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All the ideas for 'After Finitude', 'Gentzen's Analysis of First-Order Proofs' and 'The Unimportance of Identity'

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36 ideas

1. Philosophy / B. History of Ideas / 5. Later European Thought
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.
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.
1. Philosophy / B. History of Ideas / 6. Twentieth Century Thought
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!).
1. Philosophy / G. Scientific Philosophy / 3. Scientism
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.
2. Reason / A. Nature of Reason / 5. Objectivity
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).
2. Reason / B. Laws of Thought / 2. Sufficient Reason
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!
2. Reason / B. Laws of Thought / 3. Non-Contradiction
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.
2. Reason / E. Argument / 7. Thought Experiments
Imaginary cases are good for revealing our beliefs, rather than the truth [Parfit]
     Full Idea: I believe it is worth considering imaginary cases (such as Teletransportation), as we can use them to discover, not what the truth is, but what we believe.
     From: Derek Parfit (The Unimportance of Identity [1995], p.293)
     A reaction: The trouble is that we might say that IF I were suddenly turned into a pig, then I would come to believe in dualism, but that will not and cannot happen, because dualism is false. It seems essential to accept the natural possibility of the case.
4. Formal Logic / E. Nonclassical Logics / 7. Paraconsistency
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.
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)
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.
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Logic is based on transitions between sentences [Prawitz]
     Full Idea: I agree entirely with Dummett that the right way to answer the question 'what is logic?' is to consider transitions between sentences.
     From: Dag Prawitz (Gentzen's Analysis of First-Order Proofs [1974], §04)
     A reaction: I always protest at this point that reliance on sentences is speciesism against animals, who are thereby debarred from reasoning. See the wonderful Idea 1875 of Chrysippus. Hacking's basic suggestion seems right. Transition between thoughts.
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
Natural deduction introduction rules may represent 'definitions' of logical connectives [Prawitz]
     Full Idea: With Gentzen's natural deduction, we may say that the introductions represent, as it were, the 'definitions' of the logical constants. The introductions are not literally understood as 'definitions'.
     From: Dag Prawitz (Gentzen's Analysis of First-Order Proofs [1974], 2.2.2)
     A reaction: [Hacking, in 'What is Logic? §9' says Gentzen had the idea that his rules actually define the constants; not sure if Prawitz and Hacking are disagreeing]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
In natural deduction, inferences are atomic steps involving just one logical constant [Prawitz]
     Full Idea: In Gentzen's natural deduction, the inferences are broken down into atomic steps in such a way that each step involves only one logical constant. The steps are the introduction or elimination of the logical constants.
     From: Dag Prawitz (Gentzen's Analysis of First-Order Proofs [1974], 1.1)
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
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)
7. Existence / A. Nature of Existence / 1. Nature of Existence
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.
7. Existence / A. Nature of Existence / 5. Reason for Existence
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.
7. Existence / A. Nature of Existence / 6. Criterion for Existence
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.
7. Existence / C. Structure of Existence / 2. Reduction
Reduction can be by identity, or constitution, or elimination [Parfit, by PG]
     Full Idea: We can distinguish Identifying Reductionism (as in 'persons are bodies'), or Constitutive Reductionism (as in 'persons are distinct, but consist of thoughts etc.'), or Eliminative Reductionism (as in 'there are no persons, only thoughts etc.').
     From: report of Derek Parfit (The Unimportance of Identity [1995], p.295) by PG - Db (ideas)
     A reaction: Constitutive Reductionism seems the most common one, as in 'chemistry just consists of lots of complicated physics'. He doesn't mention bridge laws, which are presumably only required in more complicated cases of constitutive reduction.
10. Modality / B. Possibility / 5. Contingency
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.
10. Modality / B. Possibility / 7. Chance
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.
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
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'.
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / c. Primary qualities
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.
14. Science / B. Scientific Theories / 1. Scientific Theory
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.
14. Science / C. Induction / 3. Limits of Induction
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?
16. Persons / B. Nature of the Self / 4. Presupposition of Self
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.
16. Persons / D. Continuity of the Self / 1. Identity and the Self
Psychologists are interested in identity as a type of person, but philosophers study numerical identity [Parfit]
     Full Idea: When psychologists discuss identity, they are typically concerned with the kind of person someone is, or wants to be (as in an 'identity crisis'). But when philosophers discuss identity, it is numerical identity they mean.
     From: Derek Parfit (The Unimportance of Identity [1995], p.293)
     A reaction: I think it is important to note that the philosophical problem breaks down into two areas: whether I have numerical identity with myself over time, and whether other people have it. It may be that two different sets of criteria will emerge.
16. Persons / D. Continuity of the Self / 2. Mental Continuity / b. Self as mental continuity
If my brain-halves are transplanted into two bodies, I have continuity, and don't need identity [Parfit]
     Full Idea: If the two halves of my brain are transplanted into different bodies just like mine, they cannot both be me, since that would make them the same person. ..But my relation to these two contains everything that matters, so identity is not what matters.
     From: Derek Parfit (The Unimportance of Identity [1995], p.314)
     A reaction: I challenge his concept of what 'matters'. He has a rather solipsistic view of the problem, and I take Parfit to be a rather unsociable person, since his friends and partner will be keenly interested in the identities of the new beings.
Over a period of time what matters is not that 'I' persist, but that I have psychological continuity [Parfit]
     Full Idea: We should revise our view about identity over time: what matters isn't that there will be someone alive who will be me; it is rather that there should be at least one living person who will be psychologically continuous with me as I am now.
     From: Derek Parfit (The Unimportance of Identity [1995], p.316)
     A reaction: Parfit and Locke seem to agree on this, and it is no accident that they both like 'science fiction' examples. Apparently Parfit wouldn't bat an eyelid if someone threatened to cut his corpus callosum. I rate it as a catastrophe for my current existence.
16. Persons / D. Continuity of the Self / 4. Split Consciousness
It is fine to save two dying twins by merging parts of their bodies into one, and identity is irrelevant [Parfit]
     Full Idea: If I am largely paralysed, and my twin brother is dying of brain disease, then if the operation to graft my head onto his body is offered, I should accept the operation, and it is irrelevant whether this person would be me.
     From: Derek Parfit (The Unimportance of Identity [1995], p.308)
     A reaction: Parfit notes that the brain is a particularly significant part of the process. The fact that I might cheerfully accept this offer without philosophical worries doesn't get rid of the question 'who is this person?' Who should they remain married to?
If two humans are merged surgically, the new identity is a purely verbal problem [Parfit]
     Full Idea: If there is someone with my head and my brother's body, it is a merely verbal question whether that person will be me, and that is why, even if it won't be me, that doesn't matter. ..What matters is not identity, but the facts of which identity consists.
     From: Derek Parfit (The Unimportance of Identity [1995], p.310)
     A reaction: It strikes me that from the subjective psychological point of view identity is of little interest, but from the objective external viewpoint (e.g. the forensic one) such questions are highly significant, and rightly so.
16. Persons / E. Rejecting the Self / 4. Denial of the Self
It doesn't matter whether I exist with half my components replaced (any more than an audio system) [Parfit]
     Full Idea: It is quite uninteresting whether, with half its components replaced, I have the same audio system, and also whether I exist if half of my body were simultaneously replaced.
     From: Derek Parfit (The Unimportance of Identity [1995], p.302)
     A reaction: It is impossible to deny this, if the part replaced is not the brain. My doubt about Parfit's thesis is that while I may not care whether some modified thing is still me, my lawyers and the police might be very concerned.
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / b. Scientific necessity
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.
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.
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
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.
28. God / C. Attitudes to God / 5. Atheism
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.