Return to Hughes-Buridan
Here is an outline of what Hughes tells us about Buridan's
theory of the meaning of truth:
- Things that are true or false are propositions.
(Note 1: use Aristotle 1027b
- A proposition is a sentence token.
- Two identical utterances or inscriptions of the same proposition
are different propositions: They are equiform (isomorphic) propositions.
- 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.'
- A proposition must be assertively spoken or written.
- No part of a proposition is itself a proposition. A part
could be a proposition if it were asserted on its own.
- A proposition must be a meaningful sentence:
- A proposition has meaning.
- Convention determines meaning of a proposition
- One proposition in two or more conventions may have multiple
- One proposition may have conventional yet ambiguous meanings.
- 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.
- Languages are conventional media we use to express mental
- Words signify expressed concepts within the mind. (E.g.,
- Words signify expressed concepts
outside the mind. (E.g., horse.) Note
- Ultimate significates are outside the mind.
- Outside-the-mind-words are categorematic words. (E.g., horse
is categorematic; horseness is not.)
- Syncategorematic words
synthesize more complex concepts, (e.g., some, not, or), and
have no ultimate significates. Note
- Some words are neither purely categorematical nor syncategorematical,
but mixed, e.g. 'someone.'
- Some objective attributes, like 'white,' are categorematic.
- Simple - e.g., horse & white
- Complex - e.g., dragon & white horse
- Ultimate significates of 'white horse:' all horses with attribute
- Ultimate significates of 'white horse' are what we understand
'white horse' to mean.
- 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.
- Complex verbal expressions may be simplified, i.e., chimera
for the long verbal expression of a Minotaur.
- Ultimate significates of, e.g., 'chimera,' are: all ultimate
significates of all parts of the complex expression.
- Thoughts that express a concept are mental propositions.
- There are two kinds of propositions: (Note the classical
SOM dichotomy here.)
- Mental propositions do not have conventional signification
since mental propositions are concepts in themselves.
- There are multiple types of categorical propositions:
- Four syllogistic forms:
- A - universal affirmatives
- E - universal negatives
- I - particular affirmatives
- O - particular negatives
Of the general form: Quantity; subject; copula; predicate.
- Indefinite propositions which lack quantity (an) (Buridan
assimilated this type.)
- Singular propositions which express unity (a) (Buridan
assimilated this type.)
- 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:
- A common medieval view was that, 'as it signifies, so it
- Buridan shows that this is absurd.
- It is interesting that he does so, essentially by showing
that the rudiments of quantum science are absurd! (see p. 13)
- Another view was that a proposition as a whole signifies
some abstract entity (i.e., is a syncategorematic significate).
- Buridan shows that this is absurd.
- Buridan concludes that a theory of truth needs what logicians
Clearly, the medieval views - not
Buridan's - were problematic.
Hughes elaborates Buridan's work on
supposition theory, next:
- A view of supposition theory:
- depends on the (selected and global during use) context of
the proposition Note 5:
- assumes a propositional context
- "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:
- "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:
- "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
- There are two kinds of suppositions:
- significative (AKA personal)
- 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
- Supposition with correspondence truth conditions:
- A - Every subject is (a) predicate
- with correspondence:
- (i) Subject stands for something, and
- (ii) Everything subject stands for, predicate stands for.
- E - Negation of I
- I - Some subject is (a) predicate
- with correspondence:
- Subject and predicate stand for the same thing, i.e., subject
and predicate have some common member.
- O - Negation of A
- ...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:
- Buridan claims, "any proposition
is false from which, together with something true, there follows
something false." Hughes claims this is essentially self-contradiction.
- The implication is that (classically) if contextual inconsistency
elicits falsity, then truth demands contextual consistency. Note 10:
- "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:
- 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:
- 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
- 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.
Note 3: E.g., reviewer
interprets this as synthesis of categories. Return
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
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
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
Note 8: Classical logic
states unambiguously that classical objects "possess"
attributes. Attributes are in classical objects. Return
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
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
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
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
Whole classical objects do not exist! There is no such
thing! See Figure - Quantum
Egg 'C' Object.
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Rev. 11Nov2007 PDR Created: 3Nov1998 PDR
(9Jan2000 rev. Minor typos, etc.)
(18Jul2004 rev - Add links to QELR of 'empirical,' and 'judge.')
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