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All the ideas for 'Mathematical Methods in Philosophy', 'Penses' and 'Ancient Thought in Modern Physics'

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24 ideas

2. Reason / A. Nature of Reason / 9. Limits of Reason
The heart has its reasons of which reason knows nothing [Pascal]
     Full Idea: The heart has its reasons of which reason knows nothing.
     From: Blaise Pascal (Pensées [1662], 423 (277))
     A reaction: This romantic remark has passed into folklore. I am essentially against it, but the role of intuition and instinct are undeniable in both reasoning and ethics. I don't feel inclined, though, to let my heart overrule my reason concerning what exists.
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.
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.
12. Knowledge Sources / C. Rationalism / 1. Rationalism
The first principles of truth are not rational, but are known by the heart [Pascal]
     Full Idea: We know the truth not only through our reason but also through our heart. It is through that latter that we know first principles, and reason, which has nothing to do with it, tries in vain to refute them.
     From: Blaise Pascal (Pensées [1662], 110 p.58), quoted by Terry Pinkard - German Philosophy 1760-1860 04 n4
     A reaction: This resembles the rationalist defence of fundamental a priori principles, needed as a foundation for knowledge. But the a priori insights are not a feature of the 'natural light' of reason, and are presumably inexplicable (of the 'heart').
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
You can only explain the qualities of large objects using entities which lack those qualities [Heisenberg]
     Full Idea: It is impossible to explain the manifest qualities of ordinary middle-sized objects except by tracing these back to the behaviour of entities which themselves no longer possess these qualities.
     From: Werner Heisenberg (Ancient Thought in Modern Physics [1937], p.119), quoted by William Lycan - Consciousness 8.10
     A reaction: Compare the similar wonderful remark by Lucretius (Idea 5713). If we accept this as a general principle for all of nature (including us) - and I do - then it is silly to complain that consciousness isn't found in basic physics.
19. Language / F. Communication / 1. Rhetoric
We only want to know things so that we can talk about them [Pascal]
     Full Idea: We usually only want to know something so that we can talk about it.
     From: Blaise Pascal (Pensées [1662], 77 (152))
     A reaction: This may be right, but I wouldn't underestimate it as a worthy end (though Pascal, as usual, calls it 'vanity'). Good talk might even be the highest human good (how many people like, more than anything, chatting in pubs?), and good talk is knowledgeable.
21. Aesthetics / C. Artistic Issues / 3. Artistic Representation
Painting makes us admire things of which we do not admire the originals [Pascal]
     Full Idea: How vain painting is, exciting admiration by its resemblance to things of which we do not admire the originals.
     From: Blaise Pascal (Pensées [1662], 40 (134))
     A reaction: A lesser sort of painting simply depicts things we admire, such as a nice stretch of landscape. For Pascal it is vanity, but it could be defended as the highest achievement of art, if the purpose of artists is to make us see beauty where we had missed it.
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
It is a funny sort of justice whose limits are marked by a river [Pascal]
     Full Idea: It is a funny sort of justice whose limits are marked by a river; true on this side of the Pyrenees, false on the other.
     From: Blaise Pascal (Pensées [1662], 60 (294))
     A reaction: Pascal gives nice concise summaries of our intuitions. Legal justice may be all we can actually get, but everyone knows that what happens to someone could be 'fair' on one side of a river, and very 'unfair' on the other.
22. Metaethics / B. Value / 1. Nature of Value / d. Subjective value
Imagination creates beauty, justice and happiness, which is the supreme good [Pascal]
     Full Idea: Imagination decides everything: it creates beauty, justice and happiness, which is the world's supreme good.
     From: Blaise Pascal (Pensées [1662], 44 (82))
     A reaction: Compare Fogelin's remark in Idea 6555. I see Pascal's point, but these ideals are also responses to facts about the world, such as human potential and human desire and successful natural functions.
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
We live for the past or future, and so are never happy in the present [Pascal]
     Full Idea: Our thoughts are wholly concerned with the past or the future, never with the present, which is never our end; thus we never actually live, but hope to live, and since we are always planning to be happy, it is inevitable that we should never be so.
     From: Blaise Pascal (Pensées [1662], 47 (172))
     A reaction: A very nice expression of the importance of 'living for the moment' as a route to happiness. Personally I am occasionally startled by the thought 'Good heavens, I seem to be happy!', but it usually passes quickly. How do you plan for the present?
23. Ethics / F. Existentialism / 3. Angst
If man considers himself as lost and imprisoned in the universe, he will be terrified [Pascal]
     Full Idea: Let man consider what he is in comparison with what exists; let him regard himself as lost, and from this little dungeon the universe, let him learn to take the earth and himself at their proper value. Anyone considering this will be terrified at himself.
     From: Blaise Pascal (Pensées [1662], p.199), quoted by Kevin Aho - Existentialism: an introduction Pref 'What?
     A reaction: [p.199 of Penguin edn] Cited by Aho as a forerunner of existentialism. Montaigne probably influenced Pascal. Interesting that this is to be a self-inflicted existential crisis (for some purpose, probably Christian).
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
Majority opinion is visible and authoritative, although not very clever [Pascal]
     Full Idea: Majority opinion is the best way because it can be seen, and is strong enough to command obedience, but it is the opinion of those who are least clever.
     From: Blaise Pascal (Pensées [1662], 85 (878))
     A reaction: A nice statement of the classic dilemma faced by highly educated people over democracy. Plato preferred the clever, Aristotle agreed with Pascal, and with me. Politics must make the best of it, not pursue some ideal. Education is the one feeble hope.
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
It is not good to be too free [Pascal]
     Full Idea: It is not good to be too free.
     From: Blaise Pascal (Pensées [1662], 57 (379))
     A reaction: All Americans, please take note. I agree with this, because I agree with Aristotle that man is essentially a social animal (Idea 5133), and living in a community is a matter of compromise. Extreme libertarianism contradicts our natures, and causes misery.
28. God / B. Proving God / 2. Proofs of Reason / d. Pascal's Wager
Pascal knows you can't force belief, but you can make it much more probable [Pascal, by Hacking]
     Full Idea: Pascal knows that one cannot decide to believe in God, but he thinks one can act so that one will very probably come to believe in God, by following a life of 'holy water and sacraments'.
     From: report of Blaise Pascal (Pensées [1662], 418 (233)) by Ian Hacking - The Emergence of Probability Ch.8
     A reaction: This meets the most obvious and simple objection to Pascal's idea, and Pascal may well be right. I'm not sure I could resist belief after ten years in a monastery.
Pascal is right, but relies on the unsupported claim of a half as the chance of God's existence [Hacking on Pascal]
     Full Idea: Pascal's argument is valid, but it is presented with a monstrous premise of equal chance. We have no good reason for picking a half as the chance of God's existence.
     From: comment on Blaise Pascal (Pensées [1662], 418 (233)) by Ian Hacking - The Emergence of Probability Ch.8
     A reaction: That strikes me as the last word on this rather bizarre argument.
The libertine would lose a life of enjoyable sin if he chose the cloisters [Hacking on Pascal]
     Full Idea: The libertine is giving up something if he chooses to adopt a pious form of life. He likes sin. If God is not, the worldly life is preferable to the cloistered one.
     From: comment on Blaise Pascal (Pensées [1662], 418 (233)) by Ian Hacking - The Emergence of Probability Ch.8
     A reaction: This is a very good objection to Pascal, who seems to think you really have nothing at all to lose. I certainly don't intend to become a monk, because the chances of success seem incredibly remote from where I am sitting.
If you win the wager on God's existence you win everything, if you lose you lose nothing [Pascal]
     Full Idea: How will you wager if a coin is spun on 'Either God is or he is not'? ...If you win you win everything, if you lose you lose nothing.
     From: Blaise Pascal (Pensées [1662], 418 (233))
     A reaction: 'Sooner safe than sorry' is a principle best used with caution. Do you really 'lose nothing' by believing a falsehood for the whole of your life? What God would reward belief on such a principles as this?