Leon asked:

"Induction is rational if nature is regular." Is that a fair statement?

============

In short, the answer to your question has to be no. Whilst a very useful way of allowing humans to
function in the world, inductive reasoning is flawed as a means of determining any logically valid
conclusions and making predictions.

Inductive reasoning is the type of reasoning that makes predictions and generalisations on the basis
of experience. An example of this type of reasoning could be as follows:

It has snowed every day for the past five years. (Premise from experience)

Therefore, it will snow tomorrow. (Conclusion — prediction/generalisation).

This type of reasoning is flawed because the conclusion does not necessarily have to follow from the
premise. There is no logically compelling reason why it must snow tomorrow. This point can be made
clearer if inductive reasoning is compared with another form of reasoning called deductive reasoning.

In a deductive argument, the conclusion must necessarily follow from the premises. Take this, for
example:

All cats are black. (Premise)

"Sooty" is a cat. (Premise)

Therefore "Sooty" is black. (Conclusion)

If the premises are true (i.e. all cats are black, and "Sooty" is a cat), then the conclusion must also be
true. The conclusion necessarily follows from the premises. Of course one can question the premises
— some cats may indeed be white — but the argument itself is still valid.

The conclusions reached by inductive reasoning lack the logical certainty that those reached by
deductive reasoning possess.

Arguing for the validity of conclusions reached by inductive reasoning, one might be tempted to
respond that inductive reasoning has always worked in the past and that the conclusions reached
have always, without exception, proved to be correct. But this too would be logically invalid. It would
be to use a process of inductive reasoning to justify the process of inductive reasoning! The fact that
the conclusions reached through inductive reasoning have always turned out to be truthful
(experience) tells us nothing about the conclusions to be reached by inductive reasoning in the future,
or the status of inductive reasoning in general (prediction/generalisation).

If nature is regular, as your question states, then it might, at first glance, seem that induction is indeed
a logically valid form of reasoning. Predictions can safely be made on the basis of past experience
because we are certain that nature obeys certain laws that compel it to act in predetermined ways.

This way of thinking would, however, be mistaken. The structure of any inductive argument ensures
that the conclusion does not necessarily follow from the premises. Issues concerning nature's
regularity have no relevance here. Any past experience, no matter how many times it has been
experienced, tells us nothing about what must necessarily happen in the future.

Of course, one might be tempted to argue:

At sea level, water boils at 100 degrees Celsius. (Premise arising from nature's regularity)

I am at sea level. (Premise)

I am heating water. (Premise)

Therefore, this water that I am heating will boil at 100 degrees Celsius. (Conclusion)

This would be a perfectly valid conclusion to make. The argument would, however, be a deductive
argument!

There is always a problem in determining the validity of any premise in a deductive argument. In this
case, how could we ever know that nature is regular? We might say that in the past nature has
always behaved in a regular way. To decide on the basis of this experience that nature is regular
would, unfortunately, be to use inductive reasoning!

Simon Drew