Combining Texts

All the ideas for 'fragments/reports', 'Toward a Philosophy of History' and 'Structuralism'

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6 ideas

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism is now common, studying relations, with no regard for what the objects might be [Hellman]
     Full Idea: With developments in modern mathematics, structuralist ideas have become commonplace. We study 'abstract structures', having relations without regard to the objects. As Hilbert famously said, items of furniture would do.
     From: Geoffrey Hellman (Structuralism [2007], §1)
     A reaction: Hilbert is known as a Formalist, which suggests that modern Structuralism is a refined and more naturalist version of the rather austere formalist view. Presumably the sofa can't stand for six, so a structural definition of numbers is needed.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Maybe mathematical objects only have structural roles, and no intrinsic nature [Hellman]
     Full Idea: There is the tantalizing possibility that perhaps mathematical objects 'have no nature' at all, beyond their 'structural role'.
     From: Geoffrey Hellman (Structuralism [2007], §1)
     A reaction: This would fit with a number being a function rather than an object. We are interested in what cars do, not the bolts that hold them together? But the ontology of mathematics is quite separate from how you do mathematics.
7. Existence / A. Nature of Existence / 3. Being / h. Dasein (being human)
For man, being is not what he is, but what he is going to be [Ortega y Gassett]
     Full Idea: Being consists not in what it is already, but in what it is not yet, a being that consists in not-yet-being. Everything else in the world is what it is….Man is the entity that makes himself….He has to determine what he is going to be.
     From: José Ortega y Gassett (Toward a Philosophy of History [1941], p.112,201-2), quoted by Kevin Aho - Existentialism: an introduction 4 'Problem'
     A reaction: [p.112 and 201-2] This seems to be Ortega y Gasset's spin on Heidegger's concept, by adding a temporal dimension to it.
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
Instead of having a nature, man only has a history [Ortega y Gassett]
     Full Idea: Man lives in view of the past. Man, in a word, has no nature; what he has is history. Expressed differently: what nature is to things, history is to man.
     From: José Ortega y Gassett (Toward a Philosophy of History [1941], p.217), quoted by Kevin Aho - Existentialism: an introduction 5 'Situated'
     A reaction: Makes explicit the existentialist denial of human nature. The foundation of ethics can only be total freedom, to choose both yourself and your actions. What is inescapable is the social and culture contexts. What is the role of the 'history'?
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
     Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes.
     From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078
     A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book.
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]
     Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness.
     From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42
     A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them.