Dan quoted from Wikipedia on Anti-realism:

"The term was coined by Michael Dummett, who introduced it in his paper Realism 
to re-examine a number of classical philosophical disputes involving such 
doctrines as nominalism, conceptual realism, idealism and phenomenalism. The 
novelty of Dummett's approach consisted in seeing these disputes as analogous 
to the dispute between intuitionism and Platonism in the philosophy of 
mathematics.  ...According to intuitionists (anti-realists with respect to 
mathematical objects), the truth of a mathematical statement consists in our 
ability to prove it. According to platonists (realists), the truth of a 
statement consists in its correspondence to objective reality."



Dan said to dmb:

I am the one who threw idealism into the mix. And yes of course I understand 
the MOQ is neither. When you mentioned anti-realism I read idealism, rightly or 
wrongly. I know that to professional philosophers who are much more learned 
that I am the terms have a difference but to me they fall under the same 
umbrella.     ...Now it seems to me that anti-realism has more to do with 
mathematics than metaphysics so I was unsure why it is being brought into the 
discussion. 



dmb says:

There is a dispute between realists and anti-realists in mathematics, science, 
morality and all kinds of other areas. And, as it says in the quote you shared, 
in mathematics the Platonists are realists (with respect to numbers). Plato 
himself was a realist with respect to Ideas or Forms and he is the king of 
Idealism or Rationalism. This is a very good reason not to equate idealism with 
anti-realism. Idealists and materialists have different views about what's 
"real" but both can be considered realists and they both can subscribe to the 
appearance-reality distinction and the correspondence theory of truth, where 
true ideas are the ones that represent the way things "really" are.



That Stanford quote on "Constructive empiricism" tells us, for example, that 
scientific realism claims "to give us, in its theories, a literally true story 
of what the world is like" whereas the constructive empiricist holds that 
"acceptance of a scientific theory involves only the belief that the theory is 
empirically adequate." So, yes, constructive empiricism makes no claims about 
what is literally 'true' story about what the world is like. It says our 
conceptual models can be empirically adequate or not, they can successfully 
organize the relevant data or not, but it stops short of making any 
metaphysical claims about these models corresponding to the "real" reality 
beyond those appearances. 


The stance called constructive empiricism is very similar to (ZAMM, page 262) 
Pirsig's lesson about Poincare and
 alternative geometries. He says it doesn't really make any sense to "ask 
whether the metric system is true and the avoirdupois 
system is false; whether Cartesian coordinates are true and polar 
coordinates are false. One geometry can not be more true than 
another; it can only be more convenient. Geometry is not true, it is 
advantageous."


Or, as I'd like to put it, geometry shouldn't be taken as True in the sense 
that it corresponds to an objective, mind-independent reality but it's 
pragmatically true in the sense that it agrees with experience. Pragmatic 
truths are the ones that work in practice, the ones that work when you can 
actually use them for some purpose. What we get in the MOQ are just empirical 
claims, not metaphysical claims. In the MOQ, the primary empirical reality is 
prior to language, outside of language, and so it offers no definite claims 
about the "real" reality. It can be known in experience but as soon as we start 
talking, we're dealing with concepts and not the primary empirical reality. 
Idealists say ideas are reality and materialists say physical things are 
reality but the MOQ says reality cannot be defined. 


Ironically, the MOQ isn't metaphysical in the sense. Like the man said, it's a 
contradiction in terms, a logical absurdity.


Hope that addresses most of your concerns.



                                          
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