Well, why not play the game? — Banno

Yes, I do play the game, there's no other choice, but there's always a caveat. I think its impossible to view the world outside of some particular perspective and so in that sense I would say that our notion of objective truth is an idealization. We might say there is an objective way the world is but I don't think there is a single perspective-independent way to characterize it. If I were to say there are objective truths, I don't think I would be able to give a satisfying characterization without caveats. I don't want to conflate my belief in an objective state of the world and my ability to articulate things about them because the latter is something I cannot do.

Are you saying it is better to play the game in the wrong way? — Banno

No, I mean right way in the sense of avoiding and ignoring caveats which makes the veracity of "truths" seem obvious.

I think its impossible to view the world outside of some particular perspective and so in that sense I would say that our notion of objective truth is an idealization. — Apustimelogist

I'll not disagree with you about "objective" truth. I don't think the notion of much use. By talking to each other we can remove biases of perspective. There are true sentences about how things are. And overwhelmingly, we agree as to what is true and what false. The places we disagree tend to be either misunderstandings or differences in what one should to do about how things are.

Consider how much agreement was involved in your simply reading that paragraph.

The word "paradox" comes from ancient Greek "para" (= besides, contrary to) + "doxa" (= opinion). Indeed, it indicates something that exists or happens which is contrary to what one expects or believes to be true or happen. For example, a paradox would be raining without any cloud in the sky. Yet, it is possible, if there are very strong winds that bring rain from some other place than where we are. — Alkis Piskas

:up:
People underestimate the usefulness of etymology and dismiss it as "etymological fallacy" after a 5 minute reading session. But given some background facts about some of those who underestimate it, it does not surprise me at all.

People underestimate the usefulness of etymology and dismiss it as "etymological fallacy" after a 5 minute reading session. But given some background facts about some of those who underestimate it, it does not surprise me at all. — Lionino

This is very true. However, etymology in English --and I believe other languages too-- is often complex and even useless. This is not the case with ancient Greek and Latin, however. Esp. in Greek, one can undestand the meaning of a word just by its etymology.

But what are we talking about? People ignore or even hate dictionaries in general. People don't like definitions. This is what I learned from this and othe similar places. All the more about etymology.

However, etymology in English --and I believe other languages too-- is often complex and even useless — Alkis Piskas

It is true, and that is what I meant with "background facts".

People ignore or even hate dictionaries in general. — Alkis Piskas

And that is exactly when philosophy becomes affectation. Title drop.

People ignore or even hate dictionaries in general.
— Alkis Piskas
And that is exactly when philosophy becomes affectation — Lionino

Well said, Lionino. :up:

Yes, I think our main difference is that you want to hang on to the idea of true sentences and I do not really care for that.

if you like. Folk to attach too much to truth. There are true sentences.

Am I viewing the problem too simplistically? Isn't the point of the liars paradox, and all others, not in trying to make sense out of them, but in the very thing they expose? That is, that we can never conclude absolutes in our ideas, thoughts, Language, when our strongest tool for such conclusions (Reason/Logic) are threatened by fallibility. The mathematical paradoxes (forgive me, I am far from expertise) like Russell's and Gödel's expose that same threat, I.e., we cannot, using our most powerful language, conclude absolutely.

There is no 'Godel's paradox'.

Anyway, as best I understand your question, the answer is 'no'.

Thank you for the clarification on Godel. I see that.


My question was twofold.
1. Isn't it futile to "make sense" of paradoxes?
2. Dont paradoxes expose the limitation(s) of Logic (here, in pursuit of absolutes)?

I'll presume your answer is no; and therefore, you think that we can make sense of paradoxes, or, at least that it's a worthwhile pursuit; and, either they don't expose the limitations of logic or logic is not limited in its pursuits.

If that's the case, I'm interested in understanding your reasons.

1. I don't know what you mean by ""make sense" of".

2. Frege's system was taken to be a derivation of mathematics from logic alone. Russell's paradox showed that Frege's system was inconsistent. But does that mean that there can't be a derivation of mathematics from logic alone? Whitehead and Russell offered a system that was an attempt to derive mathematics from logic alone, but their system was not logic alone. But does that mean that there can't be a derivation of mathematics from logic alone? The Godel-Rosser theorem may discourage us even more from thinking that we can derive mathematics from logic alone. So, can we derive mathematics from logic alone? I think the preponderance of philosophers of mathematics think we cannot, but there are dissenters.

I see the relevance of your point, though indirect. It remains, then, the answer to whether or not, as you put it, we can derive mathematics from logic alone, requires at the very final stage at least, a leap from logic. Some say no, dissenters say yes, in the end, a leap must get one there.

The leap is in the form of axioms.

Just to be clear, the logic system itself is not contravened. Rather, we add non-logical axioms. We add axioms that are consistent, thus true in some models, but that are not logically true, thus not true in all models.

Good point. So simple, but something I haven't thought about properly. One I'll consider more thoroughly. Especially its implications on my personal interests about human Mind and the status/role/nature of logic. Thank you.

Any time. Thank you.

There are many fancy logical treatments of this paradox.

The sentence does not express a statement that has a truth value, which means that it does not express a statement at all. There are countless sentences like that. One could devise countless sentences like that. A sentence can be vapid and nonsensical, and "This sentence is false" is one of them.

One need not consider vapid claims, and one need not construct logical proofs of their vapidity.

Ah, if you guys had only participated in my thread on The Laws of Form, you would have discovered that such self contradictory sentences are formed by "re-entry" or recursive definition, and result in truth values that oscillate in time. — unenlightened

Agreed.

Thus we end up in a loop of "if this is true, then it is false, but if it is false, then it is true, but if it is true...". It feels as though "sentence is not true" is sentence A and everytime we try to evaluate it we in fact create a new sentence A1, then A1.1, then A1.1.1, and so on. — Lionino

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One need not consider vapid claims, and one need not construct logical proofs of their vapidity. — Faust Fiore

How do we know otherwise which claims are vapid or not? Proofs are welcome wherever we may find them.

It can be problematic to apply formal logic to a natural-language statement. In formal logic you have rules of sentence formation, and these try to exclude contradictions. Natural language has informal, often ambiguous rules and definitions.

This a particular type of statement: the only argument for it is that it can't be false; the only argument against it is that it can't be true. But in natural language not every sentence is true or false.There are many other possibilities, including meaningless, as this thread suggests.

Welcome to TPF, Gary. (Well, two weeks ago, but welcoming lasts for a while ... :smile:)

It can be problematic to apply formal logic to a natural-language statement. In formal logic you have rules of sentence formation, and these try to exclude contradictions. Natural language has informal, often ambiguous rules and definitions. — Gary Venter

I believe that both "formal logic" and "natural-language logic" are simply two different ways of expressing logic elements and logical schemes. The same applies to Math sets, probabilities, etc.: they can be expressed with symbols as well as with graphical scemes and also with words. It's like "1+2=3" (mathematical/numeric notation) and "one plus two equal three" (words). Both of them express the same conventional truth.

Thanks. Fun to have found this.

True about the logic but natural language sentences do not have to be true or false. Of course "meaningless" is one alternative, but so are "mostly right but very misleading," "ambiguous," "changed the sense of a word in the middle of the argument," etc.

This is probably hard to believe but I do not have the intuitions necessary to see the “mysteries” of some paradoxes. For example, the liar paradox “this sentence is false” simply appears meaningless to me and I do not enter the logic of: If 'This sentence is false.” is true, then since it is stating that the sentence is false, if it is actually true that would mean that it is false, and so on.
Language conveys information and I can’t extract relevant information from this sentence, this is why I do not understand why people manage to reason logically with it. — Skalidris

I had forgotten that this was also Kripke's analysis. Thanks for reminding me. This same analysis equally applies to an expression of formal language that asserts its own unprovability.

I can still see no difference. When we are talking about facts, our statements have to be true or false. E.g. saying "George is taller than Alex" is like "a > b". But of course, as you say, natural language is much richer and has more attributes than symbolic one, e.g. ambiguous and meaningless, as you pointer out. Yet, Math can also be ambiguous, e.g. sqrt(4) can be 2 and -2. And it can be also meaningness, e.g. the expression 4 + 5 x 6, besides being ambiguous, it is ill-defined and therefore meaningless.

If you look "wider", you will find more similarities between natural and symbolic languages than the obvious ones ...

On the topic that some users brought up, that self-reference paradoxes give oscillating truth-values in time, the quotes:

Since knowing the negation of a statement in intuitionism means that one can prove that the statement is not true, this implies that both A and ¬ A do not hold intuitionistically, at least not at this moment. The dependence of intuitionism on time is essential: statements can become provable in the course of time and therefore might become intuitionistically valid while not having been so before. — Intuitionism in the Philosophy of Mathematics

If we don't assume the Law of Excluded Middle is true, the Zermelo-Russell paradox still does not dissolve however, because it can be formulated in terms of the LNC.