Tag Archives: laws of logic

Atheism, Existence of God

What Explains the Laws of Logic and Mathematics?

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Post Author: Bill Pratt

The laws of thought and mathematics are absolutely true.  The law of non-contradiction, the law of identity, and the law of the excluded middle – the three fundamental principles of thought, otherwise known as the laws of logic – are all undeniable.  To deny them is to assume they are true.

They are true regardless of time, place, or who is thinking about them.  There is no possible world where they could not be true.  Likewise with mathematics.  2+3=5, and this is true regardless of time, place, or who is thinking about it.  There is no possible world where 2+3 does not equal 5.

So, any worldview which claims to explain all of reality had better have a good explanation of how this could be true.

How does atheistic naturalism explain the laws of thought and mathematics?  Since everything, on naturalism, must be reduced to physical matter, an explanation for the laws of thought and mathematics will be hard to come by, for these laws are clearly not made out of matter.

Naturalists take a couple different routes.  First, some of them say that there is no explanation for these laws; they just exist and that’s it; they are brute facts of the universe.  But surely these laws that transcend time, space, and matter, that existed before humans ever came on the scene, and will still exist after humans are extinct, are uncomfortable bedfellows with electrons, skin cells, and hydrogen atoms – the things of physical science.

How will the scientific methods of physics, chemistry, and biology explain the laws of thought and mathematics when they are built on them and rely on them? It’s like trying to explain the cinder block foundation of a house by appealing to a second-story window.

A second explanation is the following: some naturalists deny that these laws actually transcend time, space, and matter.  They claim that these are merely human conventions, laws that human beings have simply invented.  But this claim seems incredible.  Are we to really accept that 2+3 does not equal 5 unless human beings say it does?

I feel quite confident that even Klingons would agree that 2+3=5.  Can you imagine there being any dispute between a human and a Klingon over math? Of course not. The idea is absurd. This explanation just won’t fly because these laws are absolute; it doesn’t matter one bit whether any one of us ever discovered these laws, as they would still be true.  You can’t imagine a time or place where these laws aren’t true.

How does Christian theism explain the laws of thought and mathematics?  Instead of denying that these laws are transcendent, Christian theism affirms our basic intuitions that they are.  Christians identify the source of the laws of thought and mathematics with God, who is timeless, spaceless, and has always existed.

These laws are a part of God’s eternally existent nature.  They are built into God, in a matter of speaking.  So Christian theism not only provides an explanation for these laws, it also provides an explanation that makes sense of the absolute and transcendent nature of these laws.  They have always existed because God has always existed.

Philosophy, Top Ten Posts of 2011

What Is the Law of Non-Contradiction? – #3 Post of 2011

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Post Author: Bill Pratt

I am constantly amazed that there are people who try to deny the law of non-contradiction, which is the most basic principle of rational thought.  What is the law of non-contradiction?  There are at least three ways to state it:

  1. A thing cannot both be A and not-A at the same time and in the same sense.
  2. A thing cannot both exist and not exist at the same time and in the same sense.
  3. A statement cannot both be true and not true at the same time and in the same sense.

It is impossible to deny this law without invoking it in your denial, yet time and again I have heard people try do just that!

Why would I spend a blog post writing about this?  Because a person who thinks that this law is not true will become a thoroughly confused individual whose thought life is a complete mess, full of contradictions and inconsistencies.  I have met a few of these people, and they both sadden and scare me.

All of our beliefs, thoughts, and knowledge are built on top of the law of non-contradiction, so when a person tries to deny this foundation, they are bound to go way off track in their pursuit of understanding reality as it really is.

If you have any doubts about this fundamental law of rationality, try and deny it, but then write out your denial in a sentence – “The law of non-contradiction is false” – and ask whether your statement is both true and false at the same time and in the same sense.

If the law of non-contradiction is false, then your statement of denial must be both true and false.  But if your denial is false, then the law of non-contradiction is true!  By denying the law of non-contradiction, you have just affirmed it.  The more you try to deny the law, the more you will affirm it.

Trust me.  You cannot win.

Philosophy, Theology

Is God Subject to Logic?

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Post Author: Bill Pratt

Over the past couple years of blogging, one of the most common areas of confusion in the blog comments has been about the relationship between logic and God.  Did God create logic like he created humans?  Did logic exist before God, so that God is subject to logic?  Can’t God do away with the laws of logic?  Can’t he violate the laws of logic?

The first thing we need to do is define what logic is.  A simple definition of logic is “the study of right reason.”  The foundation of right reason is embodied in three laws of logic that are undeniable.

The law of non-contradiction states that a thing cannot be both A and non-A at the same time and in the same sense.

The law of excluded middle states that a thing is either A or non-A.

The law of identity states that if a thing is A, then it is A.

All logic, and thus all right reasoning, is built off of these three laws.  They are undeniable.

So now to the question.  Are these laws subject to God or is God subject to them?

The answer is that the laws of logic are part of the nature of God.  In other words, logic is built into God.  He did not create logic like he created humans, but neither did logic exist as some sort of entity outside of God.  Since God has always existed, and the laws of logic are based in God, then the laws of logic have always existed as well.

Can God violate the laws of logic?  No, because he cannot not be himself.  Whatever God is, he is eternally.  God does not shut down various attributes of his being, like cutting off lights in different parts of the house.  God is logical, he always has been logical, and he always will be logical.

Someone might object, “Doesn’t this mean God is limited by logic?”  This objection has always struck me as strange because logic is synonymous with rationality.  Is God limited to being rational?  Well yes, in the same way he is “limited” by his goodness, or his beauty, or his holiness.  God is never evil, ugly, or unholy; likewise, God is never illogical or irrational.

It is extremely important to note that humans could never know anything about God without the laws of logic.  Without the laws of logic, God could exist and not exist, God could not be God, God could be good and non-good (evil), and so forth on and on.  Logic is essential to our knowing God.  Christians who denigrate logic are, in effect, denigrating the foundational tools that we have to know anything about God.

Another objection that has been raised is that since God can do the impossible, then when we say he cannot be illogical, then we are saying he cannot do the impossible.  The misunderstanding comes from the word impossible.  Biblically, God may do what is impossible for human beings to do, but the Bible does not say that God can do what is logically impossible.

For example, objectors may argue, “God can raise people from the dead, but that’s impossible!”  Well, that’s impossible for humans, but it’s not logically impossible.  There is a big difference between the two.

In summary, logic is built into God as part of his nature, so God is not subject to logic as if logic is some force outside of him.  But he is “subject” to logic because he cannot deny himself.