45 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. |
| 21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
| Full Idea: Gödel's proof wrought an abrupt turn in the philosophy of mathematics. We had supposed that truth, in mathematics, consisted in provability. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Willard Quine - Forward to Gödel's Unpublished | |
| A reaction: This explains the crisis in the early 1930s, which Tarski's theory appeared to solve. |
| 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. |
| 17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
| Full Idea: Gödel's incompleteness results of 1931 show that all axiom systems precise enough to satisfy Hilbert's conception are necessarily incomplete. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Michael Hallett - Introduction to Zermelo's 1930 paper p.1215 | |
| A reaction: [Hallett italicises 'necessarily'] Hilbert axioms have to be recursive - that is, everything in the system must track back to them. |
| 17886 | The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner] |
| Full Idea: The inherent limitations of the axiomatic method were first brought to light by the incompleteness theorems. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Peter Koellner - On the Question of Absolute Undecidability 1.1 |
| 10071 | Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P] |
| Full Idea: Second Incompleteness Theorem: roughly, nice theories that include enough basic arithmetic can't prove their own consistency. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Peter Smith - Intro to Gödel's Theorems 1.5 | |
| A reaction: On the face of it, this sounds less surprising than the First Theorem. Philosophers have often noticed that it seems unlikely that you could use reason to prove reason, as when Descartes just relies on 'clear and distinct ideas'. |
| 19123 | If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh] |
| Full Idea: Gödel showed PA cannot be proved consistent from with PA. But 'reflection principles' can be added, which are axioms partially expressing the soundness of PA, by asserting what is provable. A Global Reflection Principle asserts full soundness. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Halbach,V/Leigh,G.E. - Axiomatic Theories of Truth (2013 ver) 1.2 | |
| A reaction: The authors point out that this needs a truth predicate within the language, so disquotational truth won't do, and there is a motivation for an axiomatic theory of truth. |
| 17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
| Full Idea: My undecidable arithmetical sentence ...is not at all absolutely undecidable; rather, one can always pass to 'higher' systems in which the sentence in question is decidable. | |
| From: Kurt Gödel (On Formally Undecidable Propositions [1931]), quoted by Peter Koellner - On the Question of Absolute Undecidability 1.1 | |
| A reaction: [a 1931 MS] He says the reals are 'higher' than the naturals, and the axioms of set theory are higher still. The addition of a truth predicate is part of what makes the sentence become decidable. |
| 10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel] |
| Full Idea: Where Gödel's First Theorem sabotages logicist ambitions, the Second Theorem sabotages Hilbert's Programme. | |
| From: comment on Kurt Gödel (On Formally Undecidable Propositions [1931]) by Peter Smith - Intro to Gödel's Theorems 36 | |
| A reaction: Neo-logicism (Crispin Wright etc.) has a strategy for evading the First Theorem. |
| 10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
| Full Idea: Gödel's far-reaching work on the nature of logic and formal systems reveals that there can be no single consistent theory from which all mathematical truths can be derived. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.8 |
| 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) |
| 10072 | First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P] |
| Full Idea: First Incompleteness Theorem: any properly axiomatised and consistent theory of basic arithmetic must remain incomplete, whatever our efforts to complete it by throwing further axioms into the mix. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Peter Smith - Intro to Gödel's Theorems 1.2 | |
| A reaction: This is because it is always possible to formulate a well-formed sentence which is not provable within the theory. |
| 3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
| Full Idea: Gödel's theorem states that either arithmetic is incomplete, or it is inconsistent. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Georges Rey - Contemporary Philosophy of Mind 8.7 |
| 9590 | Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman] |
| Full Idea: The vast continent of arithmetical truth cannot be brought into systematic order by laying down a fixed set of axioms and rules of inference from which every true mathematical statement can be formally derived. For some this was a shocking revelation. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by E Nagel / JR Newman - Gödel's Proof VII.C | |
| A reaction: Good news for philosophy, I'd say. The truth cannot be worked out by mechanical procedures, so it needs the subtle and intuitive intelligence of your proper philosopher (Parmenides is the role model) to actually understand reality. |
| 11069 | Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna] |
| Full Idea: Gödel's Second Incompleteness Theorem says that true unprovable sentences are clearly semantic consequences of the axioms in the sense that they are necessarily true if the axioms are true. So semantic consequence outruns provability. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Robert Hanna - Rationality and Logic 5.3 |
| 10118 | First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman] |
| Full Idea: First Incompleteness Theorem: If S is a sufficiently powerful formal system, then if S is consistent then S is syntactically incomplete. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: Gödel found a single sentence, effectively saying 'I am unprovable in S', which is neither provable nor refutable in S. |
| 10122 | Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman] |
| Full Idea: Second Incompleteness Theorem: If S is a sufficiently powerful formal system, then if S is consistent then S cannot prove its own consistency | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: This seems much less surprising than the First Theorem (though it derives from it). It was always kind of obvious that you couldn't use reason to prove that reason works (see, for example, the Cartesian Circle). |
| 10611 | There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P] |
| Full Idea: The original Gödel construction gives us a sentence that a theory shows is true if and only if it satisfies the condition of being unprovable-in-that-theory. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Peter Smith - Intro to Gödel's Theorems 20.5 |
| 10867 | 'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg] |
| Full Idea: An approximation of Gödel's Theorem imagines a statement 'This system of mathematics can't prove this statement true'. If the system proves the statement, then it can't prove it. If the statement can't prove the statement, clearly it still can't prove it. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.15 | |
| A reaction: Gödel's contribution to this simple idea seems to be a demonstration that formal arithmetic is capable of expressing such a statement. |
| 8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
| Full Idea: Gödel defended impredicative definitions on grounds of ontological realism. From that perspective, an impredicative definition is a description of an existing entity with reference to other existing entities. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Stewart Shapiro - Thinking About Mathematics 5.3 | |
| A reaction: This is why constructivists must be absolutely precise about definition, where realists only have to do their best. Compare building a car with painting a landscape. |
| 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. |
| 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. |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| Full Idea: Gödel in his completeness theorem for first-order logic showed that a certain set of syntactically specifiable rules was adequate to capture all first-order valid arguments. No semantics (e.g. reference, truth, validity) was necessary. | |
| From: report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Georges Rey - Contemporary Philosophy of Mind 8.2 | |
| A reaction: This implies that a logic machine is possible, but we shouldn't raise our hopes for proper rationality. Validity can be shown for purely algebraic arguments, but rationality requires truth as well as validity, and that needs propositions and semantics. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 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. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |
| 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. |