11 ideas
| 15335 | Peirce's theory offers anti-realist verificationism, but surely how things are is independent of us? [Horsten on Peirce] |
| Full Idea: Peirce's anti-realist theory of a truth is a verificationist theory. Truth is judged to be an epistemic notion. But the way things are is independent of the evidence we may be able to obtain for or against a judgement. | |
| From: comment on Charles Sanders Peirce (Pragmatism in Retrospect [1906]) by Leon Horsten - The Tarskian Turn 02.1 | |
| A reaction: This criticism doesn't quite capture the point that Peirce's theory is that truth is an ideal, not the set of opinions that miserable little humans eventually settle for when they get bored. Truth is an aspect of rationality, perhaps. |
| 14796 | Independent truth (if there is any) is the ultimate result of sufficient enquiry [Peirce] |
| Full Idea: I hold that truth's independence of individual opinions is due (so far as there is any 'truth') to its being the predestined result to which sufficient enquiry would ultimately lead. | |
| From: Charles Sanders Peirce (Pragmatism in Retrospect [1906], p.288) |
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
| A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
| A reaction: Each expansion brings a limitation, but then you can expand again. |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
| 3291 | Emergent properties appear at high levels of complexity, but aren't explainable by the lower levels [Nagel] |
| Full Idea: The supposition that a diamond or organism should truly have emergent properties is that they appear at certain complex levels of organisation, but are not explainable (even in principle) in terms of any more fundamental properties of the system. | |
| From: Thomas Nagel (Panpsychism [1979], p.186) |
| 14795 | Pragmatism is a way of establishing meanings, not a theory of metaphysics or a set of truths [Peirce] |
| Full Idea: Pragmatism is no doctrine of metaphysics, no attempt to determine the truth of things. It is merely a method of ascertaining the meanings of hard words and of abstract concepts. | |
| From: Charles Sanders Peirce (Pragmatism in Retrospect [1906], p.271) | |
| A reaction: Suddenly I recognise a prominent strand of modern philosophy of language (especially in America) for what it is. |
| 3290 | Given the nature of heat and of water, it is literally impossible for water not to boil at the right heat [Nagel] |
| Full Idea: Given what heat is and what water is, it is literally impossible for water to be heated beyond a certain point at normal atmospheric pressure without boiling. | |
| From: Thomas Nagel (Panpsychism [1979], p.186) |