John Page

The Liar Paradox is around 2,500 years old. Based on cognitive theory, here is my simple explanation which is different than any I have read to date. The explanation is extracted from my formal ontological theory and also works on the “Strengthened Liar”. If you would like to receive a copy of the formal theory send me a message with an email address I should send it to (131Kb PDF file).

The Law of Identity and the Law of Non-Contradiction are unaffected. Essentially, all that is needed is to identify the proposition that the truth-functional term is supposedly a result of and analyze that proposition (if possible). Thus, the underpinnings of propositional logic are also unaffected.

If the words “true” or “false”, or indeed other words or expressions predicating truth functionality like “that is a lie”, are used in a proposition such assertions are not to be taken literally. Truth functionality is a property of a proposition that resides at a different level of abstraction than the proposition itself – for the Liar Paradox we simply need to suspend judgment until we’ve identified a ‘substantial’ proposition. My formal paper contains a methodological approach for this process.

If you’re interested in some relevant debate on truth, check out this thread on the <a href="http://iidb.org/cgi-bin/ultimatebb.cgi?ubb=get_topic&f=56&t=000119" target="_blank">Truth Debate</a>.

Have fun.

WJ

Hi John!

If the statement of language "There exists no true propositions" is false via logical necessity, in your opinion, how does one [the logician] know it is false to begin with?

Walrus

John Page

Hi Walrus!

There are two ways I could interpret your question: a) how does the logician come to know of truth and falsity in the first place (but not beforehand) or b) how does the logician come to know the result of a propostion in the form "There exists no true propositions" beforehand.

My answer to a) is: Experience and social convention as to the words used when describing the similarity and dissimilaity between object's forms.

My answer to b) is: The logician doesn't know beforehand (unless it is a result memorized from experience). The logician perceives the expression in question and, if they consider it to match the form of a proposition, they will say that it is truly a proposition. Note this is different than saying it is a true proposition - further analysis is required to determine this as below.

How does the logician know? Assuming he/she is using ontologic on the statement "There exists no true propositions" the truth-functional result would be obtained by hunting for propositions that resolved to the truth-functional value of "true".

Using ontologic's definition of "true" the logician can refer to external reality and say, for example, "It is true that these glasses are not this table". Happy that there are true propositions a value of false would be returned for the proposition in question.

So a short answer to b) might say "The logician attains knowledge through experience of reality and expresses it using the social conventions of language." Logicians can be wrong, however....

NOTE 1 Underlying your question is the isssue of whether there is such a thing as an absolute truth. I propose we cannot know anything under the concept "absolute truth". For a truth to be absolute, the identities of the propositional subjects must merge and be indistinguishable from each other. In turn, if this were to occur in reality we would not be able to tell the subjects apart! If we cannot tell the subjects apart they are only perceived as "one".

NOTE 2 In a theoretical universe containing n identifiable (i.e. non-identical) objects, one could argue that the system of logic needed to completely describe it needs nx(n-1)/2 truth-functional values, i.e. one truth value per one-to-one relationship. However, to compute the "relative truth" of each of these truth-functional values one needs a base value. It seems logic uses "identicalness" as this base value ("true" or 1 in Boolean logic).

Cheers!

WJ

John!

Well, I don't think you'll get an argument from me! Thanks for that explanation. Just thinking aloud here; if the fact that some true propositions exist, and that it is logically impossible for there to exist no true propositions, then out of logical necessity do we find certain propositions are required to explain things about 'true existence'. (Or said another way, logically necessary propositions are in a response to (and a direct result of) a conclusion derived from a logical impossibility.) Otherwise, the analysis is incoherent, out of ignorance, etc, etc and can't be responded to in any fashion; one should stay silent.

Yes? No?

Now you mentioned ontology. I suspect there are reasons for that. And you also mentioned a suspension of judgement in your initial post. Is this where the logician is forced to take a position (subjective epistemic opinion) about an unknown? Does it also follow then that the rules of identity/lnc/and other tools of logic should remain silent on issues relative to resolving contradictory statements found in language and/or ontology?

My gut feeling is the answers are yes and yes respectively. Mainly because contradiction exists. How it is resolved is the issue. Going back to the painted ball being both green and red while perpetually spinning, we cannot know whether it is a true contradiction yet the hypothetical ball of contradiction exists by merely observing it. In other words, we see both red and green all over, but can't discern exactly how it is painted that way because it appears like a blur.

So, if I conclude after observation that "the ball is red and green all over" (same time same respect), is that proposition/statement true, false, unknown, or a logically necessary truth based on sense experience at that snapshot in time? Otherwise, it is an existing contradiction in the mind until proven differently.

My feeling is, it is the latter.

Walrus

John Page

Analogy: In a dictionary, words are defined in terms of other words. You have to look at external reality itself to know what the words mean. Reality: Its the same with the propositions that can be formulated with words, as Bill pointed out they're gibberish without context.

Logical impossibilities exist in the abstract - I would argue that a contradiction in meaning is at a greater level of abstraction than the values of "true" and "false", which are inputs to a logical impossibility. Further, I think logical impossibilities exist in the mind for a reason - they're a result of constructing hypotheses about reality in order to evaluate which ones work - you only find out their "impossibility" a posteriori.

An analysis can, therefore, be coherent in the context of the mind's contents. No need to stay silent, just keep asking questions.

Yes, the logician can't make a judgement because he/she doesn't have all the facts. Here is an analogy to demonstrate. Suppose I ask you what color the ball is but you can't see any ball. You have to identify the ball in question and work from that. Same kind of thing with the Liar.

Ontology. The reason why? Here I'm a little non-traditional. If ontology is the "what" and epistemology is the knowledge of "how", I can't see a sensible result without considering both. This is back to the very issue you started with, understanding has to be in the context of what is being understood. I believe ontologic succeeds because it focuses on the border between the mind and external reality - the frontier where the "what" and the "how" of cognition first meet. If one strays only into external reality it becomes impossible to explain how the mind works, if one concentrates solely on the mind its is easy to become lost in complexities that do not involve the lower levels of abstraction through which raw experience is filtered.

I don't think ontologic makes any subjective epistemic assumptions. Its founding observation is based on the reader's undeniable observation that it contains words and their comprehension of those words. Axiom #1 is not a dry observation, its a working experience (providing its in language you understand). Deny ontologic's axiom #1 and you end up either a liar or a nihilist.

I would say no and no! We're involved in an exploration, a stepwise refinement to reconcile observations. In the formal paper I suggest a way to modify current representational conventions in logic to reflect levels of abstraction.

Contradictions exist, I think they need to be explained rather than resolved. The evidence points to contradictions being a necessary product of seeking the truth.

Your analogy with an optical illusion is right on the mark. Sight seems to depend on a sampling approach (as evidenced by the apprent smoothness and jerkiness of films as the fps is decreased). So, the subjective observer does not necessarily report the truth that might be apparent to an observer that has examined the ball and seen it spinning at increasing velocities etc.

The subjective observer may be unaware of any contradiction and report a greeny red ball, that is the truth presented to their conscious perception. So, we philosophers can observe there are many ways in which illusions/delusions can come about, even unto our own observations.

Until we can verify precisely how these perceptions occur, all the way from the observed object through external transmission media (air, light etc.) to sense data to analysis into a "previously experienced form" etc. our "truth" remains hypothesis. My response, it is a "truth" in the mind until proven differently. After the explanation, yes, the mind might recategorize the expeience as a contradiction.

Conclusion, we need a synthesis of physics, cognitive science, neuroscience and metaphysics to crack this one with some computer science to run verifying models.

Cheers!

[ April 08, 2002: Message edited by: John Page ]</p>

Ierrellus

John:

If a mental abstraction has known centuries of "truth" by agreement, is the abstraction then true by continuity?

Ierrellus & beergnat

John Page

Hey, sorry for the long answer below - its your fault for asking a smart, succinct, question!

Short Answer: No, continuity is not required. I suggest that strong truths arise from the detection of repeat occurences. Repeat occurences, though, do not necessarily need continuity. Here's my detailed reasoning in three parts:

1. Real vs. Abstract. The mechanism of perception is no different for abstract entities than for external, physical entities. Why? - Because we only know about external objects through our senses. Raw sense data undergoes an abstraction process which puts it in the same 'realm' as 'internal' or 'synthetic' abstractions.

2. Continuity. A "truth" exists in the mind as the result of comparing experience with "axiomatic concept" (or comparing experience with experience directly). I propose that without a comparison process there can be no detection of a "truth" of existence. While comparison of two pieces of sense data is a process, the inputs do not need to exist over a period of time to be "read". (Note: I'm sure there are physicists/biologists who would argue that a phenomenon must exist over time to be sensed but I'm not going to wade into the quantum quagmire).

If a repeat comparison is carried out with the same 'informational' result this implies that the truth, external object or whatever has existed in a continuous or constant state between the two comparisons. As a comparison is a physical process that requires time to execute, we have no business stating what is happening between our two observations, we simply have no data between the two points in time.

3. Transmission. Since no human is known to have lived over multiple centuries, fully answering your question requires an understanding of how a truth appears to be 'transmitted' over space and time and between minds.

Recreating a "truth" value requires equivalence of the inputs, their context (also inputs) and the process for arriving at truth. The apparent continuity of physical objects can be tested on a repeatable basis by using direct third party observations/measured data. While we have no such luxury at this time with abstract values, proving the mechanics of abstraction (which I don't consider I have yet done) will provide some solid ground on which to advance theories of mind on a similar basis to physics.

So, for transmission of truth we end up with the same general conclusion as for the apparent continued of existence of a "truth" for an individual. A truth may arise in two different minds at two different times, but that is no evidence that the truth in question actually existed anywhere or anytime else between these experiences.

Let me know if this is unclear or I missed something

Cheers!

[ April 09, 2002: Message edited by: John Page ]</p>

WJ

Hi John!

Of course I am finding that reading your posts are most enriching, for further exploration in confidence. I think we are basically on the same page here, pardon the pun.

Though one item caught my attention with regard to the spinning ball colors analogy. You used the word illusion, probably, for good contextual reason. However, the illusion is *reality* (?).

If that has any merit (using the spinning ball of colors as an analogy to the world), this thought of *illusion* opens up other possibilities for the logician, empircist and rationalist to solve viz. paradox.

Of course as you alluded, paradox is resolvable; contradiction is not. And so, the revolving ball may not stop long enough to make a determination as to its true colors; in theory, it is possible to be both red and green all over, same time-same respect.

Hence, suspended judgement and/or logical necessity. And that brings us back to the liars paradox. Reality dictates the percieved existence of [at least one] true proposition(s) only out of logical necessity.

The contradiction (or paradox) is relative to time and motion. Can a statement of truth be both true and false at the same time and same respect? In the natural sciences [and in consciousness-Being], it can.

Walrus

John Page

First, a quibble. An illusion is an inaccurate representation of reality. We can only know reality through our means of perception, see below.

An illusion can demonstrably exist. An illusion can be defined as an inaccurate perception, a false impression. A perception is our subjective truth derived from our view of reality. Truth is something (a value, result) that exists within your mind, not within external reality. If we perceive inaccurately, what we thought was true may be false.

What is the difference between "illusion" and "non-illusion"? Its a question of accuracy in the context of additional, possibly more objective, data about the phenomenon being observed. We categorize a perception as an illusion when (we believe that) we understand it as a "false impression". Note: My tortuous wording is to acknowledge that we may be deceived about illusions themselves.

Hopefully, both are understandable! i.e. what they are and how they occur. (If not, then we will remain deluded).

I think a paradox is an apparent contradiction. The latter arises through gainsaying and is literally just stating the opposite. A paradox, however, manifests itself by resolving to a contradiction using a set of assumptions.
No, not in my theory, its just the appearance of the ball in a particular state WRT a human observer. How does this specific illusion occur exactly? I'm not enough of a physicist/cognitive scientist to answer that one. Another example excluding the ball is white light which, physicists have said, is a combination of all the wavelengths of the visible spectrum.

We're back to one of the issues we started with, though. Our conclusions are only as good as our perceptions - I don't think using a magnifying glass makes things "appear", for example, its just that our minds have different information to work with.
Hmmmmm... Presumably you perceived that "logical necessity" exists, how does that come about? (Let's suspend judgement for a moment). A system of formal logic is an abstract entity that may or may not be a good model for understanding reality. As a logician, I am seeking a system of logic that matches reality better than current systems - hence my focus on the paradox. My conclusion: reality should drive the necessities of logic, not the other way around.

Perhaps I could suggest a re-phrase of the above quote from your posting to "The process of perception itself seems to dictate that, from the standpoint of a system of logic, our perception is either true or false."
First and foremost, paradoxes exist in the mind. They are something that is perceived. Time and motion may be contributory factors - but remember these are both concepts in the mind, you might consider motion alone as a paradox, as did Zeno, we need some physics to investigate the phenomenon.

"Statement of truth" is a set of words that, when evaluated using a system of logic, may result in the abstract value "true" occuring in the mind of the observer. A different observer may use a different system of logic and arrive at a false conclusion, again, an abstract value in their mind. Writing down the results is the recording of an event, it doesn't change the (abstract) truth of the results. Note: This is a truth about truth, unless its false, QED.

Thus truths are not continuous, they exist when calculated in the mind. Like Heisenberg and his electrons, we can only look for explanations that are consistent with the facts. I think there is a mental illusion that when a thought process recurs and produces a similar result when compared with the previous instance of similar thought, that truth is somehow necessarily eternal, constant or everlasting.

Do you have any examples from the natural sciences that show truth and falsity can coexist in the same respect at the same time and place?

Interesting questions. Cheers!

[ April 10, 2002: Message edited by: John Page ]</p>

Ierrellus

John:

Thanks for the excellent response to my question. One more question--What is your interpretation of a zeitgeist?

Ierrellus