Aug 05 2008

## Is the Universe Logical?

Yes.

But I suppose you want a somewhat longer answer. This question comes up frequently among thoughtful skeptics, and also among critics of science. The critics often use a challenge to logic as a way of promoting relativism and the claim that we cannot really know anything. If all pretense to knowledge is ultimately vain and self-deception, they argue, then science holds no special position with regards to truth about the natural world. Therefore any crank notion is just as good as the mainstream scientific consensus.

When this line of reasoning is applied to logic (rather than the empiricism of science) the argument generally takes the form of – how do we know that logic, as currently defined, is correct? Perhaps it is just the way our brains work. A related question is – can the rules of logic be different in a different universe? Did we learn the rules of logic by observing our universe?

Here is a recent question on this topic from the SGU forums:

There is one challenge to materialism, though, that’s been giving me some trouble lately, so I’d love it if Dr. Novella could address it. This is sometimes called the Argument from Reason, and the basic claim is that materialism can’t make sense of reason and logic. If rational thought is nothing more than specific brain events, in what sense can those brain events be true, valid or sound, and other ones (e.g., brain events associated with logical fallacies) false, invalid or unsound? What is there to distinguish the brain thinking of modus ponens from the brain thinking of the fallacy of affirming the consequent? Thus, it would seem that the very logic and reason that is used to argue for materialism (as well as other conclusions) is undermined by materialism. If materialism is true, then it can’t be true (or false, for that matter).

The answer to these questions comes from understaning what logic is – it is simply an internal system, exactly like mathematics. Logic and math do not directly describe the outside world – therefore they are independent of the natural universe. They are systems of thought that require only internal consistency.

However, they also proceed from fundamental principles or assumptions that are so fundamental it would be absurd not to accept that they are true. At the very least they state their assumptions – in essence saying that if we assume these principles to be true, then various conclusions must follow.

For example, 1+1=2. This is true by definition – but the system of math indicates that it must always be true. It is fundamentally true. If you have one apple and I give you one apple, you have two apples.

Logic does the same thing – starting with the simplest statements that seem as if they must be true, and then carefully proceeding from there. For example, two true statements cannot contradict each other – they cannot be mutually exclusive. In other words, two true statements must be able to both be true at the same time. We can then build on such principles to more complex and subtle logic, but logic that is just as valid. Just as we can eventually get to calculus, building upon more basic mathematical principles – we can also derive fairly complex logical rules from simpler ones.

Valid logic cannot – by definition – be invalid. If the system is internally consistent and satisfies all fundamental rules, then it works.

Because such systems require only internal validity, I do not think that there can be a universe in which they are not valid. Therefore, 1+1=2 everywhere, even in a universe with different physical laws (if that is even possible).

But logic an math also do describe the real world. This does not mean, however, that they are dependent upon the physical world. Rather, they can be used to describe the real world because they are tools that can be used by empirical investigation – science. Science can use math and logic to construct its models of how the universe works. Scientific statements must be logically valid and mathematically correct, so math and logic help scientists arrive at conclusions about nature that are valid.

A scientific conclusion, however, requires more than math and logic – it also requires empirical data about the physical world. Therefore scientific conclusions, while they can be completely valid, may not be true if the empirical data is flawed. All scientific conclusions are also tentative, because all data is tentative.

To directly address the question above about materialism – the premise of the argument is that materialism is dependent upon logic, which is in turn dependent upon our material brains, and therefore materialism cannot confirm itself. But the second premise is not true – logic is not dependent upon our brains, it is what it is, an internally consistent system. Materialism is dependent upon logic only to the extent that, as an argument, it must be logically sound. But materialism is also an empirical claim about this universe, and it is therefore based to some extent also on observation. As an approach to understanding nature, materialism has worked well and continues to be very fruitful. It also does not violate logic, which is a minimum requirement for any conclusion.

For any claim to truth about physical reality we can therefore make two types of analysis. The first is about the logic of the claim. If it involved invalid logic, then the claim is not sound. This does not mean the conclusions are false, but it does mean we have no reason to accept it. A claim can therefore be rejected entirely on the basis of invalid logic.

The second type of analysis is the empirical support – the evidence. Does the evidence support or refute a particular claim. While logic can be black or white – it is either valid or not valid, evidence is never 100% for or against a claim, because data is never perfect. Regarding evidence we can only make tentative conclusions about the probability of being true or false. This probability can get very close to 100%, but never really achieve it.

In the end I think the question – is the Universe logical? – is not even a valid question. Logic is independent of the universe.