14 ideas
| 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) |
| 4304 | Descartes says there are two substance, Spinoza one, and Leibniz infinitely many [Cottingham] |
| Full Idea: Descartes was a dualist about substance, Spinoza was a monist, and Leibniz was a pluralist (an infinity of substances). | |
| From: John Cottingham (The Rationalists [1988], p.76) | |
| A reaction: Spinoza is appealing. We posit a substance, as the necessary basis for existence, but it is unclear how more than one substance can be differentiated. If mind is a separate substance, why isn't iron? Why aren't numbers? |
| 4303 | The notion of substance lies at the heart of rationalist metaphysics [Cottingham] |
| Full Idea: The notion of substance lies at the heart of rationalist metaphysics. | |
| From: John Cottingham (The Rationalists [1988], p.75) | |
| A reaction: The idea of 'substance' has had an interesting revival in modern philosophy (though not, obviously, in physics). Maybe physics and philosophy have views of reality which are not complementary, but are rivals. |
| 3986 | The 'intentional stance' is a way of interpreting an entity by assuming it is rational and self-aware [Dennett] |
| Full Idea: The 'intentional stance' is the tactic of interpreting an entity by adopting the presupposition that it is an approximation of the ideal of an optimally designed (i.e. rational) self-regarding agent. | |
| From: Daniel C. Dennett (Daniel Dennett on himself [1994], p.239) | |
| A reaction: This is Dennett's 'instrumentalism', a descendant of behaviourism, which strikes me as a pragmatist's evasion of the ontological problems of mind which should interest philosophers |
| 3987 | Like the 'centre of gravity', desires and beliefs are abstract concepts with no actual existence [Dennett] |
| Full Idea: Like such abstracta as centres of gravity and parallelograms of force, the beliefs and desires posited by the highest intentional stance have no independent and concrete existence. | |
| From: Daniel C. Dennett (Daniel Dennett on himself [1994], p.239) | |
| A reaction: I don't see why we shouldn't one day have a physical account of the distinctive brain events involved in a belief or a desire |
| 3984 | The nature of content is entirely based on its functional role [Dennett] |
| Full Idea: All attributions of content are founded on an appreciation of the functional roles of the items in question. | |
| From: Daniel C. Dennett (Daniel Dennett on himself [1994], p.239) | |
| A reaction: This seems wrong to me. How can anything's nature be its function? It must have intrinsic characteristics in order to have the function. This is an evasion. |
| 3983 | Learning is evolution in the brain [Dennett] |
| Full Idea: Learning is evolution in the brain. | |
| From: Daniel C. Dennett (Daniel Dennett on himself [1994], p.238) | |
| A reaction: This is a rather non-conscious, associationist view, connected to Dawkins' idea of 'memes'. It seems at least partially correct. |
| 4306 | For rationalists, it is necessary that effects be deducible from their causes [Cottingham] |
| Full Idea: The rationalist view of causation takes it that to make effects intelligible, it must be shown that they are in principle deducible from their causes. | |
| From: John Cottingham (The Rationalists [1988], p.92) | |
| A reaction: This has intuitive appeal, but deduction is only possible with further premises, such as the laws of physics. The effects of human behaviour look a bit tricky, even if we cause them. |
| 3985 | Biology is a type of engineering, not a search for laws of nature [Dennett] |
| Full Idea: Biology is not a science like physics, in which one should strive to find 'laws of nature', but a species of engineering. | |
| From: Daniel C. Dennett (Daniel Dennett on himself [1994], p.239) | |
| A reaction: Yes. This is also true of chemistry, which has always struck me as minitiarised car mechanics. |