This sentence is false.

The text I used in college--a commonly used text--was Irving I. Copi's Symbolic Logic.

Modus ponens (the shortened, almost universally used label for "modus podendo ponens"--"the method of affirming by affirming")--is just this:

Suppose you give labels to sentences that can be either true or false. (I'm going to keep this simple and not introduce the notion of a proposition.) You label them p, q, r, etc. It doesn't matter what they say; they just have to be capable of being true or false (although some--tautologies--can only be true, and some--contradictions--can only be false). Then modus ponens is an argument form--if sentences get filled in appropriately, it doesn't matter which ones get filled in, the argument will be valid, so that if the premisses are jointly true, then the conclusion has to be, too. Modus ponens has the premisses "If p, then q" and "p" and has the conclusion "q." "If that big feline is striped, it's a tiger; that big feline is striped; therefore, it's a tiger." "If your baseball cap has a smiling bird on it, then it's an Orioles cap; your baseball cap has a smiling bird on it; therefore, it's an Orioles cap." It's just

If p, then q; p; therefore, q.

Modus tollens (short for "modus podendo tollens," "the method of affirming by denying") has the form

If p, then q; not-q; therefore, not-p.

"If that big feline has stripes, then it's a tiger; it's not a tiger; therefore, it doesn't have stripes."

I'll note that there are two similar-appearing argument forms that are fallacies. One is the fallacy of affirming the consequent--"If p, then q; q; therefore p" ("If that horse is going to win the Kentucky Derby, then he's fast; he's fast; therefore, he's going to win the Kentucky Derby" [fallacy: maybe he's fast but will finish second]); the other is the fallacy of denying the antecedent--"If p, then q; not-p; therefore not-q" ("If that horse is going to win the Kentucky Derby, then he's fast; that horse is not going to win the Kentucky Derby; therefore, he's not fast [fallacy: maybe he's fast but is going to lose to Secretariat]).

Modus ponens ("If p, then q; p; therefore, q") and modus tollens ("If p, then q; not-q; therefore, not-p") are basic argument forms. I can list others. A couple more would be Disjunctive Syllogism ("Either p or q; not-p; therefore, q") and Hypothetical Syllogism ("If p, then q; if q, then r; therefore, if p, then r").

You can find a list of common argument forms--and, side by side, a list of common fallacies--here: http://www.siue.edu/~wlarkin/teaching/PHIL213/forms.html (What it calls "Dilemma," I'm used to seeing as "Constructive Dilemma," but that's not important. I will note that Contraposition is an important one to know, and it's important to know that taking the converse [what this site calls "Conversion"] is a fallacy.) You can also find them elsewhere--just do a Google search for "argument forms."

Thank you MindWalk!

Sentence 2 is true.

Sentence 3 is false.

Sentence 2 is false.

Which ones are true?

Looking at it from a purely logical standpoint, it could be either sentence 1 and 2 together or only sentence 3. I think I will go with the semantics of the grammar you used and assume that "ones" plural, without parentheses around the "s", means that multiple sentences must be true.

Therefore, I am guessing 1 and 2.

You are correct! That one was easy.

Stop making it so complicated, it is true and false. If true, then false, if false, then true. What will happen if Pinnochio says my nose will grow? If he is telling the truth, his nose will not grow, thereby making his statement false, causing his nose to grow, but then he is telling the truth so his nose should not grow. Both true and false.

Nothing can be simultaneously true and false.

False.

No proposition can be both true and false.

However, some sentences can be construed one way and be true in that way but, alternatively, can be construed a second way and be false in that way.

False.

Give me an example.

What=Dont get it

Maybe something like the following:

"I am tall."

"I am not short."

Although both sentences can be true at the same time, it is possible that the first can be false, but the second true as well.

Or I have no idea what I'm talking about.

"I am tall" and "I am not short" are both vague--how tall is tall? how short is short? Also, tallness may be defined as being taller than, say, six feet tall, or it may be defined as being taller than *or exactly* six feet tall. If to be tall is to be taller than six feet tall, and if to be short is to be shorter than six feet tall, then someone who is exactly six feet tall is neither tall nor short.

None of this, though, seems to have any bearing on the simultaneous truth and falsity of a statement. Which of those sentences are you saying can be simultaneously true and false? Given a precise definition of tallness, either you are tall or you're not; given a precise definition of shortness, either you are short or you're not.

Of course, one might construe "I am tall" as meaning "I am tall compared to a dwarf" (which might be true) but might construe it instead as meaning "I am tall compared to Wilt Chamberlain" (which is probably false).

It is absolutely crucial to understand that an uninterpreted sentence is neither true nor false--in fact, an uninterpreted sentence is meaningless. Words and sentences do not have intrinsic meanings. It is only when a sentence is assigned an interpretation that it can be said to be true or false, for it is not sentences by themselves but sentences under specified interpretations that are true or false.

Thus, "Jupiter is the largest planet in the Solar system" is true if interpreted as "The planet Jupiter is the largest planet in the Solar system," but it is false if interpreted as "The Roman god Jupiter is the largest planet in the Solar system." Same sentence; different interpretations. You have to specify an interpretation and only then decide on the truth-value of a sentence. But once you have settled upon an interpretation--a definite interpretation--one that says that some state of affairs obtains--you can decide the sentence's truth-value. And it can't be both true and false under the same specified interpretation.

Like I said, I probably had no idea what I was talking about. But I always like to learn.

I'm still waiting for Akatsuki64 to give what he thinks is a counterexample.

I'd imagine his counterexample would involve the same sentence being both... in different contexts, which you already allow for.

I could be 6 feet tall and 5f8in tall depending upon our relative speeds and relativistic frames of reference I suppose. But in the same context and same definitions of feet and so on then I cannot be both.

That blows. I just had a long and complicated explanation which exploited all my intellect. I suppose it must have been nonsense which explains the accidental deletion. 

That's a shame. I suggest copying your whole post before posting (the way you copy it for copying and pasting--highlighting it and hitting Ctrl-C). That way, if your post vanishes, you'll get another chance to post it.

As to Timotheous's example: it is instructive. We do have to interpret a sentence carefully enough as to specify the obtaining of a single state of affairs before assigning it a truth-value. "George fought in the Revolutionary War": true if the George in question is George Washington, but false if the George in question is George W. Bush. "The Green Bay Packers are the Super Bowl champions." True if construed as referring to the middle of 1967, but false if construed as referring to the middle of 1987.

Well, I see it as similar to shrodinger's cat, in that you can not say the cat is dead or alive. You cannot say the cat is dead or alive, but you 'can' say the cat is dead and alive. This reminds me of the Pinnochio paradox, in which Pinnochio says my nose will grow. I thought I had a hold of the paradox, but then I thought about it, and: Even if his nose grows, he does not have to tell a lie for his nose to grow, does he? Or are we making the assumption that the only way in which Pinnochio's nose could grow was if he was telling a lie?  But that can't be true, because by the paradox his nose grew when he was telling the truth. In simple, just because Pinnochio's nose grows, it does not have to imply he has told a lie. And what does this sentence is false mean? What are we saying is false? You could say this sentence is false: the boy is cold; but what do you mean when you say 'this sentence is false' is false? What does that actually mean? What is actually false? What are you assigning the word false to? By saying this setence is false is false, what is false? Think about it for a second. The sentence 'this setence is false' has no content, how can something with no content be false? In other words without even translating this setence is false into this setence is true, into this setence is false, etc, without even going through the paradox, you already have encountered a problem by trying to assign the value false to 'this setence is false.' What is 'this sentence,' there is no sentence, which is evident when you try to assign a false value to 'this sentence is false.' Interesting, by thinking deeply you're actually not thinking at all.......