**From:** Marc Geddes (*m_j_geddes@yahoo.com.au*)

**Date:** Wed Jan 04 2006 - 19:52:10 MST

**Next message:**Matt Arnold: "Re: The definitive short demolition of materialism (Was: Everything I know is wrong )"**Previous message:**Damien Broderick: "Re: Everything I know is wrong"**Next in thread:**Matt Arnold: "Re: The definitive short demolition of materialism (Was: Everything I know is wrong )"**Reply:**Matt Arnold: "Re: The definitive short demolition of materialism (Was: Everything I know is wrong )"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Yeah, damn friggin right everything you think you know

is wrong. Let me begin to relieve you of some of your

delusions....

--- In other to show where the Eliminative materialists are going wrong, I will summarize the arguments for mathematical Platonism. What is mathematical Platonism? Well it's the idea that mathematical entities are not just abstract fictions, but have a real objective existence. Further these entities cannot be completely reduced to (described in terms of) material processes. And since (according to Functionalism) the mind is equivalent to an algorithm (which is a mathematical entity), if Platonism is right the Eliminative materialists have to be wrong - qualia in fact cannot be completely reduced to material processes. First, why should we believe in the objective existence of mathematical entities? Surely, some will argue, mathematical entities are really just abstract fictions (or invented languages) we use for describing what are really material processes. This position is known as nominalism. However, there's an argument known as *The argument from Indispensability*. Certain mathematical theories (for instance analysis) are indispensable for modern physics. Physics uses quantifiers which range over domains that include mathematical entities not in space and time. Thus, the argument goes; since we have to accept our best scientific theories of the world, we should accept that the entities referred to in our theories really exist. Now one could try to remove the references to mathematical entities in scientific theories. For instance the philosopher Hartry Field (1980) has proposed this - he suggested trying to remove talk of real numbers in Newton's theory of gravity and replacing numbers with space-time points and regions. But if one tries to do this, one finds that the theories become enormously unwieldy - mathematical entities such as numbers are just so *useful* in science. If there are entities in our theories which it is very useful to refer to, this provides some pragmatic grounds for believing in their existence. The argument at work here is Occam's razor: in science the general rule of thumb is that simple explanations are favored over more complex ones. Since in science references to mathematical entities simplify scientific theories, the simplest explanation is that these mathematical entities really exist. Further it appears that there are some highly abstract mathematical entities in scientific theories which *cannot* be replaced with descriptions of material processes at all. An example of this is 'the quantum wave function' -in quantum mechanics. The wave function is necessary for the theory to work, yet the wave function is wholly abstract. See arguments by Malament (1982) to the effect that one cannot remove talk of abstract entities from quantum mechanics. Since references to abstract entities appears to be *essential* for QM to work and since QM is such a successful scientific theory, the simplest possible explanation is that these abstract entities really do exist. Returning to the principle of Ocaam's razor again, physicist David Deutsch in his book 'The Fabric Of Reality', uses the principle to establish 'Criterion for reality'. The idea is that we should regard as real those postulated entities which, if we tried to replace them with something else would complicate our explanations. Deutsch's principle was this: 'If according to the simplest explanation, an entity is complex and autonomous, then that entity is real.' ('The Fabric Of Reality', Pg 91) As Detusch points out, mathematical entities do appear to match the criteria for reality: 'Abstract entities that are complex and autonomous exist objectively and are part of the fabric of reality. There exist logically necessary truths about these entities, and these comprise the subject-matter of mathematics.' Professor of mathematics Roger Penrose also neatly makes the point that mathematicians strongly feel they are engaged in discovery, not creation, and that mathematical entities appear to have complex, autonomous structure not put there by humans: 'The Mandelbrot set provides a striking example. It's wonderfully elaborate structure was not the invention of any one person, nor was it the design of a team of mathematicians. Benoit Mandelbrot himself, the Polish-American mathematician who first studied the set, had no real prior conception of the fantastic elaboration inherent in it...Moreover, the complete details of the complication of the structure of Mandelbrot's set cannot really be fully comprehended by any one of us, nor can it be fully revealed by any computer. It would seem that this structure is not just a part of our minds, but it has a reality of its own.' In 'Shadows of the Mind', Penrose goes on to make the very telling point that mathematical theories often turn out to be useful for science in a manner which goes far far beyond what the math was originally used for. The example is given of the mathematics of Einstein's general theory of relativity: 'In the early years after Einstein's theory was put forward, there were only a few effects that supported it and the increase in precision over Newton's scheme was marginal. However, now, nearly 80 years after the theory was first produced, its overall precision has grown to something like *ten million times* greater’ ('Shadows of The Mind', Pg 415). This is not at all what we would expect if the math was just an invention of the human mind. As Penrose points out: 'Einstein was not just 'noticing patterns' in the behavior of physical objects. He was uncovering a profound mathematical substructure that was already hidden in the very workings of the world.' Accepting all this, a skeptic might concede that mathematical entities have objective existence, but try to identity them entirely with the material world. This doesn't work. For one thing, as pointed out earlier, our best scientific theories make explicit references to wholly abstract entities (for instance 'the quantum wave function') which have no concrete counter-part at all. Further more, there exist perfectly good mathematical facts which be cannot be directly or indirectly matched to any material facts. A striking example of this transfinite numbers and infinite sets- here references are clearly made to infinite entities yet all available evidence would indicate that all material entities are finite. Attempting to equate transfinite numbers or infinite sets with some nebulous property of a ‘multiverse’ (as some scientists have attempted to do) is simply begging the question about what is physical. Nor can infinite sets be argued away as fictions - they are perfectly precise and logical mathematics, having the same 'reality' as any other results in mathematics. Greg Cantor developed a rigorous treatment of transfinite numbers and later Abraham Robinson and John Conway did the same for infinitesimals. In fact one has not even have to consider such esoteric things as transfinite numbers and quantum wave functions to see that nominalism (the idea that abstract entities don't exist) has severe problems. Logical positivists used to claim that statements could not be meaningful if they could not be converted into descriptions in terms of concrete observables. The positivists were wrong. There are perfectly meaningful statements in plain every day English that cannot be converted into concrete descriptions. Here is one example from the philosophy literature: Statement: "There are shapes that are never exemplified" It can be shown that this statement cannot be converted into any description of finite length which refers only to concrete entities. Yet the statement is clearly meaningful. This shows that abstract entities do exist. In fact nominalists cannot speak the words 'No abstract entities exist' without being in serious danger of contradicting themselves. For this sentence itself makes reference to abstract entities. By the nominalist's own doctrine, the sentence is meaningless. Indeed the nominalist's cannot think that he 'saying' anything at all: he is simply making noises with his mouth! ;) Semantic considerations provide even more evidence for believing in the existence of abstract entities. 'The Fregean argument' is based on the idea that only in the context of a sentence does a word have meaning. If a certain expression functions as a singular term in a sentence, the sentence cannot be meaningful unless there is an actual real singular entity to which the term is referring. For instance if ‘2’ functions as a singular term in a sentence, there must be a real entity '2' to the terms refers. Finally, let's look at computer science and the mind. If both Platonism and functionalism is correct and the mind is a mathematical algorithm, then the mind cannot be completely reduced to material processes. By the above arguments, mathematical entities are objectively real things that exist 'out there' in reality. But note that many *different* brains (or computers) can run the *same* algorithm. This suggests that the mathematical algorithm itself cannot be identical to the material processes which are enacting a particular example of it. Penrose again: 'The mind-stuff of strong AI is the logical structure of an algorithm... the particular physical embodiment of an algorithm is something totally irrelevant. The algorithm has some kind of disembodied 'existence' which is quite apart from any realization of that algorithm in physical terms' ('The Emperor's New Mind', Pg 27) It was an argument similar to this that led to the demise of the original 'Identity Theory' of mind (a theory which attempted to identity mental states with physical processes). Again, the trouble is that many different brain states could be associated with the *same* algorithm (or have the same mental states) which shows that physical processes cannot be identified with mathematical entities in any simple way. The weaker 'Token Identity' theories concede this, but still attempt to equate mental states with physical processes. Couldn't one simply say that there's some general high-level properties of physical matter which can be equated with the algorithm, and hence dispense with ghostly mathematical entities? The reason one can't really say this boils down to Occam's razor and inference to the best explanation again. Attempting to replace the concept of 'algorithm' with some high level properties of physical matter is results in descriptions that are enormously complex and unwieldy. And therefore such an arbitrary scheme should be rejected, for reasons explained earlier. Inference to the best explanation requires that we attempt that mathematical entities such as 'algorithim's' really do have an objective existence above and beyond a particular instantiation in material processes. To conclude, strong arguments were given to the effect that mathematical entities are objectively real. Further, arguments were given that mathematical entities cannot be completely reduced to descriptions in terms of material processes. According to the most popular theories of mind, a mind is equivalent to an algorithm, which is a mathematical entity. By the arguments for mathematical Platonism given combined with the observation that many *different* brains can run the *same* algorithm, the conclusion must be that the mathematical algorithm cannot be completely identified with the material processes occurring in the brain and therefore (assuming a mind is equivalent to an algorithm), neither can mental states. It can further be concluded then, that the position known as 'Eliminative materialism' (the idea that talk of qualia can be entirely replaced with talk of material processes) must be false. -- Cheers! "Till shade is gone, till water is gone, into the shadow with teeth bared, screaming defiance with the last breath, to spit in Sightblinder’s eye on the last day” Send instant messages to your online friends http://au.messenger.yahoo.com

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