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All the ideas for 'Mathematical Methods in Philosophy', 'On the Question of Absolute Undecidability' and 'The Myth of Sisyphus'

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29 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
Life will be lived better if it has no meaning [Camus]
     Full Idea: Life will be lived all the better if it has no meaning.
     From: Albert Camus (The Myth of Sisyphus [1942], 'Abs free')
     A reaction: One image of the good life is that of a successful wild animal, for which existence is not a problem, merely a constant activity and pursuit. Maybe life begins to acquire meaning once we realise that meaning should not be sought directly.
1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Suicide - whether life is worth living - is the one serious philosophical problem [Camus]
     Full Idea: There is but one truly serious philosophical problem and that is suicide. Judgine whether life is or is not worth living amounts to answering the fundamental question of philosophy.
     From: Albert Camus (The Myth of Sisyphus [1942], p.11)
     A reaction: What a wonderful thesis for a book. In Idea 2682 there is the possibility of life being worth living, but not worth a huge amount of effort. It is better to call Camus' question the first question, rather than the only question.
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
To an absurd mind reason is useless, and there is nothing beyond reason [Camus]
     Full Idea: To an absurd mind reason is useless, and there is nothing beyond reason.
     From: Albert Camus (The Myth of Sisyphus [1942], 'Phil Suic')
     A reaction: But there is, surely, intuition and instinct? Read Keats's Letters. There is good living through upbringing and habit. Read Aristotle. If you like Camus' thought, you will love Chuang Tzu. Personally I am a child of the Enlightenment.
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
     Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory.
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro)
'Reflection principles' say the whole truth about sets can't be captured [Koellner]
     Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level.
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1)
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Logic is easy, but what about logic to the point of death? [Camus]
     Full Idea: It is always easy to be logical. It is almost impossible to be logical to the bitter end. The only problem that interests me is: is there a logic to the point of death?
     From: Albert Camus (The Myth of Sisyphus [1942], 'Abs and Suic')
     A reaction: This is a lovely hand grenade to lob into an analytical logic class! It is very hard to get logicians to actually ascribe a clear value to their activity. They tend to present it as a marginal private game, and yet it has high status.
5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic
Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew]
     Full Idea: Three periods can be distinguished in philosophical logic: the syntactic stage, from Russell's definite descriptions to the 1950s, the dominance of possible world semantics from the 50s to 80s, and a current widening of the subject.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 1)
     A reaction: [compressed] I've read elsewhere that the arrival of Tarski's account of truth in 1933, taking things beyond the syntactic, was also a landmark.
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew]
     Full Idea: Logical formalization forces the investigator to make the central philosophical concepts precise. It can also show how some philosophical concepts and objects can be defined in terms of others.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2)
     A reaction: This is the main rationale of the highly formal and mathematical approach to such things. The downside is when you impose 'precision' on language that was never intended to be precise.
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew]
     Full Idea: A (logical) model is a set with functions and relations defined on it that specify the denotation of the non-logical vocabulary. A series of recursive clauses explicate how truth values of complex sentences are compositionally determined from the parts.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3)
     A reaction: See the ideas on 'Functions in logic' and 'Relations in logic' (in the alphabetical list) to expand this important idea.
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
We have no argument to show a statement is absolutely undecidable [Koellner]
     Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable.
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3)
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
     Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable).
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4)
     A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
     Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem].
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1)
     A reaction: Each expansion brings a limitation, but then you can expand again.
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Arithmetical undecidability is always settled at the next stage up [Koellner]
     Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next.
     From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4)
7. Existence / A. Nature of Existence / 1. Nature of Existence
If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew]
     Full Idea: If there is indeed no property of existence that is expressed by the word 'exist', then it makes no sense to ask for its essence.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2)
     A reaction: As far as I can tell, this was exactly Aristotle's conclusion, so he skirted round the question of 'being qua being', and focused on the nature of objects instead. Grand continental talk of 'Being' doesn't sound very interesting.
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew]
     Full Idea: A Tarskian model can in a sense be seen as a model of a possible state of affairs.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3)
     A reaction: I include this remark to show how possible worlds semantics built on the arrival of model theory.
The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew]
     Full Idea: The notion of a possible worlds model was extended (resulting in the concept of a 'spheres model') in order to obtain a satisfactory logical treatment of counterfactual conditional sentences.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4)
     A reaction: Thus we add 'centred' worlds, and an 'actual' world, to the loose original model. It is important to remember when we discuss 'close' worlds that we are then committed to these presuppositions.
10. Modality / E. Possible worlds / 1. Possible Worlds / b. Impossible worlds
Epistemic logic introduced impossible worlds [Horsten/Pettigrew]
     Full Idea: The idea of 'impossible worlds' was introduced into epistemic logic.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4)
     A reaction: Nathan Salmon seems interested in their role in metaphysics (presumably in relation to Meinongian impossible objects, like circular squares, which must necessarily be circular).
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew]
     Full Idea: Each possible worlds model contains a set of possible worlds. For this reason, possible worlds semantics is often charged with smuggling in heavy metaphysical commitments.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3)
     A reaction: To a beginner it looks very odd that you should try to explain possibility by constructing a model of it in terms of 'possible' worlds.
Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew]
     Full Idea: When the possible worlds semantics were further extended to model notions of knowledge and of moral obligation, the application was beginning to look distinctly forced and artificial.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 5)
     A reaction: They accept lots of successes in modelling necessity and time.
16. Persons / F. Free Will / 1. Nature of Free Will
Whether we are free is uninteresting; we can only experience our freedom [Camus]
     Full Idea: Knowing whether or not a man is free doesn't interest me. I can only experience my own freedom.
     From: Albert Camus (The Myth of Sisyphus [1942], 'Abs free')
     A reaction: Camus has the right idea. Personally I think you could drop the word 'freedom', and just say that I am confronted by the need to make decisions.
16. Persons / F. Free Will / 6. Determinism / b. Fate
The human heart has a tiresome tendency to label as fate only what crushes it [Camus]
     Full Idea: The human heart has a tiresome tendency to label as fate only what crushes it.
     From: Albert Camus (The Myth of Sisyphus [1942], 'Appendix')
     A reaction: Nice. It might just as much be fate that you live a happy bourgeois life, as that you inadvertently murder your own father at a crossroads. But you can't avoid the powerful awareness of fate when a road accident occurs.
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
Discussing ethics is pointless; moral people behave badly, and integrity doesn't need rules [Camus]
     Full Idea: There can be no question of holding forth on ethics. I have seen people behave badly with great morality and I note every day that integrity has no need of rules.
     From: Albert Camus (The Myth of Sisyphus [1942], 'Abs Man')
     A reaction: I don't agree. If someone 'behaves badly with great morality' there is something wrong with their morality, and I want to know what it is. The last part is more plausible, and could be a motto for Particularism. Rules dangerously over-simplify life.
22. Metaethics / B. Value / 2. Values / g. Love
The more one loves the stronger the absurd grows [Camus]
     Full Idea: The more one loves the stronger the absurd grows.
     From: Albert Camus (The Myth of Sisyphus [1942], 'Don Juan')
     A reaction: A penetrating remark, to be placed as a contrary to the remarks of Harry Frankfurt on love. But if the absurd increases the intensity of life, as Camus thinks, then they both make love the great life-affirmation, but in different ways.
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
One can be virtuous through a whim [Camus]
     Full Idea: One can be virtuous through a whim.
     From: Albert Camus (The Myth of Sisyphus [1942], 'Abs Man')
     A reaction: A nice remark. Obviously neither Aristotle nor Kant would be too impressed by someone who did this, and Aristotle would certainly say that it is not really virtue, but merely right behaviour. I agree with Aristotle.
23. Ethics / F. Existentialism / 2. Nihilism
If we believe existence is absurd, this should dictate our conduct [Camus]
     Full Idea: What a man believes to be true must determine his action. Belief in the absurdity of existence must then dictate his conduct.
     From: Albert Camus (The Myth of Sisyphus [1942], 'Abs and Suic')
     A reaction: It is intriguing to speculate what the appropriate conduct is. Presumably it is wild existential gestures, like sticking a knife through your hand. Suicide will be an obvious temptation. But bourgeois life might be equally appropriate.
Happiness and the absurd go together, each leading to the other [Camus]
     Full Idea: Happiness and the absurd are two sons of the same earth; they are inseparable; it would be a mistake to say that happiness necessarily springs from the absurd discovery; it happens as well that the feeling of the absurd springs from happiness.
     From: Albert Camus (The Myth of Sisyphus [1942], p.110)
     A reaction: I'm not sure that I understand this, but I understand the experience of absurdity, and I can see that somehow one feels a bit more alive when one acknowledges the absurdity of it all. Meta-meta-thought is the highest form of human life, I say.
23. Ethics / F. Existentialism / 7. Existential Action
Essential problems either risk death, or intensify the passion of life [Camus]
     Full Idea: The essential problems are those that run the risk of leading to death, or those that intensify the passion of living.
     From: Albert Camus (The Myth of Sisyphus [1942], 'Abs and Suic')
     A reaction: This seems to be distinctively existentialist, in a way that a cool concern for great truths are not ranked as so important. Ranking dangerous problems as crucial seems somehow trivial for a philosopher. Intensity of life is more impressive.
Danger and integrity are not in the leap of faith, but in remaining poised just before the leap [Camus]
     Full Idea: The leap of faith does not represent an extreme danger as Kierkegaard would like it to do. The danger, on the contrary, lies in the subtle instant that precedes the leap. Being able to remain on the dizzying crest - that is integrity.
     From: Albert Camus (The Myth of Sisyphus [1942], 'Phil Suic')
     A reaction: I have always found that a thrilling thought. It perfectly distinguishes atheist existentialism from religious existentialism. It is Camus' best image for how the Absurd can be a life affirming idea, rather than a sort of nihilism. Life gains intensity.
25. Social Practice / F. Life Issues / 4. Suicide
It is essential to die unreconciled and not of one's own free will [Camus]
     Full Idea: It is essential to die unreconciled and not of one's own free will. Suicide is a repudiation.
     From: Albert Camus (The Myth of Sisyphus [1942], 'Abs free')
     A reaction: Camus' whole book addresses the question of suicide. He suggests that life can be redeemed and become livable if you squarely face up to the absurdity of it, and the gap between what we hope for and what we get.