34 votes

Can an argument be valid even though one of its premises is false?

First: we don't really say that arguments are true or false. Statements are true or false, but arguments have different kinds of properties. One of those properties is, as you are obviously aware of, ...
Bram28's user avatar
  • 2,709
21 votes

Can an argument be valid even though one of its premises is false?

Yes : Premise : All dogs are mortal (true) Premise : All birds are dogs (false) Conclusion : All birds are mortal (true) The argument is valid because there is a correct relation between premises ...
Geoffrey Thomas's user avatar
  • 35.6k
17 votes

Can an argument be valid even though one of its premises is false?

(Promoting this from @MauroALLEGRANZA's comment, since it deserves a full answer.) Yes, an argument can be valid but still not be sound. This is really just a matter of understanding the terminology: ...
BradC's user avatar
  • 439
14 votes
Accepted

Is "(1) All humans are mortal. (2) Socrates is mortal. Conclusion: Socrates is human." unsound argument?

Hence, I think this one is a sound sentence. Soundness is not a property that applies to sentences, but rather to arguments as whole. A sound argument is one that is valid and has all true premises. ...
transitionsynthesis's user avatar
13 votes

Is this argument about abortion being both right and wrong valid or invalid?

The argument is valid. It's easier to see if translated to symbols: 1. R v W premise 2. R → F premise 3. ~F premise 4. ~R entailed by 2-3 5. W → ~D premise 6. D ...
E...'s user avatar
  • 6,466
10 votes
Accepted

Is there a definition of logical validity that does not rely on possible worlds?

The short answer is, yes, there are lots. There are at least a dozen different accounts of validity, or logical consequence, and there is no need to refer to possible worlds. It is worth noting though,...
Bumble's user avatar
  • 24.2k
9 votes

Is the following statement true, false, or can't be determined? Why?

A statement of the form "If X then Y" where Y is true, is always true in classical logic. If the consequent of a conditional is true, then it matters neither what the antecedent is, nor whether there'...
Chris Sunami's user avatar
  • 29.4k
8 votes
Accepted

Is the logic of this argument valid?

This argument could hardly be rendered into a valid form without all kinds of additional assumptions and clarifications. For example, Assumes we know what God wants and what he/she might or might ...
Bumble's user avatar
  • 24.2k
8 votes

Analogy between an unknown in an argument, and a contradiction in the principle of explosion

It is common for beginning students of logic to read philosophical importance into the principle of explosion, but this is a mistake. The principle of explosion is merely a mathematical outcome of the ...
transitionsynthesis's user avatar
7 votes

valid or invalid: “S or R. Not S and Not R. Ergo, B.”

This argument is valid on most definitions of validity. The common definition of validity in use today is: if the premises are true, then the conclusion must be true. worded another way, there must ...
virmaior's user avatar
  • 24.7k
7 votes

Can an argument be valid even when its premise refutes the conclusion? (Trying to disprove my professor)

Yes, argument B is valid. However, if you write argument B in any context, including in a philosophy, logic, or math exam, you're opening yourself to very simple criticism: while argument B is valid, ...
Stef's user avatar
  • 919
6 votes

Why is Tarski's notion of logical validity preferred to deductive one?

This is an interesting and important question and merits a long answer. I shall be as concise as I can consistently with being helpful. The question asks whether we should understand validity in terms ...
Bumble's user avatar
  • 24.2k
6 votes
Accepted

What fallacy dismisses a conclusion because supporters give invalid arguments for it?

The question is vague, so it can be several different things. Generally, dismissing an argument based on who is supporting it is called ad hominem, "attack on an argument made by attacking the ...
Conifold's user avatar
  • 42.8k
6 votes

If the premises of an argument CANNOT all be true, then said argument is valid

The rules of logic lead to many counterintuitive results, and this is one of the most fundamental such results: VALID expresses a structural condition, such that it can never happen that all the ...
Chris Sunami's user avatar
  • 29.4k
6 votes

Where is the fallacy in Seth Yalcin's counterexample to the modus tollens?

The use of modus tollens is valid only when used with propositions containing valid logical predicates. And here it is not. A logical predicate is commonly understood as a boolean function P: X → {...
Jencel's user avatar
  • 380
5 votes

Is the logic of this argument valid?

The argument is not logically valid. You need a sixth step, along the line of A method of knowing God without interpretation exists. As to the point about the circularity; It's incorrect to reduce ...
Taemyr's user avatar
  • 181
5 votes
Accepted

Is it valid to prove the axioms of a system from themselves? How does it square with Gödel's incompleteness?

Yes, the axioms do trivially prove themselves. Your last derivation, however, is not valid: "A=A" can not be substituted for A because the latter is a symbol in a formal system, while the ...
Conifold's user avatar
  • 42.8k
5 votes

Can an argument be valid even when its premise refutes the conclusion? (Trying to disprove my professor)

There is a difference between soundness and validity of an argument. An argument is valid if the conclusion can be (formally) derived from the premises. For the argument to be sound, there is the ...
wra's user avatar
  • 171
4 votes

Can you make a valid inference invalid by adding extra premises?

No. In propositional logic, an argument is valid IFF (1) it is inconsistent to assert all the premises and the negation of the conclusion (semantic validity), or (2) the rules of inference allow you ...
FoolishBananas's user avatar
4 votes
Accepted

Are "All A is B" and "If A then B" always logically equivalent?

We are talking about expressing statements in two different systems. The first one is the classical syllogistic of Aristotle ("All dogs are mammals"), with categorical syllogisms, whereas the latter ("...
Conifold's user avatar
  • 42.8k
4 votes
Accepted

Can p and q in modus tollens be stated negatively?

Logical formulae are blind to the content of the assertions that fill them in, and evaluations of logical validity are accordingly content-blind. One can substitute for "P" and "Q" any given sentence, ...
Daniel Coimbra's user avatar
4 votes

Are all fallacious arguments invalid?

Bradley Dowden writes in his article "Fallacies" (Internet Encyclopedia of Philosophy): Researchers disagree about how to define the very term "fallacy." Focusing just on fallacies in sense (a) ...
Frank Hubeny's user avatar
  • 19.3k
4 votes

valid or invalid: “S or R. Not S and Not R. Ergo, B.”

Your argument in propositional logic: S v R ~S & ~R ∴ B An invalid argument, is an argument whose conclusion can be false even if the premises are true. We normally try to invalidate an argument,...
SmootQ's user avatar
  • 2,399
4 votes
Accepted

Why is there an O type conclusion in modus celaront

Celaront was not in the original Aristotle's list of valid syllogistic figures (or : moods). It was added later (during the Middles Ages ?) as one of the two subalternate moods in the first figure (...
Mauro ALLEGRANZA's user avatar
4 votes

Logic exercise (evaluation of whether an argument is valid)

Well, break it down a bit. You know that everyone who is wise is a logician. You know that only the wise love Aristotle. Therefore everyone who loves Aristotle is a logician. There exists at least one ...
philosodad's user avatar
  • 3,296
3 votes
Accepted

Soundness of a deductive argument

The answer to this question depends in part of the symbolization resources you have available to you. If we translate as follows: Anything that travels in time necessarily changes the past to T -...
virmaior's user avatar
  • 24.7k
3 votes

What fallacy dismisses a conclusion because supporters give invalid arguments for it?

Bad Reasons, or perhaps Fallacy Fallacy.
Codeswitcher's user avatar
3 votes

Is the logic of this argument valid?

You need a sixth point as said by Taemyr, that "A method of knowing God without interpretation exists". Without this point, it doesn't make sense to abandon the facts. Because if there is no such ...
Pimgd's user avatar
  • 137
3 votes

How to infer ¬Q when there seems to be no way to

The way you have chosen to express the rules implies you are assuming a non-monotonic form of reasoning. Rule #1 as stated has no exceptions, while rule #2 expresses an exception to rule #1. In a ...
Bumble's user avatar
  • 24.2k

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