Freethought & Rationalism Archive

John Page · 03-07-2003, 03:42 PM

Quote:

Originally posted by jpbrooks
John, is "truth functionality" the same as "truth value"?

No, I don't think so. Truth functionality refers to the "truth telling process". In this sense the proposition is passed over the "truth telling" process/function to arrive at either the view A or ~A.

Cheers, John

P.S. How about "Truth is in the eye of the beholder".

tk · 03-08-2003, 12:52 AM

jpbrooks:

Quote:

But how could "true" and "false" even be defined without assuming the LNC? For instance, how could the "definition" of "true" exclude what is not "true" without the LNC?

Good question. I think in a dialetheist view, "true" and "false" will just be like "yellow" and "green", or "one" and "two"; they are just convenient labels, not necessarily opposed to each other.

But "true" and "false" are definitely somewhere inside, whatever form they may take. Priest said, "dialeth(e)ism is the view that there are true contradictions." The very concepts of "true" and "contradiction" themselves imply some sort of notion of truth and falsity.

John Page:

Quote:

Yes, but you can never be completely objective under this model - you just end up with an infinite regression or circular argument.

I beg to differ. The construction does not require the use of higher-order logic: first-order predicates remain as first-order predicates. (!!! Indeed, I was also quite surprised at seeing this -- that one can build an "objective" truth from a series of "subjective" truths at almost no cost, and without switching to a logic system with different properties of soundness and completeness.)

Quote:

Perhaps you would care to illuminate our darkness with an undoubtable logical explanation.

Erm... well, I will mention the recent debate I had on II regarding Ayn Rand's Objectivism (with a capital "O"). Although some people might think that it was a "relativist" (myself) against an objectivist, it was really an issue of whether "objective morality" exists in an objective world. In other words, instead of objectivism vs. relativism, the point of contention was actually something more specific, namely the presence of objective morality vs. the absence thereof. Some people have the idea that objective truth also entails objective morals, objective gods (or objective godlessness), objective artistic standards, etc. Even as I believe in the existence of objective truth, I do not subscribe to this view.

If it is surprising that someone who seems to be an "objectivist" (small "o") at one moment can suddenly turn into a "relativist" the next... well, to me it is not that surprising actually. I find these terms to be exceedingly meaningless labels for describing people. After all, a relativist believes that objectively speaking, there is no objective truth (?!?!?!?!?!?), and an objectivist does concede that people are different. It is a thin line between the two.

* * *

While I have the time, I would also like to discuss the Ontologic paper which you have sent to me (thanks!). Let me start with a discussion on representational and represented concepts:

Mathematicians have long recognized the duality between syntax ("representational entities") and semantics ("represented entities"). In the various branch of mathematics, the tendency has been towards axiomatization -- to push everything up to the syntactic level, so that the process of derivation becomes a mechanical manipulation of symbols with no regard to their `underlying' meaning. (Thus we have, for example, the ZFC axiomatic system for mathematics itself.)

The reason for this tendency is that syntactic manipulations are ultimately more rigorous and more trustworthy than appeals to fluffy `underlying concepts'. Indeed, automatic proof checkers have actually been written to verify proofs under various axiomatic systems!

Of course though, an axiomatic system is not very useful if it cannot be tied back to some woolly `semantic concept' in the real world. The only solution really is to experiment with different axiomatic systems, discard those which lack predictive power -- e.g. Euclid's Fifth Postulate was found to be unsuitable for accurately describing the earth surface's geometry -- and hopefully prove the equivalence of the remaining axiomatic systems. The constant interplay between syntax and semantics is what pushes science forward, and deserves study in its own right.

John Page · 03-08-2003, 05:15 AM

Quote:

Originally posted by tk
....I beg to differ. The construction does not require the use of higher-order logic: first-order predicates remain as first-order predicates. (!!! Indeed, I was also quite surprised at seeing this -- that one can build an "objective" truth from a series of "subjective" truths at almost no cost, and without switching to a logic system with different properties of soundness and completeness.)

I have no issue with objective views. My issue is with the expression "completely objective". Objective views are necessarily limited by the domain (limited amount) of information fed into them and the restricted thought process that goes into analyzing that information. The technical "completeness" of a system does not guarantee that it is absolutely complete and accurate in all respects - only that it is complete w.r.t. the completeness tests applied.

BTW I concur with your other comments - the relativist and the objectivist are both limited by the above reality. The alternative is to try and achieve omniscience through the God's Eye View debated in other threads!

Cheers, John

P.S. I split off your comments about representational systems into a new thread, hope that is OK with you.

jpbrooks · 03-08-2003, 12:07 PM

Quote:

Originally posted by tk
jpbrooks:

Good question. I think in a dialetheist view, "true" and "false" will just be like "yellow" and "green", or "one" and "two"; they are just convenient labels, not necessarily opposed to each other.

True. But "yellow" does not "contradict" "green" because they are both colors that can be said to "contain" "yellow". But that "class" of colors itself is still exclusive. It excludes other colors like "red" that contain no "yellow", and other things that are not even colors at all.
Similarly the concept of "unity" in the number "one" is also "contained" in the number "two" (viz., "one" added to "one"), and thus, does not involve a contradiction. But, as before, this "class" of numbers excludes other things.
In each case, the LNC is assumed by the exclusiveness of the "class" under consideration.

Quote:

But "true" and "false" are definitely somewhere inside, whatever form they may take. ...

But, within Dialetheism, there can be no possible restriction on the form that the "definitions" can take. To impose such a restriction is to abandon Dialetheism.

However, there may be a possible way out of these kinds of problems for the Dialetheist. If Dialetheism gives up its "exclusiveness" among other views, and allows a view that doesn't reject the LNC to be true, i.e., if it restricts its "scope" from a view to something like an "approach" (or provisional methodological assumption), it may be able to escape the problems associated with it as a "view". Though, I confess, I have no idea how such a "Methodological Dialetheism" could be used.

Theli · 03-09-2003, 01:49 PM

Quote:

The result "True" is derived from or is considered a property of A which we perceive through a brain state represented as {A}. Therefore {A} -> A -> True.

For each proposition A there must be (under dialetheism) a brain state {B} under which A is false. Thus {B} -> A -> False.

Thus the truth functionality of any proposition depends on the view of the observer which in turn is determined by their brain state.

What excacly is a "brain state"?
From what I understand of Dialetheism is that it views "truth" as to a degree subjective, a thing I agree on. But I can't find anywhere what excacly would differ between 2 people's truth, what you called Brainstate A and B.

John Page · 03-09-2003, 04:24 PM

Me:

Quote:

The result "True" is derived from or is considered a property of A which we perceive through a brain state represented as {A}. Therefore {A} -> A -> True.

I think my using A in the brain state and A for the propsition was v confusing.

Quote:

Originally posted by Theli
What excacly is a "brain state"?.....But I can't find anywhere what excacly would differ between 2 people's truth, what you called Brainstate A and B.

I'm saying (or trying to!) that the truth functionality of a proposition is a function of the proposition and the state of the brain contemplating that proposition. I argue as follows.

Assuming:
a) The meaning of the proposition A is common between us,
b) Your brain state is represented by the set of values {Theli} and mine by the set of values {John}
c) You consider the proposition to be True and I consider it False

It can be deduced that the truth functionality of proposition A is determined by {Theli} and {John}. BTW I am not saying that proposition A is not relevant, just that it does not actively determine the result.

Thus, in direct answer to your question, two people's truths differ because their brains behave differently.

Am I making sense?

Cheers, John

Theli · 03-10-2003, 01:24 AM

Quote:

Am I making sense?

Yes, you are now.

Although I would argue that one of the 2 truths is more "truthfull" than the other, because it more closely describes the issue of the question.
Both yes and no can be true answers to the same question, if the 2 people use different definitions of the words in the question, or if the question or the answer is too vague.
But, if truth is completely dependent on the person answering doesn't it become an opinion?

Truth is a product of information, and is intended to communicate information between individuals. It seems then paradoxical that a statement may be true to one person but false to another. It kind of defies the whole point with truth.

John Page · 03-10-2003, 06:57 PM

Quote:

Originally posted by Theli
It seems then paradoxical that a statement may be true to one person but false to another. It kind of defies the whole point with truth.

On the other hand, if people are comprised (partly) of information and its associated processes its inevitable that such differences will arise.

Cheers, John

John Page · 03-10-2003, 08:05 PM

Thought I'd have a crack at further elaborating a system of Dialetheic Logic (actually, I'm for Multiletheic Logic but I haven't invented that yet) so here goes.

To be perverse

and to show the contra position to certain aspects of propositional logic, I thought I'd call the first axiom "Law of Non-Identity" which states:

Quote:

An identity may be conferred, by an observer, upon an entity that has been perceived as different from its surroundings. In this context, an entity may be considered as a perceived part of reality, such entity therefore comprising material that invokes a non-random pattern in our senses. Each non-random pattern (entity appearance) is unique, if it were not so then our senses would not have been able to differentiate it from other non-random patterns in reality (other entity appearances).

Example: An entity appearance is directly experienced by the "sensing body" and is represented here as the letter e. Entity appearances that have similar form may be categorized by the sensing body. The sensing body is then exposed to all the lower case letters in the English language, {a,b,c,d,e......z}, which are (by an analytical process not described here) described by the sensing body as having the same identity "lower case letters of the English alphabet".. In this example, the sensed entities {a..z} have been conferred this complex identity through similarity with all the forms {English, letters, lower case, alphabet} falling within the identity definition. Note: Symbolization is a different process where the symbol may be arbitrary and therefore meaningless without some form of semantic table relating the symbol to its indended.

This Law of Non-Identity is so named because entities have no intrinsic identity, such identities are conferred by the observer. The law of non-Identity is symbolically represented by the expression "This e cannot be that e"

John Page · 03-11-2003, 06:47 AM

Now for the second law of Multiletheism.

Quote:

The Law of Contradiction states "Every proposition for equality is a contradiction to the Law of Non-Identity." Propositions of equality, therefore, either imply or state there are both quantitative differences and similarities between the entities being equated.

Example: This e and that e are the same. Here, both e's have the same form, which appear constant (over time) to our perception, and both e's are similar in shape so they may achieve the same symbolic value, and they are different in spatial coordinates so they may be quantified as being two in number.

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