52 ideas
| 7893 | Our life is the creation of our mind [Anon (Dham)] |
| Full Idea: What we are today comes from our thoughts of yesterday, and our present thoughts build our life of tomorrow: our life is the creation of our mind. | |
| From: Anon (Dham) (The DhammaPada [c.250 BCE], §1.1) | |
| A reaction: I may adopt this as a second epigraph for the database. This idea records the subjective view, which now comes up against evolutionary psychology. Maybe philosophy is opposed to science, because it is committed to exploring the subjective view? |
| 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) |
| 8525 | Relations need terms, so they must be second-order entities based on first-order tropes [Campbell,K] |
| Full Idea: Because there cannot be relations without terms, in a meta-physic that makes first-order tropes the terms of all relations, relational tropes must belong to a second, derivative order. | |
| From: Keith Campbell (The Metaphysic of Abstract Particulars [1981], §8) | |
| A reaction: The admission that there could be a 'derivative order' may lead to trouble for trope theory. Ostrich Nominalists could say that properties themselves are derivative second-order abstractions from indivisible particulars. Russell makes them first-order. |
| 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. |
| 8518 | Events are trope-sequences, in which tropes replace one another [Campbell,K] |
| Full Idea: Events are widely acknowledged to be particulars, but they are plainly not ordinary concrete particulars. They are best viewed as trope-sequences, in which one condition gives way to another. They are changes in which tropes replace one another. | |
| From: Keith Campbell (The Metaphysic of Abstract Particulars [1981], §3) | |
| A reaction: If nothing exists except bundles of tropes, it is worth asking WHY one trope would replace another. Some tropes are active (i.e. they are best described as 'powers'). |
| 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. |
| 8513 | Two red cloths are separate instances of redness, because you can dye one of them blue [Campbell,K] |
| Full Idea: If we have two cloths of the very same shade of redness, we can show there are two cloths by burning one and leaving the other unaffected; we show there are two cases of redness in the same way: dye one blue, leaving the other unaffected. | |
| From: Keith Campbell (The Metaphysic of Abstract Particulars [1981], §1) | |
| A reaction: This has to be one of the basic facts of the problem accepted by everyone. If you dye half of one of the pieces, was the original red therefore one instance or two? Has it become two? How many red tropes are there in a red cloth? |
| 8514 | Red could only recur in a variety of objects if it was many, which makes them particulars [Campbell,K] |
| Full Idea: If there are a varied group of red objects, the only element that recurs is the colour. But it must be the colour as a particular (a 'trope') that is involved in the recurrence, for only particulars can be many in the way required for recurrence. | |
| From: Keith Campbell (The Metaphysic of Abstract Particulars [1981], §1) | |
| A reaction: This claim seems to depend on the presupposition that rednesses are countable things, but it is tricky trying to count the number of blue tropes in the sky. |
| 8522 | Tropes solve the Companionship Difficulty, since the resemblance is only between abstract particulars [Campbell,K] |
| Full Idea: The 'companionship difficulty' cannot arise if the members of the resemblance class are tropes rather than whole concrete particulars. The instances of having a heart, as abstract particulars, are quite different from instances of having a kidney. | |
| From: Keith Campbell (The Metaphysic of Abstract Particulars [1981], §6) | |
| A reaction: The companionship difficulty seems worst if you base your account of properties just on being members of a class. Any talk of resemblance eventually has to talk about 'respects' of resemblance. Is a trope a respect? Is a mode an object? |
| 8523 | Tropes solve the Imperfect Community problem, as they can only resemble in one respect [Campbell,K] |
| Full Idea: The 'problem of imperfect community' cannot arise where our resemblance sets are sets of tropes. Tropes, by their very nature and mode of differentiation can only resemble in one respect. | |
| From: Keith Campbell (The Metaphysic of Abstract Particulars [1981], §6) | |
| A reaction: You arrive at very different accounts of what resemblance means according to how you express the problem verbally. We can only find a solution through thinking which transcends language. Heresy! |
| 8524 | Trope theory makes space central to reality, as tropes must have a shape and size [Campbell,K] |
| Full Idea: The metaphysics of abstract particulars gives a central place to space, or space-time, as the frame of the world. ...Tropes are, of their essence, regional, which carries with it the essential presence of shape and size in any trope occurrence. | |
| From: Keith Campbell (The Metaphysic of Abstract Particulars [1981], §7) | |
| A reaction: Trope theory has a problem with Aristotle's example (Idea 557) of what happens when white is mixed with white. Do two tropes become one trope if you paint on a second coat of white? How can particulars merge? How can abstractions merge? |
| 8521 | Nominalism has the problem that without humans nothing would resemble anything else [Campbell,K] |
| Full Idea: The objection to nominalism is its consequence that if there were no human race (or other living things), nothing would be like anything else. | |
| From: Keith Campbell (The Metaphysic of Abstract Particulars [1981], §6) | |
| A reaction: Anti-realists will be unflustered by this difficulty. Personally it strikes me as obvious that some aspects of resemblance are part of reality which we did not contribute. This I take to be a contingent fact, founded on the existence of natural kinds. |
| 8515 | Tropes are basic particulars, so concrete particulars are collections of co-located tropes [Campbell,K] |
| Full Idea: If tropes are basic particulars, then concrete particulars count as dependent realities. They are collections of co-located tropes, depending on these tropes as a fleet does upon its component ships. | |
| From: Keith Campbell (The Metaphysic of Abstract Particulars [1981], §2) | |
| A reaction: If I sail my yacht through a fleet, do I become part of it? Presumably trope theory could avoid a bundle view of objects. A bare substratum could be a magnet which attracts tropes. |
| 8519 | Bundles must be unique, so the Identity of Indiscernibles is a necessity - which it isn't! [Campbell,K] |
| Full Idea: Each individual is distinct from each other individual, so the bundle account of objects requires each bundle to be different from every other bundle. So the Identity of Indiscernibles must be a necessary truth, which, unfortunately, it is not. | |
| From: Keith Campbell (The Metaphysic of Abstract Particulars [1981], §5) | |
| A reaction: Clearly the Identity of Indiscernibles is not a necessary truth (consider just two identical spheres). Location and time must enter into it. Could we not add a further individuation requirement to the necessary existence of a bundle? (Quinton) |
| 4033 | Two pure spheres in non-absolute space are identical but indiscernible [Campbell,K] |
| Full Idea: The Identity of Indiscernibles is not a necessary truth. It fails in possible worlds where there are two identical spheres in a non-absolute space, or worlds without beginning or end where events are exactly cyclically repeated. | |
| From: Keith Campbell (The Metaphysic of Abstract Particulars [1981], §5) | |
| A reaction: The principle was always very suspect, and these seem nice counterexamples. As so often, epistemology and ontology had become muddled. |
| 7898 | The world is just the illusion of an appearance [Anon (Dham)] |
| Full Idea: When a man considers this world as a bubble of froth, and as the illusion of an appearance, then the king of death has no power over him. | |
| From: Anon (Dham) (The DhammaPada [c.250 BCE], §13.170) | |
| A reaction: Strictly, of course, this says you can 'consider' things this way. Perhaps we could substitute 'pretends', but the world's great religions don't go in for that sort of thing. Berkeley would be shocked to learn he was approaching Buddhism. |
| 8512 | Abstractions come before the mind by concentrating on a part of what is presented [Campbell,K] |
| Full Idea: An item is abstract if 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: Keith Campbell (The Metaphysic of Abstract Particulars [1981], §1) | |
| A reaction: I think this point is incredibly important. Pure Fregean semantics tries to leave out the psychological component, and yet all the problems in semantics concern various sorts of abstraction. Imagination is the focus of the whole operation. |
| 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? |
| 7894 | Hate is conquered by love [Anon (Dham)] |
| Full Idea: Hate is not conquered by hate: hate is conquered by love. This is the law eternal. | |
| From: Anon (Dham) (The DhammaPada [c.250 BCE], §1.5) | |
| A reaction: [N.B. This thought was not invented by Jesus] The challenge to this view might be the tit-for-tat strategy of game theory, which says that hate is actually conquered by a combination of hate and love, judiciously applied. |
| 7899 | Even divine pleasure will not satisfy the wise, as it is insatiable, and leads to pain [Anon (Dham)] |
| Full Idea: Since a shower of gold coins could not satisfy craving desires and the end of all pleasure is pain, how could a wise man find satisfaction even in the pleasures of the gods? | |
| From: Anon (Dham) (The DhammaPada [c.250 BCE], §14.186) | |
| A reaction: I'm never sure how so many ancient thinkers arrived at this implausible view. They seem to think that no one knows when to stop, and that every drink leads to hangover. What is actually wrong with moderate sensible pleasure? |
| 7896 | The foolish gradually fill with evil, like a slowly-filled water-jar [Anon (Dham)] |
| Full Idea: The falling of drops of water will in time fill a water-jar. Even so the foolish man becomes full of evil, although he gather it little by little. | |
| From: Anon (Dham) (The DhammaPada [c.250 BCE], §9.121) | |
| A reaction: This coincides closely with Aristotle's view of moral education. Maybe a wise man can maintain one small vice. Not all slopes are slippery. |
| 7897 | The wise gradually fill with good, like a slowly-filled water-jar [Anon (Dham)] |
| Full Idea: The falling of drops of water will in time fill a water-jar. Even so the wise man becomes full of good, although he gather it little by little. | |
| From: Anon (Dham) (The DhammaPada [c.250 BCE], §9.122) | |
| A reaction: Again, this is like Aristotle's proposal of how to educate people in virtue. In my experience, there is no guarantee that small acts of politeness and charity will eventually guarantee goodness of character. Thought is also needed. |
| 7895 | Don't befriend fools; either find superior friends, or travel alone [Anon (Dham)] |
| Full Idea: If on the great journey of life a man cannot find one who is better or at least as good as himself, let him joyfully travel alone: a fool cannot help him on his journey. | |
| From: Anon (Dham) (The DhammaPada [c.250 BCE], §5.61) | |
| A reaction: This is a slightly disturbing aspect of Buddhism, possibly leading to contradiction. It urges friendship and love, but the finest people will have virtually no friends, and solitude is presented as a finer state than friendship. |
| 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) |
| 8517 | Causal conditions are particular abstract instances of properties, which makes them tropes [Campbell,K] |
| Full Idea: The conditions in causal statements are usually particular cases of properties. A collapse results from the weakness of this cable (not any other). This is specific to a time and place; it is an abstract particular. It is, in short, a trope. | |
| From: Keith Campbell (The Metaphysic of Abstract Particulars [1981], §3) | |
| A reaction: The fan of universals could counter this by saying that the collapse results from this unique combination of universals. Resemblance nominalist can equally build an account on the coincidence of certain types of concrete particulars. |
| 8516 | Davidson can't explain causation entirely by events, because conditions are also involved [Campbell,K] |
| Full Idea: Not all singular causal statements are of Davidson's event-event type. Many involve conditions, so there are condition-event (weakness/collapse), event-condition (explosion/movement), and condition-condition (hot/warming) causal connections. | |
| From: Keith Campbell (The Metaphysic of Abstract Particulars [1981], §3) | |
| A reaction: Fans of Davidson need to reduce conditions to events. The problem of individuation keeps raising its head. Davidson makes it depend on description. Kim looks good, because events, and presumably conditions, reduce to something small and precise. |
| 7900 | Speak the truth, yield not to anger, give what you can to him who asks [Anon (Dham)] |
| Full Idea: Speak the truth, yield not to anger, give what you can to him who asks: these three steps lead you to the gods | |
| From: Anon (Dham) (The DhammaPada [c.250 BCE], §17.224) | |
| A reaction: I don't recall either the Old or New Testament, or the Koran, placing great emphasis on speaking the truth. The injunction to give is not so simple. Give to greedy children, to alcoholics, to criminals, to the rich, to fools, to yourself? |
| 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) |