Wednesday, December 23, 2009

The Truth Hurdle - Part I

Ever since Pilate ostensibly asked Jesus "What is Truth?", people have pursued the question with great intensity. After all, if one cannot know truth, then one cannot possibly decipher untruth - at least under all circumstances. If this is so, then one must settle into a relativistic world. One in which meanings, events, and principles display no durable properties.

In the next two instalments, I want to make a foray into the issue of truth, not merely in a superficial way, but to get at the ontological base. We will then be in a better position to argue about it and indeed, whether it's even worth arguing about. Or perhaps better, replacing the truth concept with a relativistic and subjective idiom more attuned to the actual capabilities of the human brain.

Perhaps the biggest impediment to absolute truth in the last century was Godel's Incompleteness Theorems. These were propounded by the mathematicial Kurt Godel in the 1930s and state that in any consistent system which is strong enough to produce simple arithmetic there are formulae which cannot be proved-in-the-system, but which we can see to be true. Essentially, we consider the formula which says, in effect, "This formula is unprovable-in-the-system".

In a much more generic sense, the application goes way beyond mathematical formulae or arithmetic axioms to actually encompass any statements which can be framed in those terms. This is very important to grasp. Let me give examples.

Consider the simple statement of logical transitivity:

X = Y

Y = Z

therefore X = Z

What if instead we append an axiomatic statement that reads, in effect: "X=Y is unprovable-in-the-system". If this statement is provable-in-the-system, we get a contradiction, since if it is provable in-the-system, then it can’t be unprovable-in-the-system. This means the original axiom: "X= Y is unprovable-in-the-system" is false. Similarly, if X= Y is provable-in-the-system, then it’s true, since in any consistent system nothing false can be proven in-the-system, only truths.

So the statement:-axiom: "X = Y is unprovable-in-the-system" is not provable-in-the-system, but unprovable-in-the-system. Further, if the statement-axiom "X = Y is unprovable in- the-system" is unprovable-in-the-system, then it’s true that that formula is unprovable-in-the-system. Thus the statement, "X = Y is unprovable-in-the-system" is true.

With these preliminaries, let’s examine the logical structure ascribed to most religious concepts. According to Pascal Boyer (Religion Explained), we get a syllogism like:

If X, then Y

If X, then Z

so, Y = Z

But, Z /\ Y (contradiction)


If a eucharistic consecration (X) is performed, then a bread wafer (Y) becomes Jesus' body or flesh (Z).

Bread wafer = body-flesh

But, actual chemical tests show the bread wafer is starch, not flesh or protein!

Religious concept:

The identity Y = Z refers to a statement of substance.

The contradiction Z /\ Y refers to the outcome of “accidents”

Thus, the statements embodying substance: (S + 1) > S, where S denotes the axiomatic statements embodying the accidents.

We call such statements “meta-statements”.

In a manner of speaking, the religious concept claimant is in a similar position to Epimenides in his “all Cretans are liars” paradox, which itself perpetuates a causal loop with no closure. E.g.

"All Cretans are Liars"

If the speaker is a Cretan, then the statement is ipso facto unresolvable. If Cretan, he exists within the so-called abstract, formal system. Yet, he’s making a statement (meta-) about the system. Hence, is he lying? Or is he telling the truth? This cannot be resolved. An undecidable proposition, as Godel’s Incompleteness Theorem (II) applies.

Is there a way out of the loop? Yes, if one uses realist science to assess statements. For example, in the Einstein equation, E = mc^2 , scientific epistemology allows us to regard E, m and c as constructs, connected via operational definition to the P- (perceptual) facts of: energy, mass and the speed of light. Thus, we expect a correlation like:

C <-> P

This re-affirms logical closure, physical significance and no meta-linkage.

For instance, the operational definition of “mass” is accomplished by comparing inertias, using detected accelerations via: m2/ m1 = a1/a2 and Newton's 2nd law say in a collision or motion (down an inclined plane) experiment.

In effect, even if a science or research hypothesis may include some open or meta-statements (evidently leaving the room open for undecidable propositions) there are nevertheless empirical checks and tests that can close the system parameters. Nothing similar exists for supernatural claims embodied in religious concepts.

Consider the statement:

This consecrated bread wafer is the body of Christ”

Here we have neither P-facts nor C –construct. There is no confirmatory device for example, to demonstrate that the bread before me is a human body. The statement is open-ended, and could also be delirium tremens or maybe the product of a micro-seizure in the brain’s temporal lobes as researcher Michael Persinger has shown (e.g. in his special electrical helmet experiments to stimulate subjects' temporal lobes).

Worse, we can’t even identify unique and distinguishing attributes that point to the validation of the claim. Without even venturing into the realm of P-facts, the set of C-constructs (“bread”, “body of Christ”) is ripe for self-reference as well as the intrusion of incompleteness with no available cross checks!

What if, instead, one ignores this, and assigns attributes willy-nilly? Say by insisting: “well you cannot detect the body because you are only able to ascertain base physical “accidents” (e.g. starch or carbohydrate composition) using scientific analyses. In this case the claimant commits reification. He imposes his preconceived percepts on what is in reality an open-ended field. For such an open field, discussion is fruitless, since it ends up being a mental Rohrshach for the benefit of the proponent.

By contrast, the advocate of E = mc2 (e.g. from nuclear fission or fusion reactions) has no latitude or degrees of freedom to “fill in” anything, since all P-facts are already defined by specific constructs and operational definitions which have very exact meaning in physics. (e.g. c, the velocity of light, or about 300,000 km/sec) There is no wiggle room, and this lack of wiggle room means there exists pre-defined context, as well as escape from lurking Godelian loops.

In the end, we are entitled to reject the religious concept posed in contradictory or meta-language terms Though something is claimed (if only a possibility statement) the logical framework remains open since:

i)The claimant has not defined exactly what his terms mean.

ii)He lacks the critical, discriminatory P-facts to back up his claim; facts which can be confirmed outside his reference frame.

iii)He uses circular arguments to return to his original claim.

On account of this, as Herman Philipse has noted, we may legitimately show respect for religions because they reflect deep human longings. However, we are not obliged to show any respect when they “put forward claims of knowledge”.

Given the above, what is the inherent problem in articulating any alleged "truth" or more accurately, "true statement"? Scott Soames in his monograph Understanding Truth clarifies the issue of more and less general schema to arrive at truth, and what is “materially adequate”

p. 69:

“The characterization of individual instances of (different) schema has consequences for more general definitions of truth. If such instances (e.g. L1 statements) are thought of as partial definitions, then the task of defining truth for an entire language may be seen as finding a way of generalizing the partial definitions so as to cover every sentence of the language.”

He goes on to note (ibid.) Tarski’s definition, which is to say that if an earlier iterate allows for additions without contradiction to the original proposition (truth statement) then it may be called “materially adequate”.

In this sense, most scientific explanations – while admittedly 'partial' - are nevertheless “materially adequate”. But is this amounting to a true statement?

Consider the following statements referring to solar flares, and note the L1 hierarchy that presents:

1) A class X solar flare occured on the Sun last Tuesday.

2) A class X-7 solar flare occurred on the Sun at 22h 33m GMT last Tuesday.

3) A class X-7, optical class 2B solar flare occurred on the Sun at 22h 33m GMT last Tuesday.

4) A class X-7, optical class 2B solar flare occurred on the Sun at 22h 33m GMT last Tuesday and lasted a total duration of 1440 seconds.

5) A class X-7, optical class 2B solar flare occurred on the Sun at 22h 33m GMT last Tuesday, peaked 543 seconds after inception, and lasted a total duration of 1440 seconds.

Now, are ALL of the above statements (referencing the same event) true? Or better, are they all EQUALLY true? If not, why not? Can one therefore have true statements which do not express the entire truth but rather only a partial truth? If a partial truth only is expressed can it be said to be "the truth" without any reservations?

The kicker: Can the Godel Incompleteness theorem(s) be applied to all or most incomplete statements? Does this application allow for contradictions because of the latent incompleteness? Would such a partially true statement be unproveable? Do we know that the final statement (5) is the FULL, true statement of the event? If not, what does this say about any truth claim?

We will explore these issues at greater length in the next instalment!

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