Helena asked:

As a novice to all things Philosophical I'm struggling to write an essay on the question "How would
you distinguish logical and natural necessity?". Any help would be greatly appreciated, especially a
reading list.

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A wonderful question that is very complicated and to which I am not at all sure of the answer. But I'll
give you the standard answer anyway.

Logical necessity such as what you get in logic and mathematics (and, just maybe, in philosophy) is
that a true logically necessary proposition is a proposition whose negation is a self-contradiction. E.g.,
"All dogs are animals" is a necessary truth because "Some dogs are not animals" is
self-contradictory.

The standard answer to the question, what is natural necessity? is that propositions that express
natural necessities are general propositions that support counterfactuals,or 'contrary to fact'
conditional statements. (This is the answer given by the American philosopher, Nelson Goodman)

For example: the natural necessity "All metals expand when they are heated," implies the
counterfactual, "If this book were a piece of metal (which it is not), then, it would expand when
heated." Contrast this with, "All the coins in my pocket are pennies." This universal general statement
does NOT imply, "If this coin (which is a nickel) were in my pocket, then it would be a penny."

Kenneth Stern

As an introduction you could read A.C. Grayling's An Introduction to Philosophical Logicwhich will
guide you to further reading.

Basically, a proposition is logically necessary if it could not be otherwise, such as the truths of
mathematics and the principles of logic such as the law of non-contradiction, as well as Leibniz's
principle of the identity of indiscernibles. One way in which a logically necessary truth has been
defined is to say that it cannot be denied. However, Quine has argued against this "unrevisability"
thesis, claiming that any truth might be revised and there are no such things as necessary truths.

However, if you don't accept Quine's argument, and allow that a logical necessity is something we
cannot deny, a naturally necessary truth can be defined as a truth we might conceivably come to
deny. It is naturally necessary that all dogs have four legs, because the concept of a dog is of an
animal with four legs. But nature could change so that all dogs have six legs.

Alvin Plantinga rejects this on a different basis to Quine, claiming that there are non-necessary
propositions we take as true and won't give up despite evidence to the contrary, such as "Willard is
an exceedingly fine fellow".

Quine's argument can be found in "Two Dogmas of Empiricism" (in From a Logical Point of View) and
Plantinga's in The Nature of Necessity.

Rachel Browne

Some philosophers have argued, Hume most notoriously, that there are no logical relations between
'matters of fact', but only between what Hume calls 'relations of ideas', such as the definitions found in
Euclid, perhaps. A matter of fact might be that there is a tree in the wood and another might be that
there is a bird on a branch of the tree. To say there is no logical relation between these two facts, or
states of affairs, is to say that 'There is a tree in the wood but there is no bird on any of its branches'
is not self-contradictory. As we move towards relationships in the natural world that strike us as
somehow 'necessary,' for example, 'This water is heated to 100 degrees C, and this water is boiling',
it becomes tempting to say that 'This water is heated to 100 degrees C, but it isn't boiling,' is self
contradictory.

Nevertheless, while this might need explaining, it isn't, strictly speaking, a contradiction. If it were,
scientific laws would be true by definition and no possible experience would count against them. So,
Hume makes a very strong point here.

Here's another way of looking at necessity. Aristotle (in de Interpretatione,Book IX), asks us to
consider the proposition 'There will be a sea battle tomorrow.' Now, according to the Law of the
Excluded Middle, either there will be a sea battle tomorrow or there won't be. Call this proposition 'T.'
Clearly T is necessarily true, for the Law of the Excluded Middle expresses a logical truth.

Imagine then, that tomorrow comes, and there is a sea battle. Since it was necessarily true yesterday
that there would either be a sea battle or there wouldn't, it might seem that the sea battle occurred 'of
necessity,' and that yesterday it was 'necessary' that today there would be a sea battle. Apparently
logical necessity has necessitated some event in the world!

What has gone wrong is that what philosophers call necessity de dicto(applied to logical relations
between statements), has been confused with necessity de re(applied to things or events in the
world). So, you should notice that in proposition T ('Either there will be a sea battle tomorrow or there
won't'), the necessity attaches to the entire proposition: T is necessarily true.

However, this is not equivalent to 'Necessarily, there will be a sea battle, or necessarily, there won't
be a sea battle.' In the former case, the necessity attaches to the whole of T. In the latter it attaches
individually to the propositions conjoined by 'or'. And you can see, I believe, that 'Necessarily this or
necessarily that' isn't equivalent to, and can't be derived from 'Necessarily this or that.'

Something to think about: if the Second Law of Thermodynamics 'describes,' or is true of the world, it
must be possible to say, without contradiction, 'Heat can be transferred by means of some
self-sustaining process from a cooler body to a hotter one.' We may not see how it can be possible for
the world to behave that way; but to say that the Second Law can't be denied amounts to saying that
it is true by definition and thereby trivial. It is only propositions which express logical necessity, e.g.,
'Either it is raining or it isn't,' that cannot be denied without contradiction. And, although they are
necessarily true, they are uninformative.

Paul Trevor