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All the ideas for 'Philosophy of Mathematics', 'A World of Dispositions' and 'Tusculan Disputations'

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18 ideas

1. Philosophy / A. Wisdom / 2. Wise People
A wise man has integrity, firmness of will, nobility, consistency, sobriety, patience [Cicero]
     Full Idea: The wise man does nothing of which he can repent, nothing against his will, does everything nobly, consistently, soberly, rightly, not looking forward to anything as bound to come, is not astonished at any novel occurrence, abides by his own decisions.
     From: M. Tullius Cicero (Tusculan Disputations [c.44 BCE], V.xxviii)
     A reaction: Notice that the wise man never exhibits weakness of will (an Aristotelian virtue), and is consistent (as Kant proposed), and is patient (as the Stoics proposed). But Cicero doesn't think he should busy himself maximising happiness.
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
Philosophy is the collection of rational arguments [Cicero]
     Full Idea: Philosophy consists in the collection of rational arguments. [Philosophia ex rationum collatione constet]
     From: M. Tullius Cicero (Tusculan Disputations [c.44 BCE], IV.xxxviii.84)
     A reaction: A nice epigraph for this database. Philosophy is, I trust, a little more than that, because you don't just hide them away in a drawer. But if you arrange them nicely in a museum (a website, for example), not a lot more can be done.
2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
     Full Idea: Definitions are called 'predicative', and are considered sound, if they only refer to entities which exist independently from the defined collection.
     From: Leon Horsten (Philosophy of Mathematics [2007], §2.4)
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
     Full Idea: If a theory has, up to isomorphism, exactly one model, then it is said to be 'categorical'.
     From: Leon Horsten (Philosophy of Mathematics [2007], §5.2)
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
     Full Idea: Mathematicians are uncomfortable with computerised proofs because a 'good' proof should do more than convince us that a certain statement is true. It should also explain why the statement in question holds.
     From: Leon Horsten (Philosophy of Mathematics [2007], §5.3)
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
     Full Idea: The notion of an ordinal number is a set-theoretic, and hence non-arithmetical, concept.
     From: Leon Horsten (Philosophy of Mathematics [2007], §2.3)
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / e. Dispositions as potential
All structures are dispositional, objects are dispositions sets, and events manifest dispositions [Fetzer]
     Full Idea: I propose a dispositional ontology for the physical world, according to which a) every structural property is a dispositional one, b) a physical object is an ordered set of dispositions, and c) every event manifests a dispositional property of the world.
     From: J.H. Fetzer (A World of Dispositions [1977], Intro)
     A reaction: Mumford says this is consistent with ontology as a way of describing the world, rather than being facts about the world. I like Fetzer's sketch, which sounds to have a lot in common with 'process philosophy'.
9. Objects / C. Structure of Objects / 1. Structure of an Object
All events and objects are dispositional, and hence all structural properties are dispositional [Fetzer]
     Full Idea: Every atomic event in the world's history is a manifestation of some dispositional property of the world and every physical object is an instantiation of some set of dispositions; hence, every structural property is dispositional in kind.
     From: J.H. Fetzer (A World of Dispositions [1977], 5)
     A reaction: I quite like this drastic view, but there remains the intuition that there must always be something which has the disposition. That may be because I have not yet digested the lessons of modern physics.
15. Nature of Minds / A. Nature of Mind / 2. Psuche
The soul is the heart, or blood in the heart, or part of the brain, of something living in heart or brain, or breath [Cicero]
     Full Idea: Some think the soul is the heart; Empedocles holds that the soul is blood in the heart; others said one part of the brain claimed the primacy of soul; others say the heart or brain are habitations of the soul; while others identify soul and breath.
     From: M. Tullius Cicero (Tusculan Disputations [c.44 BCE], I.ix.17-19)
     A reaction: A nice survey of views. Note that many of them identify the psuché/anima with physical parts of the body; only the fourth option seems to be dualist. This is despite the contemptuous response to Democritus' atomist theory of soul.
15. Nature of Minds / A. Nature of Mind / 5. Unity of Mind
How can one mind perceive so many dissimilar sensations? [Cicero]
     Full Idea: Why is it that, using the same mind, we have perception of things so utterly unlike as colour, taste, heat, smell and sound?
     From: M. Tullius Cicero (Tusculan Disputations [c.44 BCE], I.xx.47)
     A reaction: This leaves us with the 'binding problem', of how the dissimilar sensations are pulled together into one field of experience. It is a nice simple objection, though, to anyone who simplistically claims that the mind is self-evidently unified.
The soul has a single nature, so it cannot be divided, and hence it cannot perish [Cicero]
     Full Idea: In souls there is no mingling of ingredients, nothing of two-fold nature, so it is impossible for the soul to be divided; impossible, therefore, for it to perish either; for perishing is like the separation of parts which were maintained in union.
     From: M. Tullius Cicero (Tusculan Disputations [c.44 BCE], I.xxix.71)
     A reaction: Cicero knows he is pushing his luck in asserting that perishing is a sort of division. Why can't something be there one moment and gone the next? He appears to be in close agreement with Descartes about being a 'thinking thing'.
16. Persons / C. Self-Awareness / 3. Limits of Introspection
Like the eye, the soul has no power to see itself, but sees other things [Cicero]
     Full Idea: The soul has not the power of itself to see itself, but, like the eye, the soul, though it does not see itself, yet discerns other things.
     From: M. Tullius Cicero (Tusculan Disputations [c.44 BCE], I.xxvii)
     A reaction: The soul is a complex item which contributes many layers of interpretation to what it sees, so there is scope for parts of the soul seeing other parts. Somewhere in the middle Cicero seems to be right - there is an elusive something we can't get at.
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / a. Physicalism critique
Souls contain no properties of elements, and elements contain no properties of souls [Cicero]
     Full Idea: No beginnings of souls can be found on earth; there is no combination in souls that could be born from earth, nothing that partakes of moist or airy or fiery; for in those elements there is nothing to possess the power of memory, thought, or reflection.
     From: M. Tullius Cicero (Tusculan Disputations [c.44 BCE], I.xxvi.66)
     A reaction: Interesting, but I think magnetism is an instructive analogy, which has weird properties which we never perceive in elements (though it is there, buried deep - suggesting panpsychism). Cicero would be disconcerted to find that fire isn't an element.
23. Ethics / C. Virtue Theory / 3. Virtues / f. Compassion
We should not share the distress of others, but simply try to relieve it [Cicero]
     Full Idea: We ought not to share distresses ourselves for the sake of others, but we ought to relieve others of their distress if we can.
     From: M. Tullius Cicero (Tusculan Disputations [c.44 BCE], IV.xxvi.56)
     A reaction: This strikes me as a sensible and balanced attitude. Some people, particularly in a Christian culture, urge that feeling strong and painful compassion for others is an intrinsic good, but the commonsense view is that that just increases human suffering.
23. Ethics / C. Virtue Theory / 4. External Goods / c. Wealth
All men except philosophers fear poverty [Cicero]
     Full Idea: All men are afraid of poverty, but not a single philosopher is so.
     From: M. Tullius Cicero (Tusculan Disputations [c.44 BCE], V.xxxi.88)
     A reaction: Not a thought which is encountered very often in modern philosophy journals. If a person is to be 'philosophical' in the way they live, calm endurance of the vicissitudes and hardships of life has to be a key prerequisite.
24. Political Theory / D. Ideologies / 5. Democracy / f. Against democracy
If one despises illiterate mechanics individually, they are not worth more collectively [Cicero]
     Full Idea: Can anything be more foolish than to suppose that those, whom individually one despises as illiterate mechanics, are worth anything collectively?
     From: M. Tullius Cicero (Tusculan Disputations [c.44 BCE], V.xxxvi.104)
     A reaction: Aristotle disagrees (Idea 2823). In 1906 a huge number of people guessed the weight of a cow at a fair, and the average was within one pound of the truth. In our world the healthy workings of the group are warped by the mass media.
26. Natural Theory / B. Natural Kinds / 2. Defining Kinds
Kinds are arrangements of dispositions [Fetzer]
     Full Idea: Kinds of things are specific arrangements of dispositions.
     From: J.H. Fetzer (A World of Dispositions [1977], 2)
     A reaction: A 'disposition' doesn't seem quite the right word for what is basic to the physical world, though Harré and Madden make a good case for the 'fields' of physic being understood in that way. I prefer 'power', though that doesn't solve anything.
26. Natural Theory / D. Laws of Nature / 3. Laws and Generalities
Lawlike sentences are general attributions of disposition to all members of some class [Fetzer]
     Full Idea: Lawlike sentences are conceived as logically general dispositional statements attributing permanent dispositional properties to every member of a reference class. ...Their basic form is that of subjunctive generalizations.
     From: J.H. Fetzer (A World of Dispositions [1977], 3)
     A reaction: I much prefer talk of 'lawlike sentences' to talk of 'laws'. At least they imply that the true generalisations about nature are fairly fine-grained. Why not talk of 'generalisations' instead of 'laws'? Fetzer wants dispositions to explain everything.