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All the ideas for 'After Finitude', 'Ontology and Mathematical Truth' and 'Maxims'

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41 ideas

1. Philosophy / A. Wisdom / 2. Wise People
To try to be wise all on one's own is folly [Rochefoucauld]
     Full Idea: To try to be wise all on one's own is sheer folly.
     From: La Rochefoucauld (Maxims [1663], 231)
     A reaction: I agree strongly with this. There are counter-examples, of whom Spinoza may be the greatest, and Nietzsche thought that philosophy was essentially a solitary business, but most of us are not Spinoza or Nietzsche.
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.
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.
4. Formal Logic / F. Set Theory ST / 1. Set Theory
'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien]
     Full Idea: Any set with a concrete member is 'impure'. 'Pure' sets are those that are not impure, and are paradigm cases of abstract entities, such as the sort of sets apparently dealt with in Zermelo-Fraenkel (ZF) set theory.
     From: Michael Jubien (Ontology and Mathematical Truth [1977], p.116)
     A reaction: [I am unclear whether Jubien is introducing this distinction] This seems crucial in accounts of mathematics. On the one had arithmetic can be built from Millian pebbles, giving impure sets, while logicists build it from pure sets.
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
A model is 'fundamental' if it contains only concrete entities [Jubien]
     Full Idea: A first-order model can be viewed as a kind of ordered set, and if the domain of the model contains only concrete entities then it is a 'fundamental' model.
     From: Michael Jubien (Ontology and Mathematical Truth [1977], p.117)
     A reaction: An important idea. Fundamental models are where the world of logic connects with the physical world. Any account of relationship between fundamental models and more abstract ones tells us how thought links to world.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers
There couldn't just be one number, such as 17 [Jubien]
     Full Idea: It makes no sense to suppose there might be just one natural number, say seventeen.
     From: Michael Jubien (Ontology and Mathematical Truth [1977], p.113)
     A reaction: Hm. Not convinced. If numbers are essentially patterns, we might only have the number 'twelve', because we had built our religion around anything which exhibited that form (in any of its various arrangements). Nice point, though.
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)
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
The subject-matter of (pure) mathematics is abstract structure [Jubien]
     Full Idea: The subject-matter of (pure) mathematics is abstract structure per se.
     From: Michael Jubien (Ontology and Mathematical Truth [1977], p.115)
     A reaction: This is the Structuralist idea beginning to take shape after Benacerraf's launching of it. Note that Jubien gets there by his rejection of platonism, whereas some structuralist have given a platonist interpretation of structure.
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
If we all intuited mathematical objects, platonism would be agreed [Jubien]
     Full Idea: If the intuition of mathematical objects were general, there would be no real debate over platonism.
     From: Michael Jubien (Ontology and Mathematical Truth [1977], p.111)
     A reaction: It is particularly perplexing when Gödel says that his perception of them is just like sight or smell, since I have no such perception. How do you individuate very large numbers, or irrational numbers, apart from writing down numerals?
How can pure abstract entities give models to serve as interpretations? [Jubien]
     Full Idea: I am unable to see how the mere existence of pure abstract entities enables us to concoct appropriate models to serve as interpretations.
     From: Michael Jubien (Ontology and Mathematical Truth [1977], p.111)
     A reaction: Nice question. It is always assumed that once we have platonic realm, that everything else follows. Even if we are able to grasp the objects, despite their causal inertness, we still have to discern innumerable relations between them.
Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien]
     Full Idea: The essential properties of mathematical entities seem to be relational, ...so we make no progress unless we can pick out some mathematical entities wihout presupposing other entities already picked out.
     From: Michael Jubien (Ontology and Mathematical Truth [1977], p.112)
     A reaction: [compressed] Jubien is a good critic of platonism. He has identified the problem with Frege's metaphor of a 'borehole', where we discover delightful new properties of numbers simply by reaching them.
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.
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
The empty set is the purest abstract object [Jubien]
     Full Idea: The empty set is the pure abstract object par excellence.
     From: Michael Jubien (Ontology and Mathematical Truth [1977], p.118 n8)
     A reaction: So a really good PhD on the empty set could crack the whole nature of reality. Get to work, whoever you are!
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?
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
La Rochefoucauld's idea of disguised self-love implies an unconscious mind [Rochefoucauld, by Sartre]
     Full Idea: La Rochefoucauld is one of the first to have made use of the unconscious without naming it: for him, amour-propre conceals itself in the most diverse disguises.
     From: report of La Rochefoucauld (Maxims [1663]) by Jean-Paul Sartre - Transcendence of the Ego I (C)
     A reaction: It seems odd that no one before that ever thought that someone might have hidden motives of which even they themselves were unaware. How about Iago, or Macbeth, or Hamlet? It is a profound change in our view of human nature.
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.
22. Metaethics / B. Value / 2. Values / g. Love
Judging by effects, love looks more like hatred than friendship [Rochefoucauld]
     Full Idea: If love be judged by its most visible effects it looks more like hatred than friendship.
     From: La Rochefoucauld (Maxims [1663], 072)
     A reaction: Presumably he is thinking of pursuit, possession and jealousy. The remark is plausible if you add the word 'sometimes' to it, but as a universal generalisation it is ridiculous, the product of a society where they competed to exceed in cynicism.
22. Metaethics / C. The Good / 1. Goodness / e. Good as knowledge
Supreme cleverness is knowledge of the real value of things [Rochefoucauld]
     Full Idea: Supreme cleverness is knowledge of the real value of things.
     From: La Rochefoucauld (Maxims [1663], 244)
     A reaction: Good. Right at the heart of wisdom is some kind of grasp of right values. It is so complex and subtle that it seems like pure intuition, but I am sure that reason is involved. 'Intelligent' people tend to be better at it. Some justifications can be given.
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
Realising our future misery is a kind of happiness [Rochefoucauld]
     Full Idea: To realise how much misery we have to face is in itself a kind of happiness.
     From: La Rochefoucauld (Maxims [1663], 570)
     A reaction: Probably true. Knowing that you have got hold of the truth is a sort of happiness in any area, no matter how grim the truth. However, a happy life could easily be poisoned by brooding on the future. Should the happily married brood on future solitude?
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
Virtue doesn't go far without the support of vanity [Rochefoucauld]
     Full Idea: Virtue would not go far without vanity to bear it company.
     From: La Rochefoucauld (Maxims [1663], 200)
     A reaction: Rochefoucauld's cynicism gets a bit tedious, but lovers of virtue must face up to this possibility when they consider what motivates them. At the heart of Aristotle there is a missing question, of what is so good about right-functioning and virtue.
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
True friendship is even rarer than true love [Rochefoucauld]
     Full Idea: Rare though true love may be, true friendship is rarer still.
     From: La Rochefoucauld (Maxims [1663], 473)
     A reaction: This seems to be true. Our culture doesn't encourage friendship as a high ideal. Are women better at friendship than men? Which culture, past or present, led to the greatest flourishing of friendship? Epicurus's Garden?
23. Ethics / F. Existentialism / 4. Boredom
We are bored by people to whom we ourselves are boring [Rochefoucauld]
     Full Idea: Almost always we are bored by people to whom we ourselves are boring.
     From: La Rochefoucauld (Maxims [1663], 555)
     A reaction: An obvious exception would be a celebrity being bored with their fans. Their very excess of interest is precisely what is boring. If two people communicate well, it is unlikely that either of them will ever be bored.
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.