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All the ideas for 'Remarks on the definition and nature of mathematics', 'Reflections on Value' and 'fragments/reports'

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10 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
All thought about values is philosophical, and thought about anything else is not philosophy [Weil]
     Full Idea: All reflections bearing on the notion of value and on the hierarchy of values is philosophical; all efforts of thought bearing on anything other than value are, if one examines them closely, foreign to philosophy.
     From: Simone Weil (Reflections on Value [1941], p.30)
     A reaction: If nothing else proves that Weil is a platonist, this does. She, of course, has a transcendent and religious view of values, whereas I just see them as concepts which embody what is important. That said, I'm not far off agreeing with this.
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / b. Philosophy as transcendent
Philosophy aims to change the soul, not to accumulate knowledge [Weil]
     Full Idea: Philosophy does not consist in accumulating knowledge, as science does, but in changing the whole soul.
     From: Simone Weil (Reflections on Value [1941], p.33)
     A reaction: I agree, roughly. In the sense that philosophy is a much more personal matter than any pure pursuit of knowledge, such as geology. Though a life in geology could change your soul. Not just any old change, of course….
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
Systems are not unique to each philosopher. The platonist tradition is old and continuous [Weil]
     Full Idea: People believe that every philosopher has a system that contradicts all the others! But there is a tradition, genuinely philosophical, that is as old as humanity itself. …Plato is the most perfect representative of this tradition.
     From: Simone Weil (Reflections on Value [1941], p.33)
     A reaction: I see roughly two traditions. If you believe in transcendence you follow Plato, like Simone. If you are a naturalist (like me) you follow Aristotle. A third tradition might be much more sceptical.
3. Truth / A. Truth Problems / 1. Truth
Truth is a value of thought [Weil]
     Full Idea: Truth is a value of thought. The word 'truth' cannot have any other meaning.
     From: Simone Weil (Reflections on Value [1941], p.32)
     A reaction: This makes a nice change from truth being a mere predicate. I would call truth the criterion of success in thought, and that counts as a value, so she is right.
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry]
     Full Idea: In the study of formal systems we do not confine ourselves to the derivation of elementary propositions step by step. Rather we take the system, defined by its primitive frame, as datum, and then study it by any means at our command.
     From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The formalist')
     A reaction: This is what may potentially lead to an essentialist view of such things. Focusing on bricks gives formalism, focusing on buildings gives essentialism.
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
It is untenable that mathematics is general physical truths, because it needs infinity [Curry]
     Full Idea: According to realism, mathematical propositions express the most general properties of our physical environment. This is the primitive view of mathematics, yet on account of the essential role played by infinity in mathematics, it is untenable today.
     From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The problem')
     A reaction: I resist this view, because Curry's view seems to imply a mad metaphysics. Hilbert resisted the role of the infinite in essential mathematics. If the physical world includes its possibilities, that might do the job. Hellman on structuralism?
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Saying mathematics is logic is merely replacing one undefined term by another [Curry]
     Full Idea: To say that mathematics is logic is merely to replace one undefined term by another.
     From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'Mathematics')
13. Knowledge Criteria / D. Scepticism / 3. Illusion Scepticism
A false object might give the same presentation as a true one [Arcesilaus, by Cicero]
     Full Idea: Arcesilaus said that no presentation proceeding from a true object is such that a presentation proceeding from a false one might not also be of the same form. This is the one argument that has held the field down to the present day.
     From: report of Arcesilaus (fragments/reports [c.275 BCE]) by M. Tullius Cicero - Academica II.24.77
22. Metaethics / B. Value / 1. Nature of Value / e. Means and ends
Ends, unlike means, cannot be defined, which is why people tend to pursue means [Weil]
     Full Idea: Everything that can be taken as an end cannot be defined. Means, such as power and money, are easily defined, and that is why people orient themselves exclusively towards the acquisition of means.
     From: Simone Weil (Reflections on Value [1941], p.31)
     A reaction: Nice, but too neat, because so many activities can be treated either as means or as ends, and often as both. It makes sense that people pursue what is clear to them.
22. Metaethics / B. Value / 2. Values / a. Normativity
Minds essentially and always strive towards value [Weil]
     Full Idea: For the mind essentially and always, in whatever manner it is disposed, strives towards value.
     From: Simone Weil (Reflections on Value [1941], p.31)
     A reaction: A typically platonist thought. If you accept my view that values identify what is important, the thought is plausible. We might distinguish between what the mind pointlessly entertains, and what it 'strives' for.