needs 'x is a water sample' and 'x is an H2O' sample to coincide in all possible worlds. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 10.1.) | |
| A reaction: This comment is mainly aimed at Kripke, who bases his essentialism on identities, rather than at Putnam. |
| 11899 | Why are any sortals essential, and why are only some of them essential? [Mackie,P] |
| Full Idea: Accounts of sortal essentialism do not give a satisfactory explanation of why any sortals should be essential sortals, or a satisfactory account of why some sortals should be essential while others are not. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 8.6) | |
| A reaction: A theory is not wrong, just because it cannot give a 'satisfactory explanation' of every aspect of the subject. We might, though, ask why the theory isn't doing well in this area. |
| 11906 | The Kripke and Putnam view of kinds makes them explanatorily basic, but has modal implications [Mackie,P] |
| Full Idea: Kripke and Putnam chose for their typical essence of kinds, sets of properties that could be thought of as explanatorily basic. ..But the modal implications of their views go well beyond this. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 10.1) | |
| A reaction: Cf. Idea 11905. The modal implications are that the explanatory essence is also necessary to the identity of the thing under discussion, such as H2O. So do basic explanations carry across into all possible worlds? |
| 11894 | Origin is not a necessity, it is just 'tenacious'; we keep it fixed in counterfactual discussions [Mackie,P] |
| Full Idea: I suggest 'tenacity of origin' rather than 'necessity of origin'. ..The most that we need is that Caesar's having something similar to his actual origin in certain respects (e.g. his actual parents) is normally kept fixed in counterfactual speculation. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 6.9) | |
| A reaction: I find necessity or essentially of origin very unconvincing, so I rather like this. Origin is just a particularly stable way to establish our reference to something. An elusive spy may have little more than date and place of birth to fix them. |
| 11887 | Transworld identity without individual essences leads to 'bare identities' [Mackie,P] |
| Full Idea: Transworld identity without individual essences leads to 'bare identities'. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 2.7) | |
| A reaction: [She gives an argument for this, based on Forbes] I certainly favour the notion of individual essences over the notion of bare identities. We must distinguish identity in reality from identity in concept. Identities are points in conceptual space. |
| 11890 | De re modality without bare identities or individual essence needs counterparts [Mackie,P] |
| Full Idea: Anyone who wishes to avoid both bare identities and individual essences, without abandoning de re modality entirely, must adopt counterpart theory. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 4.1) | |
| A reaction: This at least means that Lewis's proposal has an important place in the discussion, forcing us to think more clearly about the identities involved when we talk of possibilities. Mackie herself votes for bare indentities. |
| 11892 | Things may only be counterparts under some particular relation [Mackie,P] |
| Full Idea: A may be a counterpart of B according to one counterpart relation (similarity of origin, say), but not according to another (similarity of later history). | |
| From: Penelope Mackie (How Things Might Have Been [2006], 5.3) | |
| A reaction: Hm. Would two very diverse things have to be counterparts because they were kept in the same cupboard in different worlds? Can the counterpart relationship diverge or converge over time? Yes, I presume. |
| 11893 | Possibilities for Caesar must be based on some phase of the real Caesar [Mackie,P] |
| Full Idea: I take the 'overlap requirement' for Julius Caesar to be that, when considering how he might have been different, you have to take him as he actually was at some time in his existence, and consider possibilities consistent with that. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 6.5) | |
| A reaction: This is quite a large claim (larger than Mackie thinks?), as it seems equally applicable to properties, states of affairs and propositions, as well as to individuals. Possibility that has no contact at all with actuality is beyond our comprehension. |
| 11884 | The theory of 'haecceitism' does not need commitment to individual haecceities [Mackie,P] |
| Full Idea: The theory that things have 'haecceities' must be sharply distinguished from the theory referred to as 'haecceitism', which says there may be differences in transworld identities that do not supervene on qualitative differences. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 2.2 n7) | |
| A reaction: She says later [p,43 n] that it is possible to be a haecceitist without believing in individual haecceities, if (say) the transworld identities had no basis at all. Note that if 'thisness' is 'haecceity', then 'whatness' is 'quiddity'. |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| Full Idea: There are six 'reductive levels' in science: social groups, (multicellular) living things, cells, molecules, atoms, and elementary particles. | |
| From: report of H.Putnam/P.Oppenheim (Unity of Science as a Working Hypothesis [1958]) by Peter Watson - Convergence 10 'Intro' | |
| A reaction: I have the impression that fields are seen as more fundamental that elementary particles. What is the status of the 'laws' that are supposed to govern these things? What is the status of space and time within this picture? |
| 11905 | Locke's kind essences are explanatory, without being necessary to the kind [Mackie,P] |
| Full Idea: One might speak of 'Lockean real essences' of a natural kind, a set of properties that is basic in the explanation of the other properties of the kind, without commitment to the essence belonging to the kind in all possible worlds. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 10.1) | |
| A reaction: I think this may be the most promising account. The essence of a tiger explains what tigers are like, but tigers may evolve into domestic pets. Questions of individuation and of explaining seem to be quite separate. |
| 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. |
| 9814 | All great poetry is engaged in rivalry with mathematics [Badiou] |
| Full Idea: Like every great poet, Mallarmé was engaged in a tacit rivalry with mathematics. | |
| From: Alain Badiou (Mathematics and Philosophy: grand and little [2004], p.20) | |
| A reaction: I love these French pronouncements! Would Mallarmé have agreed? If poetry and mathematics are the poles, where is philosophy to be found? |
| 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) |
| 11907 | Maybe the identity of kinds is necessary, but instances being of that kind is not [Mackie,P] |
| Full Idea: One could be an essentialist about natural kinds (of tigers, or water) while holding that every actual instance or sample of a natural kind is only accidentally an instance or a sample of that kind. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 10.2) | |
| A reaction: You wonder, then, in what the necessity of the kind consists, if it is not rooted in the instances, and presumably it could only result from a stipulative definition, and hence be conventional. |
| 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) |