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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 fallacy in informal logic)

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2 Answers 2

up vote 4 down vote accepted

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.


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.

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would you mind to check the edited part? thank you very much dennis :) –  Coderama Feb 16 '13 at 8:47
yes, I've been trying to find which is the most suitable category of informal fallacies to put that conditional statement. I was considering it falls either under suppressed evidence (under the fallacy of presumption), argumentum ad ignorantiam, or from argument from uncertainty? –  Coderama Feb 16 '13 at 9:14
So to sum my original question, I'm allowed to treat the antecedent and the consequent from the conditional sentence as two premises. Is it right? –  Coderama Feb 16 '13 at 9:16
ah, I've just read the part of soundness and validity of an argument. a valid argument doesn't necessarily mean sound argument. Indeed just like what you've written @dennis :) thank you :D –  Coderama Feb 16 '13 at 9:19

Part 1

Before we can differentiate between "premise" and "proposition", we first need to define what they are.


  • When you say "proposition", I would assume you mean "proposition" as defined in A-logic; "proposition" then, refers to any message that must be either true or false.


    • "Socrates is a man." (must be either true or false, therefore a "proposition")

    • "Socrates is a frog." (ditto, therefore a "proposition")

    • "Give me some tips." (neither true nor false, therefore not a "proposition")

    Trivia: Do note that A-logic is not the only domain which uses the word "proposition". "proposition" by itself is ambiguous. In fact, some people claim that its a misleading concept that should be removed entirely from philosophy and semantics; cf. Wikipedia - Proposition.


  • "premise" as defined in A-logic, is a base "proposition" used in an "argument". An "argument" is composed of at least three "proposition"s: two base "proposition"s and one inferred "proposition".

    Examples (assume we are in a world 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 the difference between a "proposition" and a "premise" is that a "proposition" can exist without an associating "argument", but a "premise" cannot. More succinctly, we can say "no argument, no premise", but "no argument, yes/no proposition".

Part 2

Consider your first sentence:

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

It must be either true or false, thus (as explained in part 1) it's a "proposition".

Consider your second sentence:

There are apes nowadays.

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

As explained in part 1, there is no "argument" here because we only have two "proposition"s; since there is no "argument", there is therefore no "premise"s as well.

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