Combining Texts

All the ideas for 'fragments/reports', 'Experience First (and reply)' and 'Structuralism'

unexpand these ideas     |    start again     |     specify just one area for these texts

---

7 ideas

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism

8921	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

8922	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.

11. Knowledge Aims / A. Knowledge / 2. Understanding

19542	It is nonsense that understanding does not involve knowledge; to understand, you must know [Dougherty/Rysiew]
	Full Idea: The proposition that understanding does not involve knowledge is widespread (for example, in discussions of what philosophy aims at), but hardly withstands scrutiny. If you do not know how a jet engine works, you do not understand how it works.
	From: Dougherty,T/Rysiew,P (Experience First (and reply) [2014], p.24)
	A reaction: This seems a bit disingenuous. As in 'Theaetetus', knowing the million parts of a jet engine is not to understand it. More strongly - how could knowledge of an infinity of separate propositional truths amount to understanding on their own?

19543	To grasp understanding, we should be more explicit about what needs to be known [Dougherty/Rysiew]
	Full Idea: An essential prerequisite for useful discussion of the relation between knowledge and understanding is systematic explicitness about what is to be known or understood.
	From: Dougherty,T/Rysiew,P (Experience First (and reply) [2014], p.25)
	A reaction: This is better. I say what needs to be known for understanding is the essence of the item under discussion (my PhD thesis!). Obviously understanding needs some knowledge, but I take it that epistemology should be understanding-first. That is the main aim.

11. Knowledge Aims / A. Knowledge / 7. Knowledge First

19541	Rather than knowledge, our epistemic aim may be mere true belief, or else understanding and wisdom [Dougherty/Rysiew]
	Full Idea: If we say our cognitive aim is to get knowledge, the opposing views are the naturalistic view that what matters is just true belief (or just 'getting by'), or that there are rival epistemic goods such as understanding and wisdom.
	From: Dougherty,T/Rysiew,P (Experience First (and reply) [2014], p.17)
	A reaction: [compressed summary] I'm a fan of understanding. The accumulation of propositional knowledge would relish knowing the mass of every grain of sand on a beach. If you say the propositions should be 'important', other values are invoked.

26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature

1748	Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
	Full Idea: Archelaus was the first person to say that the universe is boundless.
	From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3

27. Natural Reality / G. Biology / 3. Evolution

5989	Archelaus said life began in a primeval slime [Archelaus, by Schofield]
	Full Idea: Archelaus wrote that life on Earth began in a primeval slime.
	From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus
	A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea.