How does one differentiate between premise and proposition?

Question

I find it difficult to differentiate between premises and propositions.

Given these statements:

"If men evolved from apes then there wouldn't be any ape nowadays."
"There are apes nowadays."

Are those two sentences created from two premises or two propositions?

I personally think there are two premises which construct those sentences:

P1: Men evolved from apes.
P2: There wouldn't be any ape nowadays.

Sentence 1: P1 => P2
Sentence 2: ¬P2
Conclusion: ¬P1

Even though this is valid in formal logic, I know it contains a fallacy in informal logic.

Answer 1

Ok, there seems to be some confusion here.

A premise is a step in an argument put forward toward establishing some conclusion.

A proposition is the meaning of a given sentence.

Since what you have given is a conditional sentence and not clearly an argument, I'd be inclined to say that what you have is a single proposition.

Now, depending on your view on propositions you might think that this conditional proposition has parts like the antecedent and the consequent. Likely these would also both be propositions.

EDIT:

So, to reflect your update, I'll update my answer. The argument that you give is, as you note, valid. It is an instance of modus tollens. The problem, however, is that it (plausibly) isn't a sound argument. The premise "If men evolved from apes then there wouldn't be any ape nowadays" seems very open to doubt. In fact, it seems to actually be false. Our best theory is that we evolved from apes. But there are, obviously, still apes.

I'm not sure what informal fallacy this argument contains, perhaps a hasty generalization or something? But the most damaging point is that I don't think the argument is sound since I think the conditional is false.

Answer 2

Before we can differentiate between ^‹ premise ^› and ^‹ proposition ^›, we first need to define what they are. There exists many existing definitions (cf.), but this post will use Aristotle's definition:

• A proposition is-equal any message that has a "truth value" —true xor false—. (We can say that a proposition is a claim.)

  Valid propositions:

  • "Socrates is a man." (This is either true xor false.)

  • "Socrates is a frog." (ditto)

  Invalid propositions:

  • "Give him some tips." (This is neither true nor false)

• An ^‹ argument  ^› is-belong a group of 3 or more propositions, of which, there is one conclusion —the deduced proposition— and at least 2 assumptions —the base propositions—. (Within a domain of discourse, if all of the explicit assumptions and implicit assumptions are true, then the conclusion must be true.)

• A premise is-equal a base proposition used in an ^‹ argument  ^›.

  Examples —assume we are in a domain of discourse where Socrates is a short but strong man, all men are mortal, no man is a frog, a frog is an amphibian, and all amphibians are mortal—:

  • "Socrates is a man." (true premise)

    "All men are mortal." (true premise)

    "Socrates is mortal." (true, valid conclusion)

  • "Socrates is a man." (true premise)

    "All men are mortal." (true premise)

    "Socrates is strong." (true, invalid conclusion)

  • "Socrates is a man." (true premise)

    "All men are tall." (false premise)

    "Socrates is tall." (false, valid conclusion)

  • "Socrates is a frog." (false premise)

    "All frogs are mortal." (true premise)

    "Socrates is mortal." (true, valid conclusion)

So, per Aristotle's definitions, the difference between "premise" and "proposition" is that the former is a strict subset of the latter —all premises are propositions, while not all propositions are premises—:

"premise" contains only members of "proposition" that are base propositions in the context of an argument.

Now, consider your 1st sentence:

If men evolved from apes then there wouldn't be any ape nowadays.

It must be either true or false, thus it's a proposition.

Consider your 2nd sentence:

There are apes nowadays.

It must be either true or false, thus it's also a proposition.

Therefore, we have a total of 2 explicit propositions in your quote:

"If men evolved from apes then there wouldn't be any ape nowadays" "There are apes nowadays"

With only 2 propositions, an argument cannot exist; without an argument, a premise cannot exist.

However, the reader may personally imply an argument from your quote:

1. All apes evolve at the same rate. (premise)

2. There are apes nowadays. (premise)

3. Therefore, men did not evolve from apes. (conclusion)

And he will be quick to point out that since the first premise is dubious, the conclusion will also be dubious despite being logically valid.

Answer 3

As Pacerier mentioned a premise is a special kind of proposition. The OP presents the following propositions:

"If men evolved from apes then there wouldn't be any ape nowadays."
"There are apes nowadays."

The OP symbolized the sentences and added an implied conclusion:

P1: Men evolved from apes.
P2: There wouldn't be any ape nowadays.

Sentence 1: P1 => P2
Sentence 2: ¬P2
Conclusion: ¬P1

As the OP noted this is a valid formal argument, but suspects there is an informal fallacy. The fallacy may be a form of circular reasoning. Here is how Wikipedia describes that:

Circular reasoning ... is a logical fallacy in which the reasoner begins with what they are trying to end with. The components of a circular argument are often logically valid because if the premises are true, the conclusion must be true. Circular reasoning is not a formal logical fallacy but a pragmatic defect in an argument whereby the premises are just as much in need of proof or evidence as the conclusion, and as a consequence the argument fails to persuade.

Although the conclusion is formally valid, evidence for the premises need to be provided. In an argument one side may attempt to make such an argument without the other sides agreeing with the premises. All sides need to commit to the premises being true to remove the problem with the circularity.

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Wikipedia contributors. (2019, June 14). Circular reasoning. In Wikipedia, The Free Encyclopedia. Retrieved 13:19, September 3, 2019, from https://en.wikipedia.org/w/index.php?title=Circular_reasoning&oldid=901826531

Answer 4

The proposition,

"If men evolved from apes then there wouldn't be any ape nowadays." "There are apes nowadays."

depends on the definition of "evolve." Species don't necessarily evolve forever. Erwin Schroedinger points that out in his "What is Life." So men (we) could have evolved from apes, and they would still be there if they stopped evolving.

Answer 5

The proposition "If men evolved from apes then there wouldn't be any ape nowadays" "There are apes nowadays" depends on the definition of "evolve." Species don't necessarily evolve forever. Erwin Schroedinger points this out in his "What is Life."

If apes stopped evolving, they could still be here, even though men evolved from apes.