48 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'. |
| 21122 | Liberal Nationalism says welfare states and democracy needed a shared sense of nationality [Shorten] |
| Full Idea: The Liberal Nationalist argument is that if we want to have welfare states or vibrant democracies, then we will need the kind of solidarity that shared nationality fosters. …Unwelcome democratic decisions are more acceptable when made by co-nationals. | |
| From: Andrew Shorten (Contemporary Political Theory [2016], 02) | |
| A reaction: We've just experienced this with Brexit (2016), where perfectly sensible decisions were being made in Brussels, but the popular press whipped up hostility because the British had a restricted role in the decisions. Prefer our idiots to their sages. |
| 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. |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
| Full Idea: Anaxarchus said that he was not even sure that he knew nothing. | |
| From: report of Anaxarchus (fragments/reports [c.340 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.10.1 |
| 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. |
| 21136 | Utilitarians conflate acts and omissions; causing to drown and failing to save are the same [Shorten] |
| Full Idea: Most uitlitarians do not distinguish between acts and omissions, and see no morally relevant difference between walking past a drowning child and pushing a child into a pond. | |
| From: Andrew Shorten (Contemporary Political Theory [2016], 09) | |
| A reaction: He cites Peter Singer as an instance. The notorious Trolley Problem focuses on such issues. Michael Sandel in 'Justice' is good on that. If motive and intention matter, the two cases could be very different. Too timid to push, but also too timid to help? |
| 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? |
| 21135 | There are eight different ways in which groups of people can be oppressed [Shorten, by PG] |
| Full Idea: Groups can be oppressed in seven different ways: by violence, marginalisation, powerlessness, cultural domination, exploitation, stigmatisation, neglect of interests, and lack of egalitarian ethos. | |
| From: report of Andrew Shorten (Contemporary Political Theory [2016], 08) by PG - Db (ideas) | |
| A reaction: [my summary of Shorten's summary] These headings seem to overlap somewhat. It strengthens my growing view that if one builds a political philosophy around the supreme virtue of respect, then all of these modes of oppression are undermined. |
| 21118 | Constitutional Patriotism unites around political values (rather than national identity) [Shorten] |
| Full Idea: 'Constitutional patriots' favour a 'post-national' form of political identity in which members share common political values, but not necessarily a common national identity. | |
| From: Andrew Shorten (Contemporary Political Theory [2016], 02) | |
| A reaction: Interesting. Not sure if you can keep political values distinct from community values. In theory it is an approach designed for cultural pluralism. But if the political values are liberal that implies cultural freedoms for (e.g.) women. |
| 21129 | Democracy is a method of selection, or it involves participation, or it concerns public discussion [Shorten] |
| Full Idea: Competitive democrats believe that democracy is simply a method for selecting political leaders …Participatory democrats associate the democratic ideal with living in a participatory society …Deliberative democrats identify public reasoning as key. | |
| From: Andrew Shorten (Contemporary Political Theory [2016], 05) | |
| A reaction: Personally I would favour public discussion, but that is the last thing leaders want, especially if they are not very knowledgeable or clever. |
| 21130 | Some say democracy is intrinsically valuable, others that it delivers good outcomes [Shorten] |
| Full Idea: Some theorist think that democracy is intrinsically valuable, but others believe that it is valuable because it delivers good outcomes. | |
| From: Andrew Shorten (Contemporary Political Theory [2016], 05) | |
| A reaction: It is hard to see how the majority having a dictatorship over the minority could be an intrinsic good. If we start with respect as the supreme social virtue, then participation and public discussion might be intrinsic goods. |
| 21126 | Representative should be either obedient, or sensible, or typical [Shorten] |
| Full Idea: Mandate Representation says they are delegates who should not deviate from instructions; Trustee says they use their discretion and judgement; Descriptive says they share group characteristics. | |
| From: Andrew Shorten (Contemporary Political Theory [2016], 04) | |
| A reaction: [compressed] There is also being a representative because you have an audience (such as celebrity campains). The second type was famously defended by Edmund Burke. The third implies being the same colour, or gender, or religion. |
| 21128 | There is 'mirror representation' when the institution statistically reflects the population [Shorten] |
| Full Idea: The general theory of 'mirror representation' says that a representative body or institution should be a statistically accurate sample of the wider society it represents. | |
| From: Andrew Shorten (Contemporary Political Theory [2016], 04) | |
| A reaction: How fine-grained should this be in accuracy. Should every small minority have at least one rep? Can't reps be trusted to speak for people a bit different from themselves? Maybe not! He quotes Mirabeau in support of this idea. |
| 21127 | In a changed situation a Mandated Representative can't keep promises and fight for constituents [Shorten] |
| Full Idea: An important tension in Mandate Representation seemingly requires politicians to both uphold their electoral promises and promote the interests of their constituents. These can conflict, with changed circumstances or information. | |
| From: Andrew Shorten (Contemporary Political Theory [2016], 04 Box 4.1) | |
| A reaction: So be careful what you promise, and don't take on a party loyalty that conflicts with your constituents' interests. Easy. |
| 21117 | Liberal citizens have a moral requirement to respect freedom and equality [Shorten] |
| Full Idea: The liberal theory of political community contains a moral thesis which says that members should share a moral concern for one another as free and equal citizens. …Citizens are not required to have much else in common with one another. | |
| From: Andrew Shorten (Contemporary Political Theory [2016], 02) | |
| A reaction: A key thought. Liberal hearts swell with pride at the first half, but anti-liberals are interested in the second bit. If my neighbour lives in miserable poverty, should I only ask whether they are 'equal and free'? Respect everything! |
| 21134 | Maybe the rational autonomous liberal individual is merely the result of domination [Shorten] |
| Full Idea: On a radical reading of Foucault, the very ideal of a rational, autonomous moral agent that lies at the heart of liberal governmentality is nothing more than the effect of a particular form of domination. | |
| From: Andrew Shorten (Contemporary Political Theory [2016], 06) | |
| A reaction: [Apologies for the word 'governmentality'; I'm just the messenger] Presumably Foucault's philosophy is also the result of domination, so it is hard to know where to start. The status of rationality is the central issue. |
| 21113 | Liberal equality concerns rights, and liberal freedom concerns choice of ends [Shorten] |
| Full Idea: A liberal society treats people as equals by equipping them with the same set of rights, and it respects their freedom by allowing them to choose their own freely chosen ends. | |
| From: Andrew Shorten (Contemporary Political Theory [2016], 01) | |
| A reaction: Equality of rights is fairly standard in any modern society (at least in principle). Freedom of ends is trickier. You can dismiss someone sleeping in the gutter as living a life that resulted from their choices. How many people have clear goals in life? |
| 21121 | Liberal Nationalism encourages the promotion of nationalistic values [Shorten] |
| Full Idea: 'Liberal nationalists' say liberalism is compatible with promoting nationality, by teaching national history and literature and supporting its language. Compatriot priority adds that the needs of compatriots can override those of foreigners. | |
| From: Andrew Shorten (Contemporary Political Theory [2016], 02) | |
| A reaction: [compressed] As a teacher of literature I always preferred to teach the literature of my own country, but without considering the reasons for it. But it was a combination of pride in my people's achievements, and a desire to strengthen social bonds. |
| 21115 | Liberalism should not make assumptions such as the value of choosing your own life plan [Shorten] |
| Full Idea: Communitarians say that liberalism could only justified by appealing to controversial assumptions that are not universally shared, such as the significance of choosing one's own plan of life. | |
| From: Andrew Shorten (Contemporary Political Theory [2016], 01) | |
| A reaction: In the past, at least, huge numbers of people have been perfectly happy living a life designed for them by their parents. It is not much consolation for a disastrous life that at least you planned it yourself. Liberal values are not self-evident. |
| 21114 | Liberals treat individuals as mutual strangers, rather than as social beings [Shorten] |
| Full Idea: Communitarians say that liberalism treats individuals as strangers to one another, and underestimates the extent to which individuals are 'constituted' by their societies and social memberships. | |
| From: Andrew Shorten (Contemporary Political Theory [2016], 01) | |
| A reaction: On the other hand you can have 'too much community'. Surely the test for any political system is the quality of lives led by individual citizens? There can never be a wonderful community full of miserable citizens. |
| 21123 | Liberal Nationalism is more communitarian, and Constitutional Patriotism more cosmopolitan [Shorten] |
| Full Idea: While Liberal Nationalists push liberalism in a particularist and communitarian direction, Constitutional Patriots emphasise its universalistic and cosmopolitan aspects. | |
| From: Andrew Shorten (Contemporary Political Theory [2016], 02) | |
| A reaction: So many attractive qualities to choose from! A tolerant community ought to be cosmopolitan. Being universalistic should not entail a neglect of the particular. Etc. |
| 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) |
| 21124 | Religious toleration has been institutionalised by the separation of church and state [Shorten] |
| Full Idea: One historically influential solution to the discord unleashed by the fact of religious diversity was to institutionalise the principle of toleration by separating church and state. | |
| From: Andrew Shorten (Contemporary Political Theory [2016], 03) | |
| A reaction: In 2018 Britain we still have an established religion (Anglicanism - Episcopalianism in the US), but toleration has arrived with the decline of religious belief. It must still be tough for Muslims, Jews etc to see a different religion as the official one. |
| 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) |