48 ideas
19648 | Since Kant we think we can only access 'correlations' between thinking and being [Meillassoux] |
Full Idea: The central notion of philosophy since Kant is 'correlation' - that we only ever have access to the correlation between thinking and being, and never to either term considered apart from the other. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 1) | |
A reaction: Meillassoux's charge is that philosophy has thereby completely failed to grasp the scientific revolution, which has used mathematics to make objectivity possible. Quine and Putnam would be good examples of what he has in mind. |
19674 | The Copernican Revolution decentres the Earth, but also decentres thinking from reality [Meillassoux] |
Full Idea: The Copernican Revolution is not so much the decentring of observers in the solar system, but (by the mathematizing of nature) the decentring of thought relative to the world within the process of knowledge. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 5) | |
A reaction: In other words, I take it, the Copernican Revolution was the discovery of objectivity. That is a very nice addition to my History of Ideas collection. |
19657 | In Kant the thing-in-itself is unknowable, but for us it has become unthinkable [Meillassoux] |
Full Idea: The major shift that has occurred in the conception of thought from Kant's time to ours is from the unknowability of the thing-in-itself to its unthinkability. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 2) | |
A reaction: Meillassoux is making the case that philosophy is alienating us more and more from the triumphant realism of the scientific revolution. He says thinking has split from being. He's right. Modern American pragmatists are the worst (not Peirce!). |
19675 | Since Kant, philosophers have claimed to understand science better than scientists do [Meillassoux] |
Full Idea: Ever since Kant, to think science as a philosopher has been to claim that science harbours a meaning other than the one delivered by science itself. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 5) | |
A reaction: The point is that science discovered objectivity (via the mathematising of nature), and Kant utterly rejected objectivity, by enmeshing the human mind in every possible scientific claim. This makes Meillassoux and I very cross. |
19649 | Since Kant, objectivity is defined not by the object, but by the statement's potential universality [Meillassoux] |
Full Idea: Since Kant, objectivity is no longer defined with reference to the object in itself, but rather with reference to the possible universality of an objective statement. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 1) | |
A reaction: Meillassoux disapproves of this, as a betrayal by philosophers of the scientific revolution, which gave us true objectivity (e.g. about how the world was before humanity). |
19666 | If we insist on Sufficient Reason the world will always be a mystery to us [Meillassoux] |
Full Idea: So long as we continue to believe that there is a reason why things are the way they are rather than some other way, we will construe this world is a mystery, since no such reason will every be vouchsafed to us. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 4) | |
A reaction: Giving up sufficient reason sounds like a rather drastic response to this. Put it like this: Will we ever be able to explain absolutely everything? No. So will the world always be a little mysterious to us? Yes, obviously. Is that a problem? No! |
19656 | Non-contradiction is unjustified, so it only reveals a fact about thinking, not about reality? [Meillassoux] |
Full Idea: The principle of non-contradiction itself is without reason, and consequently it can only be the norm for what is thinkable by us, rather than for what is possible in the absolute sense. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 2) | |
A reaction: This is not Meillassoux's view, but describes the modern heresy of 'correlationism', which ties all assessments of how reality is to our capacity to think about it. Personally I take logical non-contradiction to derive from non-contradiction in nature. |
16877 | A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege] |
Full Idea: We construct a sense out of its constituents and introduce an entirely new sign to express this sense. This may be called a 'constructive definition', but we prefer to call it a 'definition' tout court. It contrasts with an 'analytic' definition. | |
From: Gottlob Frege (Logic in Mathematics [1914], p.210) | |
A reaction: An analytic definition is evidently a deconstruction of a past constructive definition. Fregean definition is a creative activity. |
11219 | Frege suggested that mathematics should only accept stipulative definitions [Frege, by Gupta] |
Full Idea: Frege has defended the austere view that, in mathematics at least, only stipulative definitions should be countenanced. | |
From: report of Gottlob Frege (Logic in Mathematics [1914]) by Anil Gupta - Definitions 1.3 | |
A reaction: This sounds intriguingly at odds with Frege's well-known platonism about numbers (as sets of equinumerous sets). It makes sense for other mathematical concepts. |
16878 | We must be clear about every premise and every law used in a proof [Frege] |
Full Idea: It is so important, if we are to have a clear insight into what is going on, for us to be able to recognise the premises of every inference which occurs in a proof and the law of inference in accordance with which it takes place. | |
From: Gottlob Frege (Logic in Mathematics [1914], p.212) | |
A reaction: Teachers of logic like natural deduction, because it reduces everything to a few clear laws, which can be stated at each step. |
19663 | We can allow contradictions in thought, but not inconsistency [Meillassoux] |
Full Idea: For contemporary logicians, it is not non-contradiction that provides the criterion for what is thinkable, but rather inconsistency. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 3) | |
A reaction: The point is that para-consistent logic might permit isolated contradictions (as true) within a system, but it is only contradiction across the system (inconsistencies) which make the system untenable. |
19664 | Paraconsistent logics are to prevent computers crashing when data conflicts [Meillassoux] |
Full Idea: Paraconsistent logics were only developed in order to prevent computers, such as expert medical systems, from deducing anything whatsoever from contradictory data, because of the principle of 'ex falso quodlibet'. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 3) |
19665 | Paraconsistent logic is about statements, not about contradictions in reality [Meillassoux] |
Full Idea: Paraconsistent logics are only ever dealing with contradictions inherent in statements about the world, never with the real contradictions in the world. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 3) | |
A reaction: Thank goodness for that! I can accept that someone in a doorway is both in the room and not in the room, but not that they are existing in a real state of contradiction. I fear that a few daft people embrace the logic as confirming contradictory reality. |
16867 | Logic not only proves things, but also reveals logical relations between them [Frege] |
Full Idea: A proof does not only serve to convince us of the truth of what is proved: it also serves to reveal logical relations between truths. Hence we find in Euclid proofs of truths that appear to stand in no need of proof because they are obvious without one. | |
From: Gottlob Frege (Logic in Mathematics [1914], p.204) | |
A reaction: This is a key idea in Frege's philosophy, and a reason why he is the founder of modern analytic philosophy, with logic placed at the centre of the subject. I take the value of proofs to be raising questions, more than giving answers. |
16863 | Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege] |
Full Idea: Are there perhaps modes of inference peculiar to mathematics which …do not belong to logic? Here one may point to inference by mathematical induction from n to n+1. | |
From: Gottlob Frege (Logic in Mathematics [1914], p.203) | |
A reaction: He replies that it looks as if induction can be reduced to general laws, and those can be reduced to logic. |
16862 | The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege] |
Full Idea: Mathematics has closer ties with logic than does almost any other discipline; for almost the entire activity of the mathematician consists in drawing inferences. | |
From: Gottlob Frege (Logic in Mathematics [1914], p.203) | |
A reaction: The interesting question is who is in charge - the mathematician or the logician? |
16865 | 'Theorems' are both proved, and used in proofs [Frege] |
Full Idea: Usually a truth is only called a 'theorem' when it has not merely been obtained by inference, but is used in turn as a premise for a number of inferences in the science. ….Proofs use non-theorems, which only occur in that proof. | |
From: Gottlob Frege (Logic in Mathematics [1914], p.204) |
16866 | Tracing inference backwards closes in on a small set of axioms and postulates [Frege] |
Full Idea: We can trace the chains of inference backwards, …and the circle of theorems closes in more and more. ..We must eventually come to an end by arriving at truths can cannot be inferred, …which are the axioms and postulates. | |
From: Gottlob Frege (Logic in Mathematics [1914], p.204) | |
A reaction: The rival (more modern) view is that that all theorems are equal in status, and axioms are selected for convenience. |
16868 | The essence of mathematics is the kernel of primitive truths on which it rests [Frege] |
Full Idea: Science must endeavour to make the circle of unprovable primitive truths as small as possible, for the whole of mathematics is contained in this kernel. The essence of mathematics has to be defined by this kernel of truths. | |
From: Gottlob Frege (Logic in Mathematics [1914], p.204-5) | |
A reaction: [compressed] I will make use of this thought, by arguing that mathematics may be 'explained' by this kernel. |
16870 | Axioms are truths which cannot be doubted, and for which no proof is needed [Frege] |
Full Idea: The axioms are theorems, but truths for which no proof can be given in our system, and no proof is needed. It follows from this that there are no false axioms, and we cannot accept a thought as an axiom if we are in doubt about its truth. | |
From: Gottlob Frege (Logic in Mathematics [1914], p.205) | |
A reaction: He struggles to be as objective as possible, but has to concede that whether we can 'doubt' the axiom is one of the criteria. |
16871 | A truth can be an axiom in one system and not in another [Frege] |
Full Idea: It is possible for a truth to be an axiom in one system and not in another. | |
From: Gottlob Frege (Logic in Mathematics [1914], p.205) | |
A reaction: Frege aspired to one huge single system, so this is a begrudging concession, one which modern thinkers would probably take for granted. |
16869 | To create order in mathematics we need a full system, guided by patterns of inference [Frege] |
Full Idea: We cannot long remain content with the present fragmentation [of mathematics]. Order can be created only by a system. But to construct a system it is necessary that in any step forward we take we should be aware of the logical inferences involved. | |
From: Gottlob Frege (Logic in Mathematics [1914], p.205) |
19677 | What is mathematically conceivable is absolutely possible [Meillassoux] |
Full Idea: We must establish the thesis that what is mathematically conceivable is absolutely possible. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 5) | |
A reaction: The truth of this thesis would permanently establish mathematics as the only possible language of science. Personally I have no idea how you could prove or assess such a thesis. It is a lovely speculation, though. 'The structure of the possible' (p,127) |
16864 | If principles are provable, they are theorems; if not, they are axioms [Frege] |
Full Idea: If the law [of induction] can be proved, it will be included amongst the theorems of mathematics; if it cannot, it will be included amongst the axioms. | |
From: Gottlob Frege (Logic in Mathematics [1914], p.203) | |
A reaction: This links Frege with the traditional Euclidean view of axioms. The question, then, is how do we know them, given that we can't prove them. |
19659 | The absolute is the impossibility of there being a necessary existent [Meillassoux] |
Full Idea: We maintain that it is absolutely necessary that every entity might not exist. ...The absolute is the absolute impossibility of a necessary being. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 3) | |
A reaction: This is the main thesis of his book. The usual candidates for necessary existence are God, and mathematical objects. I am inclined to agree with Meillassoux. |
19662 | It is necessarily contingent that there is one thing rather than another - so something must exist [Meillassoux] |
Full Idea: It is necessary that there be something rather than nothing because it is necessarily contingent that there is something rather than something else. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 3) | |
A reaction: The great charm of metaphysics is the array of serious answers to the question of why there is something rather than nothing. You'll need to read Meillassoux's book to understand this one. |
19654 | We must give up the modern criterion of existence, which is a correlation between thought and being [Meillassoux] |
Full Idea: It is incumbent upon us to break with the ontological requisite of the moderns, according to which 'to be is to be a correlate'. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 2) | |
A reaction: He blames Kant for this pernicious idea, which has driven philosophy away from realist science, when it should be supporting and joining it. As a realist I agree, and find Meillassoux very illuminating on the subject. |
9388 | Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege] |
Full Idea: Of any concept, we must require that it have a sharp boundary. Of any object it must hold either that it falls under the concept or it does not. We may not allow a third case in which it is somehow indeterminate whether an object falls under a concept. | |
From: Gottlob Frege (Logic in Mathematics [1914], p.229), quoted by Ian Rumfitt - The Logic of Boundaryless Concepts p.1 n1 | |
A reaction: This is the voice of the classical logician, which has echoed by Russell. I'm with them, I think, in the sense that logic can only work with precise concepts. The jury is still out. Maybe we can 'precisify', without achieving total precision. |
19660 | Possible non-being which must be realised is 'precariousness'; absolute contingency might never not-be [Meillassoux] |
Full Idea: My term 'precariousness' designates a possibility of not-being which must eventually be realised. By contrast, absolute contingency designates a pure possibility; one which may never be realised. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 3) | |
A reaction: I thoroughly approve of this distinction, because I have often enountered the assumption that all contingency is precariousness, and I have never seen why that should be so. In Aquinas's Third Way, for example. The 6 on a die may never come up. |
19671 | The idea of chance relies on unalterable physical laws [Meillassoux] |
Full Idea: The very notion of chance is only conceivable on condition that there are unalterable physical laws. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 4) | |
A reaction: Laws might be contingent, even though they never alter. Chance in horse racing relies on the stability of whole institution of horse racing. |
19651 | Unlike speculative idealism, transcendental idealism assumes the mind is embodied [Meillassoux] |
Full Idea: What distinguishes transcendental idealism from speculative idealism is the fact that the former does not posit the existence of the transcendental subject apart from its bodily individuation. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 1) | |
A reaction: These modern French philosophers explain things so much more clearly than the English! The 'speculative' version is seen in Berkeley. On p.17 he says transcendental idealism is 'civilised', and speculative idealism is 'uncouth'. |
19647 | The aspects of objects that can be mathematical allow it to have objective properties [Meillassoux] |
Full Idea: All aspects of the object that can give rise to a mathematical thought rather than to a perception or a sensation can be meaningfully turned into the properties of the thing not only as it is with me, but also as it is without me. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 1) | |
A reaction: This is Meillassoux's spin on the primary/secondary distinction, which he places at the heart of the scientific revolution. Cartesian dualism offers a separate space for the secondary qualities. He is appalled when philosophers reject the distinction. |
19652 | How can we mathematically describe a world that lacks humans? [Meillassoux] |
Full Idea: How is mathematical discourse able to describe a reality where humanity is absent? | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 1) | |
A reaction: He is referring to the prehistoric world. He takes this to be a key question about the laws of nature. We extrapolate mathematically from the experienced world, relying on the stability of the laws. Must they be necessary to be stable? No, it seems. |
19668 | Hume's question is whether experimental science will still be valid tomorrow [Meillassoux] |
Full Idea: Hume's question can be formulated as follows: can we demonstrate that the experimental science which is possible today will still be possible tomorrow? | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 4) | |
A reaction: Could there be deep universal changes going on in nature which science could never, even in principle, detect? |
19650 | The transcendental subject is not an entity, but a set of conditions making science possible [Meillassoux] |
Full Idea: The transcendental subject simply cannot be said to exist; which is to say that the subject is not an entity, but rather a set of conditions rendering objective scientific knowledge of entities possible. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 1) | |
A reaction: Meillassoux treats this as part of the Kantian Disaster, which made an accurate account of the scientific revolution impossible for philosophers. Kant's ego seems to have primarily an epistemological role. |
5517 | Individuals don't exist, but are conventional names for sets of elements [Buddha] |
Full Idea: There exists no individual, it is only a conventional name given to a set of elements. | |
From: Buddha (Siddhartha Gautama) (reports [c.540 BCE]), quoted by Derek Parfit - The Unimportance of Identity p.295 | |
A reaction: I take this to arise from an excessively spiritual concept of a human being, which faces Descartes' problem of how to individuate non-physical minds, when they have no clear boundaries. Combine dualism with a bundle theory, and you have Buddhism. |
16876 | We need definitions to cram retrievable sense into a signed receptacle [Frege] |
Full Idea: If we need such signs, we also need definitions so that we can cram this sense into the receptacle and also take it out again. | |
From: Gottlob Frege (Logic in Mathematics [1914], p.209) | |
A reaction: Has anyone noticed that Frege is the originator of the idea of the mental file? Has anyone noticed the role that definition plays in his account? |
16875 | We use signs to mark receptacles for complex senses [Frege] |
Full Idea: We often need to use a sign with which we associate a very complex sense. Such a sign seems a receptacle for the sense, so that we can carry it with us, while being always aware that we can open this receptacle should we need what it contains. | |
From: Gottlob Frege (Logic in Mathematics [1914], p.209) | |
A reaction: This exactly the concept of a mental file, which I enthusiastically endorse. Frege even talks of 'opening the receptacle'. For Frege a definition (which he has been discussing) is the assigment of a label (the 'definiendum') to the file (the 'definiens'). |
16879 | A sign won't gain sense just from being used in sentences with familiar components [Frege] |
Full Idea: No sense accrues to a sign by the mere fact that it is used in one or more sentences, the other constituents of which are known. | |
From: Gottlob Frege (Logic in Mathematics [1914], p.213) | |
A reaction: Music to my ears. I've never grasped how meaning could be grasped entirely through use. |
16873 | Thoughts are not subjective or psychological, because some thoughts are the same for us all [Frege] |
Full Idea: A thought is not something subjective, is not the product of any form of mental activity; for the thought that we have in Pythagoras's theorem is the same for everybody. | |
From: Gottlob Frege (Logic in Mathematics [1914], p.206) | |
A reaction: When such thoughts are treated as if the have objective (platonic) existence, I become bewildered. I take a thought (or proposition) to be entirely psychological, but that doesn't stop two people from having the same thought. |
16872 | A thought is the sense expressed by a sentence, and is what we prove [Frege] |
Full Idea: The sentence is of value to us because of the sense that we grasp in it, which is recognisably the same in a translation. I call this sense the thought. What we prove is not a sentence, but a thought. | |
From: Gottlob Frege (Logic in Mathematics [1914], p.206) | |
A reaction: The 'sense' is presumably the German 'sinn', and a 'thought' in Frege is what we normally call a 'proposition'. So the sense of a sentence is a proposition, and logic proves propositions. I'm happy with that. |
16874 | The parts of a thought map onto the parts of a sentence [Frege] |
Full Idea: A sentence is generally a complex sign, so the thought expressed by it is complex too: in fact it is put together in such a way that parts of a thought correspond to parts of the sentence. | |
From: Gottlob Frege (Logic in Mathematics [1914], p.207) | |
A reaction: This is the compositional view of propositions, as opposed to the holistic view. |
19667 | If the laws of nature are contingent, shouldn't we already have noticed it? [Meillassoux] |
Full Idea: The standard objection is that if the laws of nature were actually contingent, we would already have noticed it. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 4) | |
A reaction: Meillassoux offers a sustained argument that the laws of nature are necessarily contingent. In Idea 19660 he distinguishes contingencies that must change from those that merely could change. |
19670 | Why are contingent laws of nature stable? [Meillassoux] |
Full Idea: We must ask how we are to explain the manifest stability of physical laws, given that we take these to be contingent? | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 4) | |
A reaction: Meissalloux offers a very deep and subtle answer to this question... It is based on the possibilities of chaos being an uncountable infinity... It is a very nice question, which physicists might be able to answer, without help from philosophy. |
19653 | The ontological proof of a necessary God ensures a reality external to the mind [Meillassoux] |
Full Idea: Since Descartes conceives of God as existing necessarily, whether I exist to think of him or not, Descartes assures me of a possible access to an absolute reality - a Great Outdoors that is not a correlate of my thought. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 2) | |
A reaction: His point is that the ontological argument should be seen as part of the scientific revolution, and not an anomaly within it. Interesting. |
19658 | Now that the absolute is unthinkable, even atheism is just another religious belief (though nihilist) [Meillassoux] |
Full Idea: Once the absolute has become unthinkable, even atheism, which also targets God's inexistence in the manner of an absolute, is reduced to a mere belief, and hence to a religion, albeit of the nihilist kind. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 2) | |
A reaction: An interesting claim. Rather hard to agree or disagree, though the idea that atheism must qualify as a religion seems odd. If it is unqualified it does have the grand quality of a religion, but if it is fallibilist it just seems like an attitude. |
7600 | The Buddha believed the gods would eventually disappear, and Nirvana was much higher [Buddha, by Armstrong,K] |
Full Idea: The Buddha believed implicitly in the gods because they were part of his cultural baggage, but they were involved in the cycle of rebirth, and would eventually disappear; the ultimate reality of Nirvana was higher than the gods. | |
From: report of Buddha (Siddhartha Gautama) (reports [c.540 BCE]) by Karen Armstrong - A History of God Ch.1 | |
A reaction: We might connect this with Plato's Euthyphro question (Ideas 336 and 337), and the relationship between piety and morality on the one hand, and the gods on the other. |
7601 | Life is suffering, from which only compassion, gentleness, truth and sobriety can save us [Buddha] |
Full Idea: Buddha taught that the only release from 'dukkha' (the meaningless flux of suffering which is human life) is a life of compassion for all living beings, speaking and behaving gently, kindly and accurately, and refraining from all intoxicants. | |
From: Buddha (Siddhartha Gautama) (reports [c.540 BCE], Ch.1), quoted by Karen Armstrong - A History of God Ch.1 | |
A reaction: Christians are inclined to give the impression that Jesus invented the idea of being nice, but it ain't so. The obvious thought is that the Buddha seems to be focusing on the individual, but this is actually a formula for a better community. |