Problem of Universals and Materialistic Atheism

For some time I have been having a discussion with someone about the problem of universals, and I have a hard time understanding why it is so far fetched or impossible, according to some, to conceive of mathematics, or circles, etc., as concepts without resort to a non-material realm.  Below is a link to a refutation of Materialistic Atheism.  Perhaps others will understand it better than I do.  In any case, I am seeking a better understanding of this issue and whether it is really a threat to the materialistic worldview:

http://ex-pentecostal.blogspot.com/2009/02/concise-refutation-of-materialist.html

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But I think the influence and work of the so-called Language Philosophers (Wittgenstein, Austin, Goodman, and others) indicates that there is still plenty for philosophers to do--it's just not science. The gray area I see is in cognitive science which is the umbrella beach party that tries to re-unite the logical, the philosophical, and the scientific. Just as most folks don't really understand what science is about, they don't understand philosophy either. To malign a field because of incompetent or inauthentic 'practitioners' is not terribly useful; a better tactic is to promote the work of the ones who are competent. We don't bash medicine because chiropractors exist, we go after the chiropractors and promote science-based medicine.
I think the state machine thought experiment is interesting -- but what is the state machine? How do you set it up? Would it need to iterate at all? Or would getting definition of the machine solve the problem?

re Nobels: a prize based upon the gains made from blowing things up isn't always the best reward.
Absolutely, my friend. When people try to tackle scientific questions with philosophy they are making a mistake. I don't think serious, non-theist philosopher's even attempt to do that now, though. Philosophy should tackle linguistics mostly in this day and age, for the most part. To dismiss philosophy as a discipline is wrong, for sure. The philosophies I have had the most interest in have rarely, if ever, made claims about the physical world.

I have read many philosophies that do not encroach on sciences territory.
philosophers, eh? You dismiss an entire field far too easily.
Well, I'm kind of with you on 'empirical philosophy' (philosophically and socially ;-(

I think the use of philosophy is to bring a rigor to the thinking about whatever field is being studied. I'm not sure that philosophy by itself--particularly given the success of science--is a worthwhile goal any more. But within disciplines, it helps bring discipline (wow--that almost sounds like a deepity.) Ontology and epistemology, in particular, can be useful--not as answers but as ways of thinking about the issues.

See also Alex's thought here
A final thought: I think it's interesting that the last great piece of philosophy--Wittgenstein's Tractatus begins "The world is all that is the case."
I think the difficulty (read 'mistake') begins with the misdefinition of science: Science is, briefly put, correlation of data to a model. It asks: how well does this particular model follow the data and the evidence collected?

That is part of what science does, not the whole of it.

He goes on: Also, the problem of universals shows that there are indeed non-material existents. Most or all of math is a non-material existent. One cannot find math anywhere as a physical object. Thus, one must accept the existence of non-material existents, unless one wishes to claim that mathematics does not exist. ... This opens us up to another realm where there are things that are real, and exist, apart from physical phenomena, such as mathematics and consciousness.

He then concludes that a science/materialist 'proof' is incoherent because a material process is trying to prove something about a non-material realm (his word.)

I agree that '(the concept) two' exists and is not material (a universal, in his terms.) But, nothing about these non-material existants affect the material. As powerful as math is, it never causes anything to happen in the material world, it is only used as a description of the material world. The traffic, as it were, is only in one direction. Math, and science by analogy, can make predictions which can then be tested. But it never causes the result.

So, one can end up with a non-material realm but it has no relevance to the working of the material realm; its only use is in the explication of the material world. A shorthand, if you will.

At a more sophisticated level, though, I could (and would) argue against my previous statement and even deny that 'two' exists and is a universal in some special realm. Abstract concepts arise from the actions of material objects (the brain); they are 'universal' in that they arise (or are caused to arise--learning) in the brains of others who are wired sufficiently identically. [All this assumes normal working of brains--we are much more alike than we are dissimilar.]
I love this type of argument. At first blush it seems an insurmountable problem for naturalists who posit all things in space and time. The universals - usually mathematical concepts and moral truths are raised - are the latest remnants of Platonic forms. Plato proposed that there must be a perfect form that really exists of which all physical variations are imperfect copies. All trees are limited imitations of the ideal tree and so on. There might even be a perfect atheist!!! These forms are eternal and universal unlike the transitory nature of our physical world and that we progressively discover the existences of these forms. Many people have struggled with the idea of our world or reality being transistory. Also no wonder Christians like Augustine grasped onto these ideas as a philosophical basis for the ultimate, eternal form - God.

Most people today would balk at the idea of a perfect tree or perfect watch or a perfect atheist existing somewhere beyond the physical realm. So why is a circle so special? Are we, as humans, not capable of conceptualising or generalisating from experience or even from imagination like a unicorn or a god without pretending they exist outside of our brain processing? In fact our remarkable brain capability has been the great strength of humans but also explains why many people in the past and even today don't necessarily share these so-called "universals". In many cases specific societies never were exposed to examples or never had the need for particular concepts as part of their development. The progressive conceptualisation of zero in history appears a good case in point of a not-so-obvious universal.

Alex
Yup -- nothing is a good example of everything. :-)
I disagree - the perception of numbers is happening in your brain: you see the pens as being alike enough to be a set of two. You conceptualise them as a pair or as three or as four and so on. Each of the pens does not have any inherent "one of two-ness" property. It's like colour - they are not actually green or red. It is part of your perception and interpretation (body-brain processing). Other creatures will not see the objects as sets nor see the colours. Humans share the similar methods of brain processing and perception (by the way some brain damaged people do not perceive items as collections even though they can still perceive other aspects of their lives in usual ways) and therefore naturally feel that the numbering must "exist" separate from us in some ontologically different way. Alex
"Other creatures will not see the objects as sets nor see the colours."

Not quite accurate.

Single cells in the monkey brain encode abstract mathematical concepts

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