= 27d567bc2d48d9f40e9ccc20ea370b15)
ZoltanBerrigomo comments on Why CFAR's Mission? - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (55)
I believe you are nitpicking here.
If your reason tells you 1+1=2 but your emotions tell you that 1+1=3, being rational means going with your reason. If your reason tells you that ghosts do not exist, you should believe this to be the case even if you really, really want there to be evidence of an afterlife.
CFAR may teach you techniques to align your emotions and reason, but this does not change the fundamental fact that being rational involves evaluating claims like "is 1+1=2?" or empirical facts about the world such as "is there evidence for the existence of ghosts?" based on reason alone.
Just to forestall the inevitable objections (which always come in droves whenever I argue with anyone on this site): this does not mean you don't have emotions; it does not mean that your emotions don't play a role in determining your values; it does not mean that you shouldn't train your emotions to be an aid in your decision-making, etc etc etc.
Being rational involves evaluating various claims and empirical facts, using the best evidence that you happen to have available. Sometimes you're dealing with a domain where explicit reasoning provides the best evidence, sometimes with a domain where emotions provide the best evidence. Both are information-processing systems that have evolved to make sense of the world and orient your behavior appropriately; they're just evolved for dealing with different tasks.
This means that in some domains explicit reasoning will provide better evidence, and in some domains emotions will provide better evidence. Rationality involves figuring out which is which, and going with the system that happens to provide better evidence for the specific situation that you happen to be in.
And how should you (rationally) decide which kind of domain you are in?
Answer: using reason, not emotions.
Example: if you notice that your emotions have been a good guide in understanding what other people are thinking in the past, you should trust them in the future. The decision to do this, however, is an application of inductive reasoning.
Sure.
On of the claims is analytic.
1+1=2is true by definition of what2means. There's little emotion involved.When it comes to an issue such as
is there evidence for the existence of ghosts?neither rationality after Eliezer's sequences nor CFAR argues that emotions play no role. Noticing when you feel the emotion of confusion because your map doesn't really fit is important.Beauty of mathematical theories is a guiding stone for mathematicians.
Basically any task that doesn't need emotions or intuitions is better done by computers than by humans. To the extend that human's outcompete computers there's intuition involved.
Russell and Whitehead would beg to differ.
"True by definition" is not at all the same as "trivial" or "easy". In PM the fact that 1+1=2 does in fact follow from R&W's definition of the terms involved.
I learned math with the Peano axioms and we considered the symbol
2to refer to the1+1, 3 to(1+1)+1and so on. However even if you consider it to be more complicated it still stays an analytic statement and isn't a synthetic one.If you define 2 differently what's the definition of 2?
When you write "1+1" you may mean two things: "the result of doing the adding operation to 1 and 1", and "the successor of 1". It just happens that we use "+1" to denote both of those. The fact that successor(1) = add(1,1) isn't completely trivial.
Principia Mathematica, though, takes a different line. IIRC, in PM "2" means something like "the property a set has when it has exactly two elements" (i.e., when it has an element a and an element b, and a=b is false, and for any element x we have either x=a or x=b) and similarly for "1" (with all sorts of complications because of the hierarchy of kinda-sorta-types PM uses to try to avoid Russell-style paradoxes). And "m+n" means something like "the property a set has when it it is the union of two disjoint subsets, one of which has m and the other of which has n". Proving 1+1=2 is more cumbersome then. And PM begins from a very early point, devoting quite a lot of space to introducing propositional calculus and predicate calculus (in an early, somewhat clunky form).
One popular definition (at least, among that small class of people who need to define 2) is { { }, { { } } }.
Another, less used nowadays, is { z : ∃x,y. x∈z ∧ y∈z ∧ x ≠ y ∧ ∀w∈z.(w=x ∨ w=y) }.
In surreal numbers, 2 is { { { | } | } | }.
In type theory and some fields of logic, 2 is usually defined as (λf.λx.f (f x)); essentially, the concept of doing something twice.