53 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) |
| 23367 | Even pointing a finger should only be done for a reason [Epictetus] |
| Full Idea: Philosophy says it is not right even to stretch out a finger without some reason. | |
| From: Epictetus (fragments/reports [c.57], 15) | |
| A reaction: The key point here is that philosophy concerns action, an idea on which Epictetus is very keen. He rather despise theory. This idea perfectly sums up the concept of the wholly rational life (which no rational person would actually want to live!). |
| 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. |
| 15477 | Ontology is highly abstract physics, containing placeholders and exclusions [Martin,CB] |
| Full Idea: Ontology sets out an even more abstract model of how the world is than theoretical physics, a model that has placeholders for scientific results and excluders for tempting confusions. | |
| From: C.B. Martin (The Mind in Nature [2008], 04.6) | |
| A reaction: Most modern metaphysicians accept this account. The interesting (mildly!) question is whether physicists will accept it. If the metaphysics is really rooted in physics, a metaphysical physicist is better placed than a metaphysician knowing some physics. |
| 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? |
| 15471 | Truth is a relation between a representation ('bearer') and part of the world ('truthmaker') [Martin,CB] |
| Full Idea: Truth is a relation between two things - a representation (the truth 'bearer') and the world or some part of it (the 'truthmaker'). | |
| From: C.B. Martin (The Mind in Nature [2008], 03.1) | |
| A reaction: That truth is about representations seems to me to be exactly right. That it is about truthmakers is more controversial. There are well known problems with negative truths, general truths, future truths etc. I'm happy with 'facts'. |
| 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. |
| 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. |
| 15484 | A property is a combination of a disposition and a quality [Martin,CB] |
| Full Idea: I take properties to have a dual nature; in virtue of possessing a property, an object possesses both a particular dispositionality and a particular qualitative character. | |
| From: C.B. Martin (The Mind in Nature [2008], 04.6) | |
| A reaction: That leaves you with the question of the relationship between the disposition and the quality. I say you must choose, and I choose the disposition. Qualities (which are partly subjective, obviously) arise from fundamental dispositions. |
| 15478 | Properties are the respects in which objects resemble, which places them in classes [Martin,CB] |
| Full Idea: If objects belong to classes in virtue of resemblances they bear to one another, they resemble one another in virtue of their properties. Objects resemble in some way or respect, and you could think of these ways or respects as 'properties'. | |
| From: C.B. Martin (The Mind in Nature [2008], 04.6) | |
| A reaction: If you pare the universe down to one object with five distinct properties, they resemble nothing, and fail this definition. Resemblance seems like the epistemology, not the ontology. |
| 15483 | Properties are ways particular things are, and so they are tied to the identity of their possessor [Martin,CB] |
| Full Idea: The redness or sphericity of this tomato cannot migrate to another tomato. This is a consequence of the idea that properties are particular ways things are. The identity of a property is bound up with the identity of its possessor. | |
| From: C.B. Martin (The Mind in Nature [2008], 04.6) | |
| A reaction: This is part of his declaration that he believes in tropes. At the very least, properties can be thought of separately, and have second-order properties that don't seem tied to the particulars. |
| 15480 | Objects are not bundles of tropes (which are ways things are, not parts of things) [Martin,CB] |
| Full Idea: The bundle theory for tropes treats properties inappositely as parts of objects. Objects can have parts, but an object's properties are not its parts, they are particular ways the object is. | |
| From: C.B. Martin (The Mind in Nature [2008], 04.6) | |
| A reaction: The 'way an object is' seems a very vague concept. Most things that get labelled as tropes are actually highly complex. Without mention of causal powers I think these discussions drift in a muddle. |
| 15489 | A property that cannot interact is worse than inert - it isn't there at all [Martin,CB] |
| Full Idea: A property that is intrinsically incapable of affecting or being affected by anything else, actual or possible, is not merely a case of inertness - it amounts to a no-thing. | |
| From: C.B. Martin (The Mind in Nature [2008], 06.6) | |
| A reaction: In the end Martin rejects Shoemaker's purely causal account of properties, but he clearly understands Shoemaker's point well. |
| 15487 | If unmanifested partnerless dispositions are still real, and are not just qualities, they can explain properties [Martin,CB] |
| Full Idea: Given a realist view of dispositions as fully actual, even without manifestations or partners, a purely dispositional account of properties has a degree of plausibility, which is enhanced because properties lack purely qualitative characterisations. | |
| From: C.B. Martin (The Mind in Nature [2008], 06.4) | |
| A reaction: In the end Martin opts for a mixed account, as in Idea 15484, but he gives reasons here for the view which I favour. If he concedes that dispositions may exist without manifestation, they must surely lack qualities. Are they not properties, then? |
| 15479 | Properties endow a ball with qualities, and with powers or dispositions [Martin,CB] |
| Full Idea: Each property endows a ball with a distinctive qualitative character and a distinctive range of powers or dispositionalities. | |
| From: C.B. Martin (The Mind in Nature [2008], 04.6) | |
| A reaction: I think this is the wrong way round. Do properties support powers, or powers support properties? I favour the latter. Properties are much vaguer than powers. Powers generate the required causation and activity. |
| 15488 | Qualities and dispositions are aspects of properties - what it exhibits, and what it does [Martin,CB] |
| Full Idea: For any intrinsic and irreducible property, what is qualitative and what is dispositional are one and the same property considered as what that property exhibits of its nature and what that property is directive and selective for in its manifestation. | |
| From: C.B. Martin (The Mind in Nature [2008], 06.6) | |
| A reaction: This is supposed to support qualities and dispositions as equal partners, but I don't see how 'what a property exhibits' can have any role in fundamental ontology. What it exhibits may be very misleading about its nature. |
| 15469 | Dispositions in action can be destroyed, be recovered, or remain unchanged [Martin,CB] |
| Full Idea: Three forms of dispositionality are illustrated by explosives (which are destroyed by manifestation), being soluble (where the dispositions is lost but recoverable), and being stable (where the disposition is unchanged). | |
| From: C.B. Martin (The Mind in Nature [2008], 02.7) | |
| A reaction: [compressed] Presumably the explosives could be recovered after the explosion, since the original elements are still there, but it would take a while. The retina remains stable by continually changing. There are no simple distinctions! |
| 15467 | Powers depend on circumstances, so can't be given a conditional analysis [Martin,CB] |
| Full Idea: Nobody believes, or ought to believe, that manifestations of powers follow upon the single event mentioned in the antecedent of the conditional independently of the circumstances. | |
| From: C.B. Martin (The Mind in Nature [2008], 02.4) | |
| A reaction: Another way of putting it would be that the behaviour of powers is more ceteris paribus than law. |
| 15466 | 'The wire is live' can't be analysed as a conditional, because a wire can change its powers [Martin,CB] |
| Full Idea: According to the conditional analysis of 'the wire is live', if the wire is touched then it gives off electricity. What ultimately defeats this analysis is the acknowledged possibility of objects gaining or losing powers. | |
| From: C.B. Martin (The Mind in Nature [2008], 02.3) | |
| A reaction: He offers his 'electro-fink' as a counterexample, where touching the wire changes its disposition. The conditional analysis is simple and clearcut, but dispositions in reality are complex and unstable. |
| 15476 | Structural properties involve dispositionality, so cannot be used to explain it [Martin,CB] |
| Full Idea: I take it as obvious that any structural property involves dispositionality and, therefore, cannot be used to 'explain' dispositionality. | |
| From: C.B. Martin (The Mind in Nature [2008], 04.3) | |
| A reaction: I think this is the right way round. The so-called 'categorical' properties seem to be close in nature to the 'structural' properties. |
| 15465 | Structures don't explain dispositions, because they consist of dispositions [Martin,CB] |
| Full Idea: It is self-defeating to try to explain dispositionality in terms of structural states because structural states are themselves dispositional. | |
| From: C.B. Martin (The Mind in Nature [2008], 01.2) | |
| A reaction: No doubt structures have dispositions, but are they entirely dispositional? Might there be 'emergent' dispositions which can only be explained by the structure itself, rather than by the dispositions that make up the structure? |
| 15481 | I favour the idea of a substratum for properties; spacetime seems to be just a bearer of properties [Martin,CB] |
| Full Idea: I favour the old idea of substratum: the haver of properties not itself had as a property. Space-time might itself be the bearer of properties, not itself borne as a property. | |
| From: C.B. Martin (The Mind in Nature [2008], 04.6) | |
| A reaction: A very nice idea. The choice is between saying either that fundamentals like space-time and physical fields are the propertyless bearers of properties, or that they purely consist of properties (so properties are fundamental, not substrata). |
| 15474 | Properly understood, wholes do no more causal work than their parts [Martin,CB] |
| Full Idea: There is no causal work for the whole that is not done by the parts, provided the complex role of the parts is fully appreciated. | |
| From: C.B. Martin (The Mind in Nature [2008], 04.1) | |
| A reaction: It seems like a truth that because some parts are doing particular causal work (e.g. glue), the whole can acquire causal powers that the mereological sum of parts lacks. |
| 15486 | Only abstract things can have specific and full identity specifications [Martin,CB] |
| Full Idea: Abstract entities (as nonspatiotemporal) seem to be the only candidates for specific and full identity specifications. | |
| From: C.B. Martin (The Mind in Nature [2008], 05.2 n1) | |
| A reaction: Martin says that only the 'mad logician' seeks such specifications elsewhere. Some people like persons to have perfect identity. God is a popular candidate too. Can objects have perfect 'macroscopic' identity? |
| 15475 | The concept of 'identity' must allow for some changes in properties or parts [Martin,CB] |
| Full Idea: We must avoid a use of 'identity' that implies that any entity over time must be said to lack continuing identity simply because it has changed properties or has lost, added, or had substituted some parts. | |
| From: C.B. Martin (The Mind in Nature [2008], 04.3) | |
| A reaction: This may the key area where the logical-mathematical type of philosophy comes into contact with the natural-metaphysical type. Imagine Martin's concept of 'identity' in mathematics. π changes to 3.1387... during the calculation! |
| 15472 | It is pointless to say possible worlds are truthmakers, and then deny that possible worlds exist [Martin,CB] |
| Full Idea: To claim that the truthmaker for a counterfactual, for example, is a set of possible worlds, but to deny that these worlds really exist, seems pointless. | |
| From: C.B. Martin (The Mind in Nature [2008], 03.3) | |
| A reaction: Lewis therefore argues that they do exist. Martin argues that possible worlds are not truthmakers. He rests his account of modality on dispositions. I prefer Martin. |
| 15492 | Explanations are mind-dependent, theory-laden, and interest-relative [Martin,CB] |
| Full Idea: Explanations are mind-dependent, theory-laden, and interest-relative. | |
| From: C.B. Martin (The Mind in Nature [2008], 10.2) | |
| A reaction: I don't think you can rule out the 'real' explanation, as the one dominant causal predecessor, such as the earthquake producing a tsunami. |
| 15495 | Analogy works, as when we eat food which others seem to be relishing [Martin,CB] |
| Full Idea: The long-derided way of analogy works! Otherwise why, when someone else is relishing a food we have not tried, is it reasonable for us to try it ourselves? | |
| From: C.B. Martin (The Mind in Nature [2008], 12.2) | |
| A reaction: Why wouldn't we rush to eat something an animal was relishing? Nice idea. |
| 15493 | Memory requires abstraction, as reminders of what cannot be fully remembered [Martin,CB] |
| Full Idea: Selectivity and abstraction are required for the development of memory, because reminders and promptings are rarely replicas of what is being remembered. | |
| From: C.B. Martin (The Mind in Nature [2008], 10.3) | |
| A reaction: I take the key idea of mental life to be that of a 'label'. This need not be verbal, so 'conceptual label'. It could be an image, as on a road sign. Labelling is the most indispensable aspect of thought. We label objects, parts, properties and groups. |
| 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) |
| 15485 | Instead of a cause followed by an effect, we have dispositions in reciprocal manifestation [Martin,CB] |
| Full Idea: The two-event cause-and-effect view is easily avoided and replaced by the view of mutual manifestations of reciprocal disposition partners, suggesting a natural contemporaneity. | |
| From: C.B. Martin (The Mind in Nature [2008], 05.1) | |
| A reaction: This view, which I find much more congenial than the traditional one, is explored in the ideas of Mumford and Anjum. |
| 15491 | Causation should be explained in terms of dispositions and manifestations [Martin,CB] |
| Full Idea: Disposition and manifestation are the basic categories by means of which cause and effect are to be explained. | |
| From: C.B. Martin (The Mind in Nature [2008], 07.8) | |
| A reaction: 'Manifestation' sounds a bit subjective. The manifestation evident to us may not indicate what is really going on below the surface. I like his basic picture. |
| 15468 | Causal counterfactuals are just clumsy linguistic attempts to indicate dispositions [Martin,CB] |
| Full Idea: 'Causal' counterfactuals have a place, of course, but only as clumsy and inexact linguistic gestures to dispositions, and they should be kept in that place. | |
| From: C.B. Martin (The Mind in Nature [2008], 02.6) | |
| A reaction: Counterfactuals only seem to give a regularity account of causation, by correlating an effect with a minimal context which will give rise to it. Surely dispositions run deeper than that? |
| 15470 | Causal laws are summaries of powers [Martin,CB] |
| Full Idea: Causal laws are summaries of what entities are capable and incapable of. | |
| From: C.B. Martin (The Mind in Nature [2008], 02.8) | |
| A reaction: That's a pretty good formulation. Personally I favour a Humean analysis, perhaps along Lewis's lines, but on a basis of real powers. This remark of Martin's has got me rethinking. |
| 15482 | We can't think of space-time as empty and propertyless, and it seems to be a substratum [Martin,CB] |
| Full Idea: It makes no sense in ontology or modern physics to think of space-time as empty and propertyless. Space-time nicely fulfils the condition of a substratum. | |
| From: C.B. Martin (The Mind in Nature [2008], 04.6) | |
| A reaction: At the very least, space-time seems to be 'curved', so it had better be something. Time has properties like being transitive. Space-time (or fields) might be a pure bundle of properties (the only pure bundle?), rather than a substratum. |
| 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) |