Renwhqb

Perhaps the main difference between what might be called a premise and an assumption by different authors is their use in a proof with inference rules. Here is an example of this difference in a natural deduction proof using a Fitch-style of presentation.

Note that the first two lines above the horizontal line could be called either premises or original assumptions. One can use these sentences without deriving them to help derive the goal.

Note that on line 3 an assumption has been made, Q. That would be an additional assumption. It opens a subproof. It also has a horizontal line below it. When that subproof is closed through an inference rule this additional assumption can no longer be used. It is discharged.

Regardless of this use, one should consult the definitions of these terms in whatever logic textbook one is using. Here is how the forallx textbook describes such a subproof. Instead of P and Q, they use A and B: (page 107)

The general pattern at work here is the following. We first make an additional assumption, A; and from that additional assumption, we prove B.

For these authors, premise and assumption appear to be nearly synonymous: (page 98)

A formal proof is a sequence of sentences, some of which are marked as being initial assumptions (or premises).

Furthermore, (page 99)

Note also that we have drawn a line underneath the premise. Everything written above the line is an assumption. Everything written below the line will either be something which follows from the assumptions, or it will be some new assumption.

In this text premises and assumptions are similar. They are sentences one does not have to derive. To distinguish them is to distinguish their use in a proof. Some assumptions are called "initial assumptions" or "premises" which are the first lines in a Fitch-style proof above the horizontal line. Others are called "additional assumptions" which start subproofs.

Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/

P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Fall 2019. http://forallx.openlogicproject.org/forallxyyc.pdf

First of all, a premise is a statement. As such, a premise is therefore explicit.

A premise is a statement which is assumed true for the purpose of an argument, where the conclusion will be considered as following from the given premise. As such a premise may be actually true or actually false. In many cases, it doesn't matter for the purpose of the argument whether the premise is true or false. We just need to be able to assume that it is true because we may be only interested in whether the argument is valid.

An assumption is usually understood as something else altogether. To confuse the matter somewhat, the noun "assumption" has the same origin as the verb "to assume" (13th, from Latin assūmptiō, the act of taking up, from Latin assūmere, which is ... to assume).

So, making assumption and assuming a premise may seem to mean the same thing. However, you assume a premise for the purpose of an argument and the premise is explicit.

And assumption is usually understood as a proposition taken for granted or accepted as true without proof.

It is routine for philosophers to talk about looking for hidden assumptions. Suppose your conclusion happens to be falsified one way or the other. Then the advice is to look for a hidden assumption that may need to be reconsidered.

The difference is rather slim, though.

We tend to talk of premises in the case of arguments considered in the context of discussing logical validity, somewhat like Aristotle discussed the validity of his example syllogisms.

In this context, premises are usually all explicit statements but in the case of enthymemes, one premise is usually left implicit. However, in this case, the implicit premise is normally absolutely obvious.

Suppose for example that some guys in a bar are talking about Barack Obama. After ten minutes, one of the guy says, "Yeah, well, politicians, they're all liars anyway", or something more colourful. Everyone listening to that will understand the libellous implication even though it isn't spelled out, and even though one premise, that Obama is indeed a politician, has been left out.

Nobody would talk of an assumption in such a case. Everybody present knows Obama is a politician. It's not an assumption, it's a fact. But it is nonetheless a premise and the premise is left out in such cases because we all understand what is meant without the need to spell it out. To spell it out would be somewhat counterproductive, like wasting everybody's time asserting trivia and thereby compromising the punch of the conclusion. Essentially, you let people draw the conclusion by themselves, which is an effective way of implicating them into your argument and into accepting the conclusion.

We tend to talk of assumptions in the context of real-life arguments, and often to suggest there is a hidden assumption that is simply false. The arguments we make in real life are never formally valid since that would be impractical. We have to make many hidden assumptions, sometimes consciously, sometimes unconsciously.

An assumption may be consciously hidden to avoid drawing everybody's attention on it if you think most people won't accept it. And we also all make arguments for ourselves when we reason and we usually can't possibly identify all our assumptions, hence the need sometimes to look for the one which may be false.

This also explains why philosophical arguments and debates are necessary, to draw out the assumptions that would remain otherwise hidden.

All philosophical views are based on any number of assumptions and usually it is impossibly to make them explicit. Which is why Leibniz worked on a calculus ratiocinator, a theoretical and universal method of logical calculation to solve the problem of endless and inconclusive philosophical debates.

Well, we are still having endless debates.