1. What is Reality?
A recent issue of New Scientist (Oct.2, 2012) had a number of interesting articles on reality.
Philospher Jan Westerhoff, in Reality: Is Matter Real?, argues that the fundamental reality is not matter but, rather, mathematics.
He argues:
"The scientific reductionist sets out to reduce the human mind to the activity of the brain, the brain to an assembly of interacting cells, the cells to molecules, the molecules to atoms, the atoms to subatomic particles, the subatomic particles to collections of space-time points, the collections of space-time points to sets of numbers, and the sets of numbers to pure sets."
He concludes that there are two possibilities.
(1)The fundamental reality is a Platonic realm where mathematical objects exist. They are not made of matter, do not exist in space or time, do not change, cannot be created or destroyed, and could not have failed to exist.
or
(2) Mathematical objects are mental objects that exist only in our minds. But the mind has already been reduced to the brain, to atoms and to sets. Hence, reducing sets to mind puts us into a closed explanatory loop.
Westerhoff seems to prefer the second option. However, if mathematical sets reside only in human minds, this entails that reality depends on human minds. This rules out any evolutionary account of origins that posits reality existed before the advent of human minds.
Another article in that issue, “Reality: Is everything made of numbers?”, by Amanda Gefter, is in the same vein. She writes, "Perhaps if we dig deep enough, we would find that physical objects like tables and chairs are ultimately not made of particles or strings, but of numbers."
Moreover, she contends that all mathematical structures can be derived from the empty set. Hence, mathematics is literally based on nothing. Gefter concludes,
"Reality may come down to mathematics, but mathematics comes down to nothing at all. That may be the ultimate clue to our existence - after all, a universe made of nothing doesn't require and explanation."
Furthermore, she contends that mathematical structures don't require a physical origin, since they can't be created or destroyed but just exist.
2. What are we to make of this?
It is nonsense.
First, to obtain mathematics we need a great deal more than merely the empty set. We also need the laws of logic, proper axioms for set theory, and various highly sophisticated definitions and techniques. Mathematics is not a trivial discipline.
Second, physical objects cannot be reduced to mathematics. The two are quite distinct. Physical objects are concrete, contingent, temporal particulars existing in 3-d space. Mathematical entities, on the other hand, are abstract, necessary, timeless universals existing in an ideal realm of pure thought.
Just because the position of a particle can be represented by a set of three numbers does not entail that the particle itself can be reduced to a set of numbers. To think it does is to commit the fallacy of misplaced concreteness, where the abstract mathematical model of reality is mistaken for concrete reality itself.
Theoretical physicists are particularly susceptible to this error. Take, for example, the recent book The Grand Design (2010) by Stephen Hawking and Leonard Mlodinow. On the one hand, they contend that physics can explain everything, hence God is not needed. On the other hand, they try to explain everything in terms of physical laws. This leads them to conclude:
"It is hard to imagine how free will can operate if our behaviour is determined by physical law. So it seems that we are no more than biological machines and that free will is just an illusion."
The danger is that we become so enthralled by the beauty and predictive power of our mathematical models that these are seen to be reality and, consequently, our actual concrete experiences, upon which the model must ultimately be based, are then relegated to mere subjective illusion.
We must never forget that the model is just an abstract representation of reality, not reality itself. Just like a map should not be mistaken for the actual landscape.
Finally, the underlying difficulty with the above authors is that they all accept a naturalist, evolutionary account of origins, where mind emerges from matter, which emerges from nothing. Such radical reductionism is untenable, as it must inevitably fail to explain the intricate relationship between matter, mind and mathematics.
This issue is addressed by atheistic philosopher Thomas Nagel in his recent book Mind and Cosmos: Why the Materialist Neo-Darwinian conception of Nature is almost certainly false (2012). Nagel contends:
"If materialism cannot accommodate consciousness, then we must abandon a purely materialist understanding of nature. Since minds are features of biological systems, the standard materialist version of evolutionary biology is fundamentally incomplete. And the cosmological history that led to the origin of life cannot be a merely materialist history."
Acknowledging the failure of materialism is a certainly step in the right direction. However, Nagel offers no detailed alternative.
A viable worldview should be able to account for the reality of all three realms of matter, mind and mathematics. A Christian view would stress that God--not matter or math-- is the ultimate reality. God has created the physical universe according to a rational plan. Since God created man--body and soul-- in His image, we can discern the underlying rationality of the universe.
A recent issue of New Scientist (Oct.2, 2012) had a number of interesting articles on reality.
Philospher Jan Westerhoff, in Reality: Is Matter Real?, argues that the fundamental reality is not matter but, rather, mathematics.
He argues:
"The scientific reductionist sets out to reduce the human mind to the activity of the brain, the brain to an assembly of interacting cells, the cells to molecules, the molecules to atoms, the atoms to subatomic particles, the subatomic particles to collections of space-time points, the collections of space-time points to sets of numbers, and the sets of numbers to pure sets."
He concludes that there are two possibilities.
(1)The fundamental reality is a Platonic realm where mathematical objects exist. They are not made of matter, do not exist in space or time, do not change, cannot be created or destroyed, and could not have failed to exist.
or
(2) Mathematical objects are mental objects that exist only in our minds. But the mind has already been reduced to the brain, to atoms and to sets. Hence, reducing sets to mind puts us into a closed explanatory loop.
Westerhoff seems to prefer the second option. However, if mathematical sets reside only in human minds, this entails that reality depends on human minds. This rules out any evolutionary account of origins that posits reality existed before the advent of human minds.
Another article in that issue, “Reality: Is everything made of numbers?”, by Amanda Gefter, is in the same vein. She writes, "Perhaps if we dig deep enough, we would find that physical objects like tables and chairs are ultimately not made of particles or strings, but of numbers."
Moreover, she contends that all mathematical structures can be derived from the empty set. Hence, mathematics is literally based on nothing. Gefter concludes,
"Reality may come down to mathematics, but mathematics comes down to nothing at all. That may be the ultimate clue to our existence - after all, a universe made of nothing doesn't require and explanation."
Furthermore, she contends that mathematical structures don't require a physical origin, since they can't be created or destroyed but just exist.
2. What are we to make of this?
It is nonsense.
First, to obtain mathematics we need a great deal more than merely the empty set. We also need the laws of logic, proper axioms for set theory, and various highly sophisticated definitions and techniques. Mathematics is not a trivial discipline.
Second, physical objects cannot be reduced to mathematics. The two are quite distinct. Physical objects are concrete, contingent, temporal particulars existing in 3-d space. Mathematical entities, on the other hand, are abstract, necessary, timeless universals existing in an ideal realm of pure thought.
Just because the position of a particle can be represented by a set of three numbers does not entail that the particle itself can be reduced to a set of numbers. To think it does is to commit the fallacy of misplaced concreteness, where the abstract mathematical model of reality is mistaken for concrete reality itself.
Theoretical physicists are particularly susceptible to this error. Take, for example, the recent book The Grand Design (2010) by Stephen Hawking and Leonard Mlodinow. On the one hand, they contend that physics can explain everything, hence God is not needed. On the other hand, they try to explain everything in terms of physical laws. This leads them to conclude:
"It is hard to imagine how free will can operate if our behaviour is determined by physical law. So it seems that we are no more than biological machines and that free will is just an illusion."
The danger is that we become so enthralled by the beauty and predictive power of our mathematical models that these are seen to be reality and, consequently, our actual concrete experiences, upon which the model must ultimately be based, are then relegated to mere subjective illusion.
We must never forget that the model is just an abstract representation of reality, not reality itself. Just like a map should not be mistaken for the actual landscape.
Finally, the underlying difficulty with the above authors is that they all accept a naturalist, evolutionary account of origins, where mind emerges from matter, which emerges from nothing. Such radical reductionism is untenable, as it must inevitably fail to explain the intricate relationship between matter, mind and mathematics.
This issue is addressed by atheistic philosopher Thomas Nagel in his recent book Mind and Cosmos: Why the Materialist Neo-Darwinian conception of Nature is almost certainly false (2012). Nagel contends:
"If materialism cannot accommodate consciousness, then we must abandon a purely materialist understanding of nature. Since minds are features of biological systems, the standard materialist version of evolutionary biology is fundamentally incomplete. And the cosmological history that led to the origin of life cannot be a merely materialist history."
Acknowledging the failure of materialism is a certainly step in the right direction. However, Nagel offers no detailed alternative.
A viable worldview should be able to account for the reality of all three realms of matter, mind and mathematics. A Christian view would stress that God--not matter or math-- is the ultimate reality. God has created the physical universe according to a rational plan. Since God created man--body and soul-- in His image, we can discern the underlying rationality of the universe.
*****
6 comments:
Do I detect a certain degree of post-modernism in the these statements in Westerhoff and Gefter or am I missing something?
Not quite. They follow the logical implications of modern naturalism, which stresses the reliability of scientiic knowledge of an external world but ends up denying the reality of a purposeful, subjective human knower. Without a knower there can be no knowledge.
Post-modernity is a backlash to this naturalist destruction of ojective knowledge. It stresses the centrality of the subjective human self and questions our ability to obtain objective knowledge of the external world.
A viable worldview should give proper recognition to both notions of a subjective self and objective knowledge of the external world.
So let me see if I understand Dr. Westerhoff:
Westerhoff says, "Mathematical objects are mental objects that exist only in our minds."
The number two is represented by the figure 2; it is the abstraction our mind makes to think about something that is more than one.
But two does not really exist. No one has ever seen a two. 2 exists, though, because it is the representation of the abstraction which the mind makes; but two doesn’t exist.
But then 2 no longer represents two anymore, because two doesn’t exist, and therefore there is nothing to represent or to abstract.
So 2 is not really an abstraction of two either; it is not an abstraction of anything. It’s something our minds created because somehow our minds have to deal with more than one of something, which isn’t really more than one of anything in the realm where numbers primarily exist. Or rather don’t exist.
So Westerhoff is saying that he doesn’t know what numbers are, hence he doesn’t know what math is, hence he doesn’t know what he’s talking about.
Dr. Byl, I don’t know if I understand him but isn’t it a lot easier for him to just not say anything than to say a lot of nothing?
Hi John
You ask: wouldn't it be easier for Dr. Westerhoff not to say anything rather than to say a lot of nothing?
But he is something very important: he acknowledges that reality is a lot more than merely matter. He recognizes that there are mysterious connections between matter, mind and math that are very difficult to explain via scientific reductionism. If his proposed solutions hold no water, this illustrates the short-comings of a naturalist explanation of reality.
Dr. Byl:
I couldn’t link to his article so I couldn’t read it. I was referring only to the summary statement, “Mathematical objects are mental objects that exist only in our minds,” which was Dr. Westerhoff’s option #2.
Considering the rest of option 2, “…But the mind has already been reduced to the brain, to atoms and to sets. Hence, reducing sets to mind puts us into a closed explanatory loop”, I think that’s where you are coming from. Your point is well made, pointing out that it is no solution. It is just nonsense.
It seems important, though, to point out that the evolutionist’s argument, whether secular or religious, rests on the equivocation of the word ‘science’; especially the religious evolutionists. Their argument, in a nutshell, is
Evolution = science; science = general revelation; therefore, evolution = general revelation,
and neglect completely that the word ‘science’ has a different definition in the first equation than it does in the second. General revelation (for the religious evolutionist), or true factual knowledge (for the secular evolutionist), does not refer to men’s best educated guesses, but to hard, knowable, inviolable facts.
That a theory which stands on man’s abstractions eventually falls in on itself is nothing new. We would be better off with Westerhoff’s option #1 than with #2. We may not be able to demonstrate that numbers have a superior existence all on their own, but we would have a theoretically unchanageable universal, something to ground mind onto; and therefore have a hope of a solution.
We would be best off with a third option: the Christian view of the universals: all knowledge finds its perfection in God, whose existence cannot be denied, whose testimony we have. With this view man has the universals to answer all three areas of questions: of how we came to be, of how we know, and of moral standards.
JohnV
Hi John
Thanks for your interesting comments. I concur that we cannot equate evolution with general revelation (which, strictly speaking, has to do with God's self-revelation of knowledge about Himself).
Words such as evolution, creation, science, general revelation, etc. can all be used in different senses. Hence, when using such words, their intended meaning should be made clear in order to avoid ambiguity or deception.
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