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Here is an outline of what Hughes tells us about Buridan's theory of the meaning of truth:

  1. Things that are true or false are propositions. (Note 1: use Aristotle 1027b 18-20)
  2. A proposition is a sentence token.
  3. Two identical utterances or inscriptions of the same proposition are different propositions: They are equiform (isomorphic) propositions.
  4. Existence of any proposition may be a function of time. If the proposition exists it may be true or false. If it does not exist it is 'mu.'
  5. A proposition must be assertively spoken or written.
  6. No part of a proposition is itself a proposition. A part could be a proposition if it were asserted on its own.
  7. A proposition must be a meaningful sentence:
    1. A proposition has meaning.
    2. Convention determines meaning of a proposition
    3. One proposition in two or more conventions may have multiple meanings.
    4. One proposition may have conventional yet ambiguous meanings.
    5. As long as the convention(s) and meaning(s) are unambiguous and the participants agree to abide them, propositions may be assessed for bivalent truth or falsity on those assumptions.
  8. Languages are conventional media we use to express mental concepts.
  9. Words signify expressed concepts within the mind. (E.g., horseness.)
  10. Words signify expressed concepts outside the mind. (E.g., horse.) Note 2:
  11. Ultimate significates are outside the mind.
  12. Outside-the-mind-words are categorematic words. (E.g., horse is categorematic; horseness is not.)
  13. Syncategorematic words synthesize more complex concepts, (e.g., some, not, or), and have no ultimate significates. Note 3:
  14. Some words are neither purely categorematical nor syncategorematical, but mixed, e.g. 'someone.'
  15. Some objective attributes, like 'white,' are categorematic.
  16. Concepts:
    1. Simple - e.g., horse & white
    2. Complex - e.g., dragon & white horse
  17. Ultimate significates of 'white horse:' all horses with attribute white.
  18. Ultimate significates of 'white horse' are what we understand 'white horse' to mean.
  19. Therefore, the ultimate significates of a complex verbal expression consist of the sum total of ultimate significates of all the categorematic words that occur in it. Note 4:
  20. Complex verbal expressions may be simplified, i.e., chimera for the long verbal expression of a Minotaur.
  21. Ultimate significates of, e.g., 'chimera,' are: all ultimate significates of all parts of the complex expression.
  22. Thoughts that express a concept are mental propositions.
  23. There are two kinds of propositions: (Note the classical SOM dichotomy here.)
    1. linguistic
      1. spoken/verbal
      2. written
    2. mental
  24. Mental propositions do not have conventional signification since mental propositions are concepts in themselves.
  25. There are multiple types of categorical propositions:
    1. Four syllogistic forms:
      1. A - universal affirmatives
      2. E - universal negatives
      3. I - particular affirmatives
      4. O - particular negatives
        Of the general form: Quantity; subject; copula; predicate.
    2. Indefinite propositions which lack quantity (an) (Buridan assimilated this type.)
    3. Singular propositions which express unity (a)  (Buridan assimilated this type.)
  26. Hypothetical propositions contain: and, or, if, when, must, can, impossible, etc.

    The above covers what Buridan says propositions are and forms of propositions are.
    Next Hughes considers what Buridan had to contend with among his philosophical peers of medieval times:
  27. A common medieval view was that, 'as it signifies, so it is.'
    1. Buridan shows that this is absurd.
    2. It is interesting that he does so, essentially by showing that the rudiments of quantum science are absurd! (see p. 13)
  28. Another view was that a proposition as a whole signifies some abstract entity (i.e., is a syncategorematic significate).
    1. Buridan shows that this is absurd.
  29. Buridan concludes that a theory of truth needs what logicians call supposition.

    Clearly, the medieval views - not Buridan's - were problematic.

    Hughes elaborates Buridan's work on supposition theory, next:

  30. A view of supposition theory:
    1. depends on the (selected and global during use) context of the proposition Note 5:
    2. assumes a propositional context
  31. "There are even significant words and phrases that never have any supposition in any proposition: 'chimera,' as we saw, signifies a great many things, but it never stands for anything since there are no such things as chimeras." See p. 15. Note 6:
  32. "In general, a categorematic term in a given proposition stands for each member of a certain sub-class (possibly empty) of its ultimate significates, a sub-class that consists of just those objects that have to be taken into account in determining the truth or falsity of the proposition. Precisely what objects fall into this sub-class is determined by various features of the proposition as a whole." See p. 15. Note 7:
  33. "The above account has to be modified in one respect for terms that signify attributes rather than objects. Such terms as we have seen, signify all instances of the relevant attributes, but what they are said to stand for are not these but the objects that possess them — or some appropriate sub-class of these objects." See p. 15. (Reviewer comments on term 'possess.') Note 8:
  34. There are two kinds of suppositions:
    1. significative (AKA personal)
    2. material (self reference to a word in a sentence - 'Water has five letters.' 'Water' becomes objective/substance)
      - Use vis-à-vis mention: a crucial distinction in suppositional and modern logic.

      Next Hughes covers Buridan's supposition with correspondence:
  35. Supposition with correspondence truth conditions:
    1. A - Every subject is (a) predicate
      1. with correspondence:
        1. (i) Subject stands for something, and
        2. (ii) Everything subject stands for, predicate stands for.
    2. E - Negation of I
    3. I - Some subject is (a) predicate
      1. with correspondence:
        1. Subject and predicate stand for the same thing, i.e., subject and predicate have some common member.
    4. O - Negation of A
  36. ...Buridan treats all affirmative propositions 'existensially.' I.e., the subject must be non-empty to achieve truth. Emptiness is a sufficient condition for falsity. See p. 18. (More SOM legacy!)

    Next Hughes covers Buridan's views on contextually inconsistent propositions:
  37. Buridan claims, "any proposition is false from which, together with something true, there follows something false." Hughes claims this is essentially self-contradiction. Note 9:
  38. The implication is that (classically) if contextual inconsistency elicits falsity, then truth demands contextual consistency. Note 10:
  39. "As we have seen, in order to be true or false at all, a proposition must first of all exist. Given then that it does exist, it is true if and only if (1) the relevant correspondence truth-conditions are satisfied and (2) it is contextually consistent; otherwise - i.e., if either the relevant correspondence truth-conditions are not satisfied or it is contextually inconsistent - it is false." See p. 19. Note 11:
  40. Is the requirement for contextual consistency needed/important? Buridan says, "Yes," for the self-referent sophisms, "Yes!" The self-referent sophisms (SRSs) introduce contextual inconsistency! But he says it can only happen in SRSs. Note 12:
  41. Buridan states, "No proposition whatever, SR or NSR (self-referent or non-SR) can be true if it is contextually inconsistent. See p. 20. Note 13:
  42. Hughes states, "Moreover, I can see nothing arbitrary about the requirement of contextual consistency in any case: it seems to be no more than a spelling out of one of the fundamental principles that underlie any sound theory of deductive inference, that true premises never entail a false conclusion." Note 14:


Note 1 - Quote from Aristotle, 1027b, 18-20:

"But since that which is in the sense of being true, or is not in the sense of being false, depends on combination and separation, and truth and falsity together depend on the allocation of contradictory judgments..."

Here we see SOM's glorious TRUE vs. FALSE: versus (opposition), either/or, separability, and contradiction (opposition) as empirics of dialectical logic. We see Aristotle's veiled suggestion that SOM logic contrives its one global truth by "combination and separation" to achieve one global, conventional context. We also see Aristotle's emphasis on the bivalence of contradiction and its errant agent: human judgment. What logic is this which depends on simple bivalence and finite intellect to judge? Return 1:

Note 2: Reviewer - Notice how Buridan treats the mind as an objective entity. I.e., mind has an inside and an outside, just like other classical objects. Return 2:

Note 3: E.g., reviewer interprets this as synthesis of categories. Return 3:

Note 4: Gedanken experiment: Consider the SOM aspect (e.g., separateness or integrability) vis-à-vis the Quantonic commingling/interpenetration aspect (E.g., consider white genes inside/co-within horse as inseparable, non-integrable. Where SOM sees 'white' as a singular objective property of the ultimate significate objective 'horse,' Quantonics sees white as value interrelationships among the genetic codes which specify white, plus skin and other quantum systems whose color interrelationships reflect the color values in the codes.). Return 4:

Note 5: Pirsig would say here that we can suppose a context, but DQ will always provide more-and-changing context than we can suppose. SOM assumes that you can select a context and then use it as the, one global context. Pirsig and the quantum realm show us that you may select a context, but it is not global! It is, to a greater or lesser extent, affected by an infinity of other contexts which commingle the selected context. This is perhaps one of the most problematic SOM assumptions, i.e., one global truth in one global (selected) context. Return 5:

Note 6: Reviewer note: Hughes tells us that Buridan believed that which does not exist within the conventional, accepted context has no supposition. He uses chimeras as examples. Yet today, we know that chimeras exist. Buridan, just as Pirsig told us 19th century zoologists did, would have called platypi, "contrived." Since platypi did not exist (in the sense that people in Western culture did not know platypi existed then) in Buridan's time, supposing such was impossible. Classical logic places that which (it claims) does not exist beyond supposition for assertion of a sound proposition. Does the reader detect a bit of arrogance here? Classical logic presumes to know what — that only what it knows — exists. Return 6:

Note 7: An empty subject term would make an affirmative proposition false. Also, the statement, "Precisely what objects fall into this sub-class is determined by various features of the proposition as a whole," is telling. Might we infer from this statement that the proposition is both in and part of the context, and further that the objects supposed by the proposition are in the proposition? If the objects in the proposition are determined by the features of the proposition, does the proposition exist objectively? The reviewer wants to hear from any reader who might help us to see what both Hughes and Buridan really meant in this particular situation. Return 7:

Note 8: Classical logic states unambiguously that classical objects "possess" attributes. Attributes are in classical objects. Return 8:

Note 9: Pay attention to Hughes' and Buridan's focused presumption on one selected global context during evaluation of the proposition. In reality there are at least (for this specific instance) two contexts and the quantum reality of being both true and false, not the classical either/or. Return 9:

Note 10: In simpler terms one truth, "demands contextual consistency." The insistence on classical SOM's one truth leads to ludicrousness! Note that neither Buridan nor Hughes discerns the falsity due to contextual inconsistency being imposed by their insistence on selecting one particular context from a choice of multiple (infinite) concurrent contexts! It is extraordinary to see both of them allow for the concept of context, even multiple-but-disparate and time sequential (i.e., non-concurrent) contexts, and then insist on one global truth! What is extraordinary is their blindness to the reality of an infinity of concurrent contexts. This is fundamentally what is problematic with classical reason. It derives from the Subject-Object schism at the heart of classical metaphysics. See p. 18. Return 10:

Note 11: All they need do is allow for multiple contexts, and the issue of contextual inconsistency dissolves. Return 11:

Note 12: We disagree: we think paradice (paradoxes) in general arise from SOM-perceived contextual inconsistencies. Many truths (~local context relative truths) when managed assiduously and concurrently (ideally at a Planck rate, with relativistic considerations when appropriate) repairs SOM paradice. Sophisms are not problems! Sophisms are not insoluble. Sophisms demand that we perceive a new reality of many contexts and many truths. Indeed, we must perceive existence of many contexts and many truths is a verifiable quantum reality. (This is a major point about Hughes' and Buridan's classical SOM philosophical assumptions. They deny reality and dictate one selected/used/contrived global context during the evaluation of sophisms! But the new quantum/quantonic/MoQ reality shows us unambiguously an infinity of local contexts in concurrent existence!) Return 12:

Note 13: This is pure SOM! The quantum reality we know today is vastly contextually inconsistent, therefore we must agree that truth and falsity are a complementary relationship — a quanton! I.e., there is an uncertainty relationship twixt truth and falsity! Quantum-logical truth is not absolute!!

It is clear to the reviewer that formal logicians are philosophically incapable of accepting the reality of multiple contexts. To do so, causes such great upheaval in their beliefs as to garner their own instant insanity viewed both by self and peers. Return 13:

Note 14: We disagree strongly! Especially when the truth of the premises stands on the existence of a classical object. The Western classical SOM philosophical underpinnings of the last 2500 years are simply wrong! The edifices, empires, and reputations built on those underpinnings have to fall. Both Pirsig's MoQ and quantum science show us unambiguously that classical objects are intrinsically incomplete. The models built, based on those incomplete objects are WRONG! (See Stein's work reviewed nearby.) SOM severs the subject from the object, and because of that classical science insists on an objective reality. Then to make matters even worse, classical science denies the existence of the quantum complement to all (both subject and object combined) actuality, not just the objective part.

We can state with certainty now, that premises of formal logic based upon the existence of classical objects in a single, conventional context will, in general, often be false. Why? Because basing premises on the existence of whole classical objects is fundamentally wrong.

Whole classical objects do not exist! There is no such thing! See Figure - Quantum Egg 'C' Object.
Return 14:


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©Quantonics, Inc., 1998-2009 Rev. 11Nov2007 PDR — Created: 3Nov1998 PDR
(9Jan2000 rev. Minor typos, etc.)
(18Jul2004 rev - Add links to QELR of 'empirical,' and 'judge.')
(11Nov2007 rev - Reformat slightly.)