The Difficulty Of Communicating Absolute Truth Statements

Barely gagging on my egg sandwich as I watched Trump at a National Prayer Breakfast this morning, I had to smirk when he babbled "And freedom is a gift from God".   This from an imbecile who likely wouldn't be able to find chapter and verse of a biblical quote from his bible - assuming he even has one. 

But it interjects the question of how much of what he said is true, and how much is BS.  Or was it all just made up crap - like in his exec orders (actually written by Steve Bannon) to get applause from the dopey peanut gallery?  Can there even be an absolute truth statement in religion (or science) and if so what attributes must it have?  What are the criteria, or are we limited to only relatively true statements?

Philosopher Herman Philipse has noted we may legitimately show respect for religions (or religious statements)  because they reflect deep human longings. However, we are not obliged to show any respect when they put forward claims of knowledge  (Philipse.: Free Inquiry (Feb./Mar. 2007, 37). In this sense, Trump's claim that freedom "is a gift from God" is meaningless. He could as well be blabbering about flying monkeys taking over the world.

Given the above, one may inquire into the inherent problems in articulating any alleged true statement. Scott Soames (1) clarifies the issue by appeal to more and less general schema to arrive at truth in a convergent way. Soames defines what is materially adequate.

He does this by referencing “Level 1” or L1 statements, depicted as partial definitions.¹ The task of communicating truth in language then reduces to consistently generalizing partial definitions to cover every type of sentence and condition. This also assumes the subjects, objects included in the statement have specific meanings - or "operational definitions", in the case of scientific statements.

He goes on to note that Tarski’s definition, i.e. that if an earlier iterate allows for additions without contradiction to the original proposition (truth statement), then we can arrive at materially adequate sentences. In this sense, most scientific explanations – while admittedly partial – are nevertheless materially adequate. But do they amount to true statements?

Consider the following sequence of L1 statements for solar flares and note the ascending hierarchy of information presented:

1) A class X-7 solar flare occurred last Tuesday.

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

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

4) A class X-7, optical class 2B solar flare occurred at 22h 33m GMT last Tuesday, and lasted 1440 seconds.

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

Are all of the above statements, referencing the same event, true? 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 is expressed can it be said to be the truth without reservation?

Obviously, the statements given are successively more materially adequate by degrees, but none of the statements are wholly materially adequate unto themselves. For example, using any of the statements (1) - (3) one would not be able to obtain an estimate of the power or energy released which requires knowing the flare’s duration. As one moves in ascending order each statement contains more material adequacy, hence arguably more truth than its predecessor, simply because one can obtain more from the information. Thus (5) is more true than (4), (4) more so than (3) and so forth. Is (5) the last word? Consider this description of the event:

A class X-7, optical class 2B solar flare, occupying an area 1800 millionths of a solar hemisphere and located at heliographic longitude 90 degrees, and latitude 22 degrees, occurred at 22h 33m GMT last Tuesday, peaked 543 seconds after inception, and lasted a total duration of 1440 seconds.

Thus, one is unlikely to deliver all the material and relevant truth on the solar flare at once since data generally aren’t processed simultaneously, certainly about a complex physical event. Even in the course of normal human interactions, and particularly teaching, total conveyance of information is unlikely. Is this a lie by omission? Hardly! In the case of physics teaching, even attempting to convey the full basis of Newton’s laws of motion would take one hundred times longer than the standard classical mechanics course if all details and exceptions were included. In the interest of time and convenience, therefore, one must often omit the whole truth, assumed to be a complete description of a phenomenon or the principle that governs it.

“The whole truth and nothing but the truth” may well be a fine courtroom bromide but it doesn’t make the practicality cut. Can one have true statements which do not express the entire truth but rather only a partial truth? Yes, and these are none other than the L1 statements by Soames’ definition. As Soames puts it²:

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.

Carrying this further, there is no way any practical expression of language can encompass more than limited truth. What does all of this say about any truth claim?  It says that in general truth claims must be treated with great skepticism, and in the case of scientific claims, confidence levels for them must be demanded.. At any rate, one must always assume the initial claim for truth is partial, or at the L1 level. The claimant must be then pushed as far as possible to disclose the maximum content of the truth as he understands it, especially if the truth claim is made dogmatically.

In terms of scientific publications and the formulations of scientific methods - as I will show in a later blog post- it implies one must treat them carefully. For example, one must be aware the different scientific methods exist, not one frozen in stone. These will therefore differ depending on whether the object of inquiry is a stochastic one, say like climate change, or a deterministic one - say like computing the orbit of Enceladus.

By contrast,, Trump's statement that "freedom is a gift from God" is totally devoid of even a limited truth aspect. For example, he hasn't even defined what he means by 'God" and we can't assume ab initio that he knows or that it comports with any traditional versions. 

Indeed, most people are unaware that when they use the word G-o-d they’re not talking or writing about an actual entity  (i.s. that they know like I do a solar flare) but a limited construct or ideation configured as a noun, which is really a God concept. Further, because it’s limited by content and comprehension, i.e. by finite minds with finite intelligence which can’t grasp all aspects, then all such concepts must be relative and subjective. This means that the Jewish concept of Yahweh, the Muslim concept of Allah, the Hindu concept of Brahmin and the Christian concept of the Trinity all stand in the same epistemological relation.  From an informational point of view, none can be selected as “true” to the exclusion of the others.

What this means is that neither Trump, Pence or any of their other cohort can show in an absolute sense that what they mean by "God" is distinct from what the Muslim means - and hence that their version is superior.  In science, at least, we have the advantages of future observations and experiments which ultimately will be able to isolate verified hypotheses or theories from failures - say like the basis for the downfall of the steady state theory because the 2.7 K background cosmic radiation was discovered that supported the Big Bang - not the steady state.

In religion, no similar observational or experimental measures apply, hence the religionist is compelled to fall back on faith, nothing more. In other words, Trump and those he was talking to can believe freedom is "a gift from God", but there is no substance behind it for the rationalist or scientist. We instead accept that humans crafted the concept of freedom with their brains - honed by evolution- and that they also defined the markers, criteria for human freedom. This enabled it to be referenced in documents that underlie our governance.  The Founders themselves who may have referenced a deity, were actually not Christians - but Deists - with their own limited God concept at variance with that of the orthodox Christian version.

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1 Soames: Understanding Truth, 69.

2 Ibid.

Extending the Power of Logical Argument: Coherent Propositions and Truth Functions

While some may question the extensive application of logic (see e.g. my previous post on logical fallacies) to human disputation, it is important to bear in mind logical rigor doesn't come naturally to most humans. We are not all 'Mr. Spocks', after all, nor is it likely our significant others would want that. Hence, when we are confronted by a debate or having to make a logical and coherent case we have to be prepared to summon great energy and often investment of time to ensure: a) we don't mix 'apples' and 'oranges', and b) we consistently use each in its proper reference frame.

A certain level of rigor or discipline then must be applied to ensure coherent, critical thinking, especially taking care that  truth categories are not mixed up and that claims of truth aren't confused with attitudes to truth! Sadly, most who pontificate on matters of religion, or economics,  have probably never taken a logic or philosophy course in their lives, so end up flying by the seat of their pants - and end up crashing and burning.

The purpose of this post is to extend the power of logical argument beyond the basics laid out in recognizing assorted logical fallacies.  I do not promise the going will be 'easy' only that the energetic reader should be much better able to handle him (her-)self in a debate or argument afterward.

Preliminaries:

1) One cannot assume a "logical deduction" unless there exists a relationship between the premise and the conclusion such that we have a right to expect the conclusion IF we know the premise is true (cf. Russell, Introduction to Mathematical Philosophy, p. 145)

Said relationship then ought to be between analogous truth claims OR attitudes,  but not mixing up both.

2) From (1) it follows that two truth functions which have the same truth value for all values of the argument are indistinguishable. Thus, p and q are the negations of not-p and not-q.

In terms of propositional functions, let q = S(A) and p = S(B). Then if p = f(q) the contradictory hypothesis is p' = f(~q) .

Example: if p = f(q) = "The Bible is the actual word of God verbatim and cannot have either errors or contradictions"

BUT - if one error or contradiction is found in it, we must have: p' = f(~q) or:

"The Bible has a contradiction in it, so cannot be the actual word of God, but of mentally-limited humans."

3) Five basic truth functions exist (op. cit.)and are not all independent:

i) The 'negator': Not-p

Expresses that function of p which is true when p is false, and that which is false when p is true.

Note: The truth of a proposition or its falsehood is referred to as its "truth value". This can be either TRUE or FALSE, i.e. the true value of a true proposition is true, and the falsehood of a false proposition.

Thus: Mars has two Moons, Deimos and Phobos, is a true proposition, and

Saturn does not have 101 Moons, is a true proposition

ii) The disjunction: p OR q:

This is a function whose truth value is 'truth' when p is true and also when q is true. (It can be mechanically-electronically embodied by the logical OR - gate)

But the truth value is falsehood when both p and q are false.

iii) The conjunction: p AND q:

Has 'truth' for its truth value when BOTH p and q are true, otherwise falsehood.

It is denoted by the logical AND gate.

Example: p : "Solar flares erupt with large areas and temperatures in the millions of degrees"

q: "Solar flares result from magnetic instability in the associated plasma"

iv) Incompatibility: ~ (p /\ q)

E.g. p and q are not both true, or the negation of conjunction (iii). It is also the disjunction of the negations of p and q, i.e. not-p or not-q. The truth value appends 'truth' when p is false, and also when q is false. Likewise, the truth value appends falsehood if both are true.

v) Implication: p->q (p implies q) or "if p, then q"

Example: If the New Moon is aligned with the Sun we can get a total eclipse of the Sun

Here: p = alignment of Sun and New Moon

q = total eclipse of the Sun

This can be generalized in various ways, e.g.

"Unless p is false, q is true" OR

"Either p is false or q is true"


4) Further generalizations are possible using (1)-(3), e.g.

a) Negation is the incompatibility of a proposition with itself, or p/p

E.g. "the Apollo astonauts brought back Moon rocks made of green cheese"


b) Disjunction is the incompatibility of not-p and not-q or (p/p)[(q/q)

Example: "Saturn is not a very large or hot star"

c) Implication is the incompatibility of p and not-q, or p[(q/q)

Example: "If the Moon rises tonight, the Sun will not rise tomorrow"

d) Conjunction is the negation of incompatibility, e.g. (p/q)[

Example: "Saturn and Earth are both member planets of the solar system"

5) Gödelian Truth Limits:

Consider a 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. Since in any consistent system nothing false can be proven in-the-system, the proposition is undecidable.


Now, given all these basics, let's see if we can apply them to the assertions or alleged propositions made by a recent blogger:

Example (1):

"All TRUTH is exclusive ! The truth that "two plus three equals five" is very exclusive too . It does not allow for any other conclusion ."

The basic and most fundamental error is that he mixes up an absolute general statement, with a particular one. "All Truth is exclusive" is in fact unprovable by the same set of axioms or axiomatic statements that would prove "2 + 3 = 5". The reason is that the first is a meta-statement about the WHOLE Truth system! To be more concise, the offender is rendering an ALL-inclusive truth statement about what he insisted is an absolute exclusivity! He claims "all truth is exclusive" but his statement itself is all-inclusive and implied to be the exception to his own proposition! Thus it violates the Gödelian Truth Limits (5).

It helps here to present a more concrete illustration and example, to show why the most general statement is false. We take here the original claim of Epimenides in his “all Cretans are liars” paradox:

"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 Gödel’s Incompleteness Theorem (II) applies.

In like manner, the statement "All Truth is exclusive" emerges as an undecidable proposition at the very least. (And it may also be false in the framework earlier considered).

Scott Soames in his monograph Understanding Truth further 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.”

In other words, in order to make the claim: "All Truth is exclusive" one would have to: a) have access to ALL COMPLETE truth statements that can exist in the universe, and b) show that no two of them exhibit disjunction, or incompatibility of other problems. In addition, one would have to articulate his proposition as compatible with the claim: in other words, one cannot formulate an all-inclusive truth statement to apply to one for which "All Truth is exclusive". This is not feasible, because no human mind is capable of formulating an absolute exclusive truth statement via an all-inclusive truth claim.

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) EXCLUSIVELY 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? Obviously, the answers are in succession: NO - they can't all be exclusively true (on account of factual intersection), NO - they are not all equally true (since they embody different levels of knowledge about the event), but YES - one can have TRUE statements which only convey a partial truth.

Now, if one can have partial truth statements then one can still access truth or true valued assertions at some level.

Let's go on:

Example (2):

"The same is true for value statements , such as "Racism is wrong" and "People should not be cruel." These views do not tolerate any alternatives . "

The problem here is that he has not proven the values are actual truth values, as opposed to the subjective values of a moralism in his own mind. In particular, he's violated Precept (1): "One cannot assume a "logical deduction" unless there exists a relationship between the premise and the conclusion such that we have a right to expect the conclusion IF we know the premise is true". But he has formulated no premise, because he's not defined either "racism" or "cruel" - he simply assumes everyone knows exactly what he means! Hence, he leaves us no testable proposition that can be put into any logical relationship, far less link a premise to a conclusion.

Questions then occur: E.g. : Is drawing or portraying President Obama as a witch doctor with a bone through his nose, racism? If not, why not ? The first step in setting out a premise that portends a "truth value" is therefore to carefully define one's terms, don't assume everyone knows what you mean!

So, IF he defines both "racism" and "cruelty" and then integrates them into a premise, tied to a conclusion that relates them- we may then consider whether "These views do not tolerate any alternatives". (In which case, depicting President Obama as a witch doctor with a bone through his nose may not meet the criterion of an "alternative" to him, hence can be "tolerated" - but as he's framed his case, we can't say so because it's too vague.)

Example (3)


"All truth CLAIMS are exclusive . For example , if humanism is true , then all non-humanisms are false . If atheism is true , then all who believe in God are wrong . Every truth claim excludes its opposite ."

As I already showed (Example (1)) the first statement is an undecidable proposition by virtue of en embedded contradiction. Thus, we behold an all-inclusive truth statement intended to apply to the proposition that "all truth is exclusive"! Thus it is a meta-statement about truth claims, not a statement within an axiomatic system concerning a class of truth claims. Thus, it is a non sequitur to flip from this most general, undecidable proposition to saying "thus if humanism is true all non-humanisms are false". In addition, it's an oversimplification, since one can have a conjunction (3(iii)) such that a truth value exists when BOTH p and q are true. (And again, we note he's neither defined "humanism" nor "non-humanism" so we've no idea what he means.)

But let's use the conjunction of propositions to show discrete and particular possibilities that defy his simple conclusions. It is known that in its most generic sense "humanism" means :

That philosophy or coherent attitude supportive of human values, i.e. those values that elevate, sustain and integrate a society beyond its merely physical or mechanical operations

Thus, our society provides physical infrastructure - such as roads, sewers, water mains, etc. and also mechanical contrivances (buses, or cars, trains) to help the people survive but humanism allows support systems beyond these basics, for example, decent and affordable health care. The reason is that a society without quality affordable health care (accessible to all) cannot function to its optimum. If too many are ill, then they can't be productive and if not productive, the society deteriorates because too few must work to care for the many who are ill or otherwise disabled.

The underlying conjunction here (p and q) is:

p: Humans are worthwhile beings to support in other ways besides purely mechanicalq: All humans have the same essential needs for humane support, so all should thereby be provided with said humane support

Since (p -q) defines the conjoint truth value, then "non-humanisms" would have to mean non-humans and would thereby be ab initio excluded from the proposition putatively concerning HUMANS. Hence, the claim of "non-humanisms" implicit in a human domain is a falsehood since it wouldn't apply to humans anyway! (Though one can argue that an "extended humanism" would also confer health care on animals in need, or at least certain classes of them, i.e. personal pets)

The statement about atheism is also invalid, because it reduces atheism to one meaning, ignoring all others. (For example, implicit atheism, and agnostic atheism). It would be like me writing: "If evangelical Christianity is true , then all other Christians who believe in God are wrong". This is arrant nonsense. Moreso since it hinges on the claimant providing the necessary and sufficient conditions for his (exclusive) deity to exist - thereby showing why its conditions supersede those of other Christians. To append a truth value to the statement then, a specific definition of atheism is needed, not an open-ended term that invites any reading.

Finally, the appended proposition:

"Every truth claim excludes its opposite ."

Has already been shown invalid, since it omits consideration of the fact that conjunction is the negation of incompatibility, e.g. (p/q)[. If one can have any conjunction, uniting propositions of truth p and q, then clearly a contingent truth claim p does not exclude its co-contingent q. As a more or less trivial example:

p: "Every photon of light is a particle"

q: "All light is waves"

In fact, as noted before in a previous blog:

http://brane-space.blogspot.com/2010/06/more-on-heisenberg-microscope-in.html

Both statements can be true, provided the optical limits of observation are made clear. It is this very example, underscored by quantum mechanics, which displaces the either-or exclusionary absolutism of the claim. In other words, the actual experiments of QM show that observables in the form of propositions can be BOTH and not merely one OR the other! This is the very basis for the development of quantum logic, see e.g.

http://brane-space.blogspot.com/2009/09/foray-into-quantum-logical-and.html