How about a more simple example.
“If it is raining, then there are clouds in the sky.”
Suppose there are no clouds in the sky. Is the statement false?
No. Not unless it is raining.
Well I’m glad to se that we both agree on that.
What was your point exactly?
It certainly can be. In this case it isn’t. Houses weigh considerably more than an ounce you realise? No one ever claimed that those statements couldn’t be true. That is your own strawman construction.
The point is that a compound proposition can also be false when the consequent is or could be false and I gave an example of such. I also demonstrated how one could make observations that show it to be false. And hence falsifiable.
They couldn’t.
What excatly is your point?
Now will you be providing those references I asked for, or can I ignore you from here on in?
That is also not by any stetch a tautology. I can easily envisage a world in which it rains without any clouds in the sky, it happens in this plaent occassionally.
The statement may be true but it’s also not an example of what we are talking aboyt.
So what excatly is your point.
Dude I really am having ahard time seeing what point you are trying to make here. Can you state it clearly?
And can you please provide the reference I asked for.
And can you please adress the apparent non sequitur you posted earlier.
You sem to be making lots of posts but just any demonstration that they are baseless or flawed.
Look here. Scroll down; the relevant part is under “implication.”
If you have a conditional statement (If p, then q–and let’s leave negations out of it for the time being for clarity’s sake), then there are four possible ways it could go [this is the same as the table from the website with the 1’s and 0’s, but a bit more clear]:
P is false, Q is false = whole statement is true (that is, its “truth value” is true, NOT that it is factually true).
P is true, Q is true = whole statement is true.
P is false, Q is true = whole statement is true.
P is true, Q is false = whole statement is false.
An easy way to remember this is that all conditionals are true, except those that lead one from truth (in the antecedent) to falsehood (in the consequent).
Take careful note of this part from the website; I think this is what is causing all the confusion:
That is, it doesn’t matter what bricks/houses weigh in real life. The actual, factual trueness of this statement in the real world is not important. What matters is, if you reduce these statements to how they are logically related to each other (If p, then q), what is their truth value?
If you have the statement, “If a brick weighs 1/1000th of an ounce and a house is made up of a thousand bricks, then a house weighs an ounce,” then you must assert that the truth value of your antecedent is true, but that your consequent is false, for the truth value of the entire statement to be false. In other words, “It is true that a brick weighs 1/1000th of an ounce (NOT necessarily factually true). It is true that a house is made up of a thousand bricks. It is false that a house weighs an ounce” for you to be able to declare that the truth value of this statement is false.
You can’t say it’s false simply because you have declared that a brick is not 1/1000th of an ounce. Regardless of the truth-value of your other conjunct, stating “a brick is not 1/1000th of an ounce” would make your whole antecedent false, and a conditional with a false antecedent can’t have a truth value of false for the statement as a whole.
Cite:
http://www.ee.surrey.ac.uk/Teaching/Courses/MathComp/logic/thes.html
No you haven’t.
“If an object is red, then it is red” is a tautology.
Notice the distinction between a tautology and a falsifiable true statement.
With a falsifiable true statement, we will not observe the observation which would make the statement false.
With the tautology, there is no observation which would make the statement false. There is no observation that has anything whatsoever to do with the truth value of the statement. There is no observation we know we won’t see; any and all observations are equally irrelevant. So why in the world would you think it was falsifiable?
Incidentally, do you think the statement “A implies A” is falsifiable?
Bzzzzt. Worng.
For this discussion what bricks/houses weigh in real life is the only thing that does matter. We are discussing whether there are any potential real life observations that will contradict statement. And that is all we are discussing.
To say that what bricks weighs in real life is unimportant to establishing whether there are any potential real life observations that falsify a statement regarding the weight of bricks is oxymoronic.
Of course what bricks weigh in real life is impornat. It’s the only thing that is important. If we are going to say that what real life observations don’t factor into falsifiability then obviously nothing is faslifiable.
Well that’s a webpage. And nowhere on that webpage does it say that “Tautologies are not falsifiable.”
You apparently don’t understand that a citation is supposed to actually agree with what you say. It needs to do more than simply mention the same subject.
Correct. That’s about the umpteenth example of a tautology so far in this thread. I don’t think that anyone here is having any problems with what tautology is
Notice from where? What am I supposed to be taking notice of?
Everyone had resolved well before you jumped in that there is no actual observation which would make a tautological statement false.
However that does not allow you to conclude that there is no potential observation which would make the statement false. Which is what you appear to be trying to do here. That is a total non sequitur. You’ve arrived at the conclusion from nowhere.
I have already told you that this point has been well resolved. Repeating it yet again won’t make us any more in agreement on this point you know?
Do you want me to post it in big bold letters so you don’t feel a need to put it in every second post and I don’t need to agree with it in every second post? I can if it will help?
I have also posted the response to this question before. Could you please go back and re-read the thread rather than getting me to repeat myself? If you don’t understand the original answer then ask for clarification, but getting me to repeat it is futile.
For the last time: Because there exists a potential observation that would contradict the statement. It’s that simple. Such an observation will never be made if this is a true oxymoron. But such an observation will never be made for any true statement. That does not mean no true statement is scientifically valid. It just means that the falsifying observation can’t be made because the statement is true.
Nonetheless the possibility exists for observations to be made which contradicts some tautologies. And that is why they can be falsified. That’s what falsify means.
Since A is totally undefined WRT objective reality of course not. Of course it can’t be falsified by objective data. That is inescapable.
Do you think that “zigrib never exists without tiglib” is falsifiable without ever defining either of those terms WRT reality? Does that mean that no statements of that nature are ever falsifiable?
This statement is inconsistent with knowledge of what a tautology is.
Try to understand that tautologies have nothing to do with obervation, potential or otherwise. They are part of logic itself, nothing more.
A implies A.
“The ball is red” implies “The ball is red.”
These are equivalent. The truth value is based solely on logical form. Observation never comes into play.
If by that you mean the possibility exists to assign truth values to statements that make the tautology false, this is wrong and goes against the definition of tautology.
Objective reality is not the issue. A is any statement, objective or not. In any case “A implies A” cannot be falsified. Objective reality is only important to assign truth values to statements. All you need to prove a tautology is a truth table. Do the table.
Of course, this is a different statement (B => A or ~A => ~B). “zigrib implies zigrib” is a tautology if “zigrib” is a statement (something to which a truth value may be assigned).
You are misconstruing my words, I fear. What I meant was this:
A wise man once told me that the purpose of logic is to separate the good arguments from the bad. For example, is “If p, then q. P exists, therefore q exists” a valid argument (regardless of whether we’re talking about mountains or about little green spacemen)?
Regardless of the actual weight of bricks/houses, it is an invalid statement if one says, “If p, then q. P is false, and therefore, the truth value of the conditional is false.” That doesn’t work whether we’re talking about real-life examples or about Queen Victoria and New York.
You have used two different terms in your example, which is not the issue. Without ever having to examine what “zigrib” is, it is perfectly possible to state without fear of contradiction that
zigrib if zigrib
is a true statement. We can of course make no inferences about the relationship between zigrib and tiglib, since we have no idea what they are. Yet we can be entirely certain that if one of them is true, it is also true.
This question is entirely reasonably dealt with in the abstract. For
A if A
to be invalid, A has to be both simultaneously true and false. It doesn’t matter what A is; this is a logical impossibility. There is no potential set of observations in which something can be simultaneously true and false. A does not need to be “defined WRT objective reality”. It is a variable, and there is no possible substitution you can make for its value that makes the statement
A if A
untrue, because if you change one instance of A, you change the other. You seem to want to substitute one thing for the first A, and one thing for the second. That’s not how substitution works, and if you do so, then you are in fact constructing a completely different sentence of the form
A if B
which is, of course, not a tautology, and is thus falsifiable.
Yes it does, it says it right here:
tautology a compound proposition that is true irrespective of the truth values of the atomic propositions that it consists of.
This is saying that in every possible set of truth values you might assign to any possible set of atoms, the compound proposition is still true. That means that there is no possible observation that makes the compound proposition untrue. That is what unfalsifiability is.
Actually, if A = “The number of times this proposition appears in the sentence so far is 1”, then A does not imply A :D. Or if A is “The current proposition is on the left side of the implies”.
Yes! Absolutely that is what I’m saying.
In logic, a statement of the form “If P then Q” is considered TRUE in all cases where P is false, no matter whether Q is true or false, as well as in cases where P and Q are both true. The only time “If P then Q” is considered FALSE is if P is true but Q is false. (I’m just repeating what has been explained before—see La Llorona’s Post #44. It’s an agreed-upon convention of logic; it’s how implication is defined.)
So the only way to disprove “If P then Q” is to demonstrate both that P is true and that Q is false.
So if we observed life on Uranus, “There is no life on Uranus given that there is no life on Uranus” (or, to explicitly use the if-then wording, “If there is no life on Uranus then there is no life on Uranus”) would be considered a TRUE statement.
I think we’ve gotten kind of side tracked.
It’s impossible to disprove a tautology. It is also impossible to disprove any true statement. And yet there are true statements that are falsifiable, so clearly that in and of it self doesn’t prove that tautologies aren’t falsifiable.
Let’s consider two examples:
(1) “My name is Tim” is a true statement. I can propose an experiment to test it (e.g., taking out my drivers liscence and reading the name on it. I am presupposing that the information on my drivers liscence is correct.) That experiment only has one possible outcome: I will discover my name is Tim. However, if that statement were false, there would be another outcome, namely that I would discover my name isn’t Tim. Thus, the statement is falsifiable, even though it is impossible to prove false.
(2) A = A is a true statement. I can propose an experiment to test it (e.g., take something that is A, and check if it’s A.) That experiment has only one possible outcome: I will find that the thing which is A is A. However, if A = A were false, there would be another possible outcome, namely that I could find something that was A which was not A. The reason that’s impossible is that A = A is true.
So what’s the differnce? It’s impossible to prove my name isn’t Tim, because it is Tim. It’s also impossible to find a case where A = A isn’t true, because it is true. But if one were false, it would be possible to prove it’s false. The only difference is that A = A can be proven by logic alone, whereas you couldn’t determine my name by logic alone. That has no bearing on falsifiability that I can see.
In the first example, “so far” is not equal in both instances of the substitution, and thus the substitution proposed is not a valid one (you are substituting different things for each occurrence of A).
In the second example, “current proposition” refers to two different entities, and thus again you’re substituting different things for each occurrence of A.
Apologies if you were kidding - I couldn’t tell, so I thought I’d just clear this up. 
I was, hence the :D. But who defines what is a valid substitution? Just because it is self-referential doesn’t neccesarily mean that it is invalid. There are quite a few useful, self-referential statements. In short, this is a variant of the Betrand Russell Set Theory paradox. However, this has almost completely diverged from the point of the OP.
You misunderstand my point: anything is a valid substitution for A, but you have to substitute the same thing in every instance in the sentence being instantiated. So, for example,
t if t
is a valid instantiation of
A if A,
in which the substitution A/t has been made. What you are doing is essentially claiming that
p if q
is a valid instantiation of
A if A
which is not the case, unless p = q, which in the examples you gave they are not. Since the propositions you are substituting are not equal, they can’t both be simultaneously substituted for the same variable. I agree that the differences between your two propositions are subtle, but like I say, the crux is in the phrases “so far” and “current proposition”. In each case, they refer to different things each time they are used, making the propositions they are contained within distinct from each other.
Anyway, as you say, this is a bit of a hijack, but it’s kind of crucial since if I’m wrong then you have indeed presented a falsification of a tautology, and have single-handedly re-written the entire field of logic as it has been understood since ancient Greece or thereabouts. 