Friday, 25 December 2009

Part 5: Logic

From the series: 6 Ultimate Reasons Not To Be An Atheist?

#5 Atheists cannot believe in the absolute laws of logic
It seems like the ultimate defeater argument and destructive to any empiricist. As it is laid out, logic indeed cannot be empirically measured, nor can it be proven by example. Take two blocks and two more blocks and one has four blocks. If one were to measure this empirically, then the problem of induction would apply. We couldn't take two apples and two apples and be certain that there would be four apples, or that if we repeated the experiment that it would give the same result.

So there are in effect universals, and it's these universals that are means to understand the empirical data. So the universals aren't empirically-derivable in the same sense as forces. We empirically measure the force of gravity, but while we can measure the the sum of angles on a drawn triangle, the drawn triangle is only a representation of the idea of a triangle. No amount of drawn triangles will be sufficient to draw the conclusion that a triangle must add up to 180 degrees.

The problem being is that if these abstract forms aren't measurable in nature, then how can it come to be that they are universals? While gravity almost certainly exists and is measurable, the same cannot be said for the law of identity or the law of non contradiction or the law of excluded middle. Even 2 + 2 = 4 cannot be understood to be a universal unless there is a form by which it could be universal.

So again it's pertinent to ask whether it is necessary. It would seem like it is necessary if logic is the basis of all thought, but to explore the concept some more. Say logic is a human-derived system, that the law of identity is something that the human mind has created in order to understand the world. Does it make it any less wrong to build an argument on the basis of logic without it being universal?

To put it another way, does being able to add 2 and 2 to get 4 rest on the ability to account for the abstract itself? Here I could contend otherwise, it's not contingent to put mathematics as anything other than a human construct to be able to use it. Do I need to account for the existence of a shovel in order to use one? No. But the fact that a shovel exists needs some explanation. So in there I will concede that yes the laws of logic do require explanation.

So how would positing a god help with this? I don't think it will for the same reason as I don't think that positing a god helps with morality. It comes back to a question of God's omnipotence, the old classic of whether God can make a four-sided triangle. Now one might say "that's absurd" by very definition a triangle has to have three sides so if it had 4 sides it's not a triangle. And thus the absurdity of the proposition is shown.

Are the laws of logic dictated by God? In other words, could the laws of logic be anything other than they are? Is the law of identity true only because God says it is, or is the truth of the law of identity external to the truth of God? If it's external to the truth of God, then how does theism solve this problem?

It could be that the law of identity is only true because God says so. But consider the implications for this position. Take the abstract of 2 + 2 = 4. If it were that theism solves this problem, then 2 + 2 = 4 is only true while God holds it to be true. It could be on a whim that 2 + 2 = 5, or 2 + 2 = pi. This clearly is absurd, the absolute nature of 2+2=4 is undermined by the fact that it couldn't be any other way.

So to that objection, it might be that the laws of logic are absolute and external to any notion of a deity. However, as an atheist you don't have the ability to recognise absolutes. So on that...

We ask the third question, how can an atheist account for the absolute nature of the laws of logic? They are self-evident. If they can't be any other way then what more needs to be said? Bertrand Russell in The Problems Of Philosophy gives a good account of universals and out they can be distinguished from matters of observation. That there are some probable truths and some universal truths.

Look at the text typed here. Immediately to the left of the word "typed" was the word "text". Regardless of the meaning of the words themselves the relationship in position is absolute. "text" is left of "typed" thus a universal relationship is established. Just as the relationship between two apples and two more apples being put together makes four apples. The general principle of relationships is based on universals.

Apples (the particular) is contingent on our observations, but the general principle underneath is not. We don't need to see that two phones and two more phones makes four phones, and two tissues and two more tissues makes four tissues. The relationship is self-evidently true.

This doesn't address the question of how we come to know these absolutes. Take something like a circle. Now when we see something circular, it's never an exact circle - only the appearance of a circle. One could draw a circle, take measurements and use that observation to reason about the circle, but the idea of the circle cannot be derived empirically. How would one measure pi for example? Now pi can be worked out mathematically from the idea of a perfect circle.

So to cut a long story short, to think of logic in the same way as boiling water is misleading. Although experience may be at the core of both, there is a means to distinguish between the abstract and the actual. The abstract holds absolute because it is not a measurement of reality, but of relationships that are universal. The laws of logic are not arbitrary concepts cooked up by the mind, but self-evident truths about reality. As for knowing probabilistic truths...

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