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2
votes
2answers
56 views

How does abstraction/generalization in mathematics fit into inductive reasoning?

I have a question about the nature of generalization and abstraction. Human reasoning is commonly split up into two categories: deductive and inductive reasoning. Are all instances of generalization ...
2
votes
2answers
95 views

Definition of concept

What definition does contemporary analytic philosophy give of 'concept'? And what is the difference between a concept of something and a conception of something? Then what's the difference between ...
1
vote
0answers
43 views

What are the biggest advances in formal philosophy? [closed]

e.g. Is the formalization of occam's razor as minimum description length (Solomonoff induction) an example of this? Or the formalization of complexity as kolmogorov complexity?
1
vote
0answers
71 views

Logic as a (bad) model language

Can someone name the most well known philosophers to explicitly put forward an idea along the lines that formal systems can only be used descriptively, not prescriptively - that they're just a model, ...
1
vote
1answer
66 views

What are the ramifications of the limitations of ZFC set theory?

In the Wikipedia article on Zermelo-Fraenkel set theory says that the theory sets out to formalize a notion of sets such that "all entities in the universe of discourse are such sets." It goes on to ...
5
votes
2answers
192 views

How does “higher-order logic” differ from “normal” (first order?) predicate logic?

How does “higher-order logic” differ from “normal” predicate logic? I assume the latter is consistently called ”first order logic”. So where are the differences between these? What kinds of statements ...
16
votes
1answer
730 views

Is First Order Logic (FOL) the only fundamental logic?

I'm far from being an expert in the field of mathematical logic, but I've been reading about the academic work invested in the foundations of mathematics, both in a historical and objetive sense; and ...
5
votes
2answers
167 views

Is there a formal presentation of Maturana's “Autopoiesis”

I have been reading through "Autopoiesis and Cognition" by Humberto R. Maturana and Francisco J. Varela. One of their goals in defining autopoiesis and the supporting concepts of simple and composite ...
17
votes
11answers
857 views

Is it possible to scientifically determine good and evil?

Sam Harris has argued on many occasions - the earliest of which I'm aware of being in his book, The End of Faith, as well as later on in The Moral Landscape - that it is (at least theoretically) ...
12
votes
4answers
3k views

What are the philosophical implications of Gödel's First Incompleteness Theorem?

Gödel's First Incompleteness Theorem states Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any ...