## An Argument for the Unity of Truth?

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I was thinking about truth, and came up with an outline for an argument that there is only one truth. However, this is just an outline and it is flawed, so I'm hoping you can help me critique and fix it.

Here is my outline:

1. No Truth is itself a statement of truth, which means it's a contradiction, hence false. Thus there is truth.
2. More than 1 truth implies an infinity of truths. I can't really explain this, but perhaps it has something to do with induction, reductio ad absurdum and/or the infinite divisibility of properties?
3. 1 & 2 imply there is only one truth.

This may seem vacuous and perhaps even a caricature, but I've used this argument as a way of explaining monotheism, although that argument could seem far fetched.

So I have the following questions:

• What are the flaws in this argument?
• Can I put it on a more rigorous footing? How?
• If this can't be salvaged, where are the fatal flaws?
• Is (2) workable? Is the existence of an infinity of truths even a problem?
• What is the closest argument that can be salvaged from the above?
• Can this be tied in to an argument for monotheism?
• Are there any similar philosophical arguments?

As for the connection to monotheism: are you sure that the uniqueness of god has the importance you would like, if god is a phenomenon less like an engaged creator and more like the unity of nature? – Niel de Beaudrap – 2015-01-03T09:49:34.923

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It is interesting, though hard to declare logical. The primary issue is that you have not stated what system of logic you are using. Because it is the lowest-common-denominator, I will compare it to First Order Logic (FOL):

• "'no truth' is a truth" is not a well formed statement. For FOL, the statement needs to be in the form of a predicate. I believe you are trying to say "'There is no truth' is true."
• I'm going to get a little finer detailed than this in a moment
• "'More than one truth' seems to lead to an infinity of truths, I couldn't really explain why it just seems so." may qualify as the antithesis of logic. It is provided axiomatically, so readers must accept that more than one truth leads to an infinity of truths as an axiom before admitting your logic.
• "That leaves us with one truth, which is a truth therefore the one truth. It just sounds good to me." Once again, there is a lack of logical construction. You make an axiomatic statement.

Your argument thus is reduced to:

• Assume: More than one truth leads to infinite truths.
• Declare: "There is no truth" is paradoxical (why this is paradoxical will be covered shortly)
• Result: There must be one truth.

Unfortunately we must treat the result as an axiom as well, for it does not follow from the assumptions. Nowhere does it state there cannot be infinite truths. In fact, the claim that there cannot be infinite truths is highly questionable because arithmetic suggests there are indeed infinite truths. Consider "for each a,b from Z, the set of all integers, there exists a c from Z such that a + b = c" is true. Arithmetic would claim this statement is true. From this one truth, we can create a series of truths in the form "for each b from Z, there exists a c from Z such that A + b = c is true", where we may use any integer value for A to construct this new truth. Since there are infinite potential values for A within Z, we have already constructed an infinite number of truths.

I believe you are working towards an argument Whitehead and Russel were working towards until Gödel showed their work impossible

I believe the "one truth" you are working toward is more accurately phrased as a "Formal System" of truth, and you seek "One True Formal System of the Universe". A formal system consists of:

• A finite set of symbols, the alphabet for the system, used to construct formulas (strings of symbols)
• A grammar, describing how to make "well formed" systems
• A set of axioms which are declared "true"
• A set of inference rule to manipulate formulas and prove their truthfulness.

If you combine First Order Logic and a set of axioms, you get a Formal System. If you want, you may define your own logic, instead of using FOL. However, declaring something powerful like "there is only one truth" is going to require more than a paragraph, for you will have to define the Formal System you are using.

If we can limit ourselves to FOL, all we need is a set of axioms to create a formal system. This means the search is for "The One True Set of Axioms," which is starting to sound a whole lot like your original search for one truth. This search just needs a little linguistic nudge to make it mathematical. It is easy to show that if you take a set of axioms, and add a derived truth from them as an axiom, you get a consistent Formal System. You may be looking for a "minimal set of axioms to admit all truths in the universe under First Order Logic."

And with that in mind, I'd like to give Gödel some attention.

Gödel devised a few theorems known as his Incompleteness Theorems. These are proven using the rules of first order logic as part of his approach to your paradox. "There is 'no truth'" is a Liar Paradox: "This sentence is false." Gödel sought to resolve some of these issues. The standard resolution of this paradox is simple: "This sentence" is not a valid symbol in FOL. It simply isn't. One of the rules of FOL is that you must define the symbols you use up front, and there is simply no valid FOL formula of that sorts.

Russel was approaching one such solution, which involves carefully crafting the set of symbols in a way which permits "This sentence" to be a valid predicate. In doing so, he identified the "Russel Paradox" which dealt with sets that contain themselves (tail chasing sets), vs. sets that do not contain themselves(normal sets).

While Russel was trying to do what you have been doing, finding a way to make this valid, Gödel came in and showed it impossible. Not just Russel's paradox... Gödel proved that an entire swath of potential systems had a fundamental flaw, including the system I believe you are working towards.

Gödel concerned himself with systems which could "admit arithmetic." Of course arithmetic is such a system, but any super-system which can define arithmetic and its trules (such as our universe) is bound by the law he found. He showed that any system which could admit arithmetic must have at least one of the following characteristics:

• Incomplete: it must fail to give a result for some value
• Incorrect: if must arrive at an incorrect result for some values
• Unprovable: it cannot be proven using the laws of the system
• Intractable: the laws of the system are not recursively enumerable (which is a really specific wording which can be generally translated as "can never be written down without infinite paper")
• Illogical: the system must violate its own laws

(His wording is more precise, but I find these to be the most human accessible versions. For example, his theorem does not actually include "illogical," because his proof was valid only for logical systems. I include it because non-mathematicians often make arguments which can only be described as "illogical." Also, technically he targeted ω-consistent systems, though Rosser strengthened it to all consistent systems in 1936)

His second incompleteness theorem used the first to prove a powerful statement that strikes to the core of the "no truth" argument. It is, as always, tremendously detailed mathematical speech, but Wikipedia is kind enough to gloss it:

For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, if T includes a statement of its own consistency then T is inconsistent.

This is very much directed at the Liar paradox, basically stating that you can never prove your own provability (unless you target a weak system which cannot describe arithmetic).

On Monotheism

This does not disprove any argument about monotheism. It does not even make dangerous statements such as "The bible is a lie because it claims provability about itself." What it does say is that claims such as "the Bible is true, and it says so" will inherit at least one of those five characteristics (gloss: self-referential text admits Peano arithmetic, so it is in Gödel's domain. Most all "book" religious people I talk to (Jews, Christians, Muslims, etc.) choose to accept "unprovable" as their characteristic of choice. It is completely admissible by Gödel for the Bible to be true and claim so, if it is unprovable using formal logic. Likewise, those who profess to believe in the Dao can trivially prove their belief, but the cost for this is that the Dao is intractable (it is said "If you can write down the Dao, you have done it wrong").

It is also completely effective to define a non-infinite system, which cannot describe arithmetic. This avoids Gödel's incompleteness theorem as well. However, I am unaware at this time of any religious institutions that take this approach.

"For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, if T includes a statement of its own consistency then T is inconsistent." If the universe is a logical system that can admit arithmetic. How can the universe include the very source of that system? How can the universe include the human mind that thought the system? Doesn't that make it inconsistent? – Alexandre Babeanu – 2015-01-03T12:07:21.107

@AlexandreBabeanu: No, it only makes it inconsistent if the system includes a statement of its own consistency. A system which does not contain such a statement can be consistent. The universe is not obligated to contain such statements. And, in fact, there are many examples of just how hard it is to make such consistency statements once the human mind is involved. Consider just how much effort went into arriving at "I think therefore I am," and even that statement is not made as a "provable" statement. – Cort Ammon – 2015-01-03T17:56:57.867

Gödel's work was also in response to works such as Russel and Whitehead's Principia Mathematica. They sought a Formal System which could prove all mathematically true statements (specifically, they sought a set of axioms and FOL). They were not even trying to prove all truths, just those within mathematics as we know it. Gödel showed that, as long as your system was ω-consistent (read: admits integer arithmetic), it could not be proven with formal logic. Thus, any attempt to make sense of the world, which includes math, using such logic has to inherit one of those five characteristics. – Cort Ammon – 2015-01-03T18:05:02.277

If you are interested in the corner cases, there's a new class of Formal Systems invented by Dan Willard which side-step Gödel's theorem. They are weaker than Peano arithmetic, and specifically constructed to be unable to express diagonalization, a lemma Gödel used in his first incompleteness theorem, by refusing to let multiplication be a provably total function. However, care should be taken when building a philosophy on this unless you have an advanced Mathematics degree. It took all of mathematics 70 years to identify this class of systems... – Cort Ammon – 2015-01-03T22:12:26.843

... and anyone using them must be brutally cautious to avoid accidentally adding an axiom that admits diagonalization. It is difficult to avoid such things without a strong math background to warn you when you are approaching a dangerous axiom. – Cort Ammon – 2015-01-03T22:14:57.460

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There are multiple truths. There's the truth that there is a head on my neck, that there is a shoe on my foot, and so on. If this strikes you as vacuous, then the natural question is this:

How are you defining truth?


Once you do that, then maybe you've got something. You'd still need to work out how more than one truth implies an infinity of them (inductive argument perhaps?), and why that would even be a problem. Once you did that, you'd need to show how this has any bearing on monotheism.

Having said that, there's a somewhat similar (and I think more justifiable) line of reasoning you can pursue. If truth is everything that is, then you could tie that in with a pantheistic or panentheistic view of God. This essentially takes you to non-dualism, which has found expression in (AFAIK) all major religions, although not as the majority view. It also leads to some very interesting and potentially life-changing practices, but we're probably outside the realm of philosophy at this point.

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This is a normal question of all the truth seekers. Upanishads have proclaimed it as Mahavakyas. Read from page 90 onwards for Ultimate & conventional Truth

For those who seek earnestly, I suggest reading the book 'SOME ASPECTS OF VEDANTA PHILOSOPHY' by SWAMI SIDDESWARANANDA. Its Preface is given in one of my posts

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I propose: A statement is a true statement if and only if the claimed issue asserts a fact. So we have statements on one hand, and facts on the other hand. Facts refer to reality - I will not define this concept here. While a statement is a sentence; in the present context I consider only sentences referring to reality.

Considered from this point of view, the question about one, several or even infinitely many true statements is simple: There are infinitely many true statements. If you adopt the 2-valued propositional logic, there is the same number of false statements: Just negate a true statement and vice versa. Each statement is either true or false - even if one does not know which property holds.

After you feel at home with a theory like propositional logic, dealing with true and false statements, I would recommend to think about the concept of "Truth" as an abstraction from the adjective "true". In my opinion, a concept like "Truth" needs the sticker: Handle with care!

Interestingly enough, your proposal has a name. It's a Tarskian truth, after Alfred Tarski. His truths all take the form "'P' is true if and only if P." where P is any sentence in a language. (The quotes around the first 'P' are important). – Cort Ammon – 2015-01-03T23:05:43.140

You are right. I consider Tarski's definition a useful approach to an old problem. On the basis of his definition one can deal with further questions, e.g., how to determine whether a statement is true? – Jo Wehler – 2015-01-04T08:39:08.923

@jo wehler: "Light is a particle." Is that sentence an example of a statement of fact? – Little Eva – 2015-01-04T23:13:04.433

In my opinion "Light is a particle" is not an example of a statement of fact, the statement is not true. Only in certain situations does light show particle properties, e.g., at the photoelectric effect. Hence I prefer "In certain situations light behaves like a particle" as an example of a statement of fact. Anyhow, we cannot say what light actually is. We can only judge how useful different models of light are. The best models at hand are the classical theory of electromagnetism (Maxwell theory) and the theory of quantum electrodynamics from the 20. century. – Jo Wehler – 2015-01-05T08:17:02.743

@jo wehler - yes, your example of a statement of fact begs the question, What is Light? It seems to demonstrate our inability to arrive at a final or satisfying answer to many (or all) issues of fundamental import, leaving us with answers that are conditioned by our method of inquiry. – Little Eva – 2015-01-06T18:57:01.490

@Little Eva 1. Please let me know why my example begs the question. 2. Maxwell's electrodynamic was a big scientific progress: Light can be treated as an electromagnetic wave satisfying the Maxwell equations, propagating at fixed speed. Maxwell's theory is the base for all wireless communication. 3. "Leaving us with answers that are conditioned by our method of inquiry": What other do you expect? Science can make only small steps to emancipate from our initial anthropomorphic models. Science gives us no final answers, but its answers are often better founded than answers from other sources. – Jo Wehler – 2015-01-06T20:09:00.457

@jo wehler - sir, I'm a high school dropout and certainly no physicist. I bow to your superior knowledge of Maxwell's equations (though controversy seems to attend Heaviside and Gibbs' treatment of those original equations). Rather, I was pondering epistemological dilemmas. Yes, though encumbered with its own limitations, science is definitely an improvement on mere superstition. – Little Eva – 2015-01-06T21:16:54.763