In the prior instalment we looked at how truth is difficult to encompass in any absolute or final mode. We left off with a number of statements pertaining to an actual solar flare, and then questions followed concerning the level of truth applicable to each.
We revisit the statements first:
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.
We now consider each of the questions in turn:
(1) Are ALL of the above statements (referencing the same event) true? Or better, are they all EQUALLY true? If not, why not?
Obviously, the statements are successively true by degrees, but none of the statements are wholly and completely true. Each one, as one moves in ascending order, contains more "truth" than its predecessor. Thus (5) is more true than (4), (4) is more true than (3) and so forth. Is (5) the last word? Not even close, for one can still write:
A class X-7, optical class 2B solar flare, of area 1800 millionths of a solar hemisphere and located at heliographic longitude 90 degress, and latitude 22 degrees, occurred on the Sun at 22h 33m GMT last Tuesday, peaked 543 seconds after inception, and lasted a total duration of 1440 seconds.
Thus, one cannot deliver all the truth on the solar flare at once, certainly about a physical event. In the course of normal conversation, and particularly teaching - one will therefore be forced to lie. In the case of teaching, even attempting to convey the basis of Newton's laws of motion would take 100 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 "subvert" the whole truth. (Another reason we ask students to read extensively outside the course).
2) Can one therefore have true statements which do not express the entire truth but rather only a partial truth?
Yes, and these are called L1 or level 1 truth statements, by Soames' definition (see previous entry). As Soames put it:
"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 realistic language - practically based- can encompass more than limited truth. Take this exchange:
"Where is Mr. Jones, our accountant?"
"He had to go to the bank to cash a check".
But the more accurate statement might be:
"Jones had to go the bank on 18th street to cash a check because the bank on 11th street was too crowded, so he had to take a detour around the 12th street Viaduct, and come in from the south side overpass. He then had to walk a mile, because the closest parking was a mile from the bank across the river."
Technically speaking, the responder told a white lie. That is, he neglected many key elements that otherwise might account for Jones' tardiness from his desk. But the conveyance of the total information omits many details that do not add to the substance of the original or L1 statement.
Thus, the way our language is constructed, it is designed to omit more information than is actually true, and so limits the full exposure of any given truth statement unless it is almost a tautology.
3) If a partial truth only is expressed can it be said to be "the truth" without any reservations?
Obviously, as seen from the above, and the solar flare example, it cannot. When one uses the phrase "THE Truth" it is implied that the embodiment is totally, 100% complete, not partial. There is a good reason for this, because partial truth statements can be contradicted.
For instance, if one says: "Jones was at the 12th Street Viaduct", and "Jones was at the River near 11th Street" these may appear to contradict each other, because they are partial (L1) statements only. However if the more complete versions are conveyed:
"Jones was at the 12th Street Viaduct near where it crosses River Street"
"Jones was at the River near 11th Street, adjacent to River Street across from the 12th St. Viaduct"
then the contradiction may be seen to vanish.
4) Can the Godel Incompleteness theorem(s) be applied to all or most incomplete statements?
As we see, they could if the statements are incomplete and these may be construed as contradictions. A good way to test statements, then, is to try to write them in Boolean or some symbolic language or form, then compare them after. Consider these two statements, pertaining to material evidence in the JFK assassination case:
p: 'All of the bullet fragments recovered were from a 6.54 mm Mannlicher-Carcano'
q: 'All of the bullet fragments recovered were from a 7.65 mm Swedish Mauser'
We write the symbolic form for these:
~ (p /\ q) e.g.
Two statements p and q, are contrary if they cannot both hold. Note, however, that two contrary statements may both be false!!
Note also that all contradictory statements are contrary, but many contrary statements are not contradictory, i.e.:
'Lee Harvey Oswald was observed in a 6th floor window of the Texas Book Depository'
'A swarthy man was observed in a 6th floor window of the Texas Book Depository''
They are not contradictory because a man was observed in a 6th floor window. The "swarthiness" is not fundamental to the falsity of the statement because a shadow may have fallen at the time of the observation.
5) Does this application allow for contradictions because of the latent incompleteness? Would such a partially true statement be unprovable?
In the case of the solar flare example, not very likely unless the flare was homologous (e.g. occurring almost simultaneously at two nearby locations) and the L1 statements aren't refined enough to separate the heliographic coordinates. The residual statements would then remain unprovable only if no higher resolution observations were forthcoming.
6)Do we know that the final statement (5) is the FULL, true statement of the event?
Obviously, as I've shown, (5) wasn't the FULL true statement of the event. One came after it which also appended the heliographic coordinates as well as the area of the flare in millionths of a solar hemisphere.
7)If not, what does this say about any truth claim?
It says that ALL truth claims must be taken with great skepticism. at any rate, one must always assume the initial claim for truth is made only at the L1 level, so the claimant must be pushed as far as possible to disclose the maximum content of the truth as he understands it, for his claim.
For example, the claim:
"The Bible is the actual word of God verbatim"
Can be pressed in multiple ways. What Bible? If the KJV, which we know is subject to gross errors in translation from the Latin Vulgate, why? What led to certain parts being omitted? Which God? What is the ontological basis for it, necessary and sufficient conditions for its existence...that we may distinguish it from: Allah, Brahmin, Yahweh, etc. ?
Unless these questions are all addressed and answered fully, the person can't be regarded as having made a truth claim, but rather a casual conjecture about his personal reality, as HE believes it. He may believe, for example, that his bible holds 100% of the absolute truth in every passage, but that is not what L1 levels of partial truth definitions indicate. They say rather that not only are all the passages of the bible (any bible) partial statements, but they are also likely false partial statements as well. Particularly as many paired off together yield contradictions.