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Review of Hughes' John Buridan on Self Reference

This book review is about John Buridan's Sophismata. It is a review about sophisms. It is about fundamental concepts of self-reference.

Sophisms arose long before Aristotle. Philosophers, dialecticians, and logicians grappled with sophisms for millennia. Yet neither formal logic, nor predicate logic, nor propositional logic, nor any logic based upon classical Greek philosophical assumptions has been able to resoundingly solve apparently insoluble sophisms. Until Buridan's time, early 14th century, sophisms were indeed insoluble from a classical perspective. Buridan tried valiantly and claims he did solve all (20) sophisms he presented in his Sophismata. Hughes in his own study of Buridan's works, even now in late 20th century, concurs with Buridan's results.

Hughes uses his following approach in a review of Buridan's Sophismata:

Sophism 1 - 

Every proposition is affirmative, therefore no proposition is negative.

Quantonics' 20Jan2003 commentary on Buridan's Sophism 1:

SOM's OGC, treats this sophism as a single proposition in a single classical context. Too, Hughes and Buridan treat both "no" and "negative" above as classically objective. Further, "affirmative" classically depends upon absence of any negation, which is why Buridan and Hughes concluded all 20 sophisms listed here are false (and more generally that all self-contradicting sophisms are false). Objective negation depends upon Aristotle's three syllogisms. All sophisms listed here implicitly presume classical reality which is analytic and thus stoppable (to achieve classical objective 'state').

In quantum reality, we can show that Aristotle's 'tautologous' syllogisms are animately included-middle self-referent and thus they are 'sophisms' themselves and may lack any means of 'correct' interpretation in OGC. To understand more fully that previous sentence, see our numbered Connections on this page's parent. All classical tautologies become, from a classical perspective, animately-evolving 'sophisms' when we introduce absolute unstoppable quantum flux.

~Classically we can interim 'solve' nearly all 'sophisms' by creating multiple yet-classical contexts and allow switching among them as iterative 'state' changes (thus, a rough classical approximation, analogue, interpretation of quantum flux). Readers may note that this technique appears viable for many/most 'sophisms.' We tried it successfully on Buridan (here), Escher (his 'impossible' stairs, etc.), Fred Alan Wolf's "mind numbing loops," and several mathematical 'paradice.' See our Connections. What is missing in this ~classical approach is quantum reality's included-middle and absolute flux. Ponder how classical reality and its CTMs outright denies both.

Readers may be able to infer how any classical notion of ideal scalar 'state' is wholly absent and becomes a complex of n¤n-objectively representable flux 'phasicities' in quantum reality. Why? Due quantum reality's own abs¤lute changæ amd everywhere-associative included-middle. As David Bohm suggests, we have to invent n¤vel intuemes of anihmatæ quantum comtext now to stindyanically interpret and monitor quantum pr¤cessings as they emerge amd evolve.

This update text applies, in general to all 20 of Buridan's sophisms. Detailed descriptions for each sophism might vary.
Doug - 20Jan2003.

This sophism, when viewed ihn n¤vel quantum lightings, remarkably becomes a quantum truthing!


We can ihnterpret this sophism quantum hermeneutically as saying that quantum reality is positive! In quantum reality, that is a quantum truthing.

How can that be?

Quantum reality is abs¤lute flux which we can m¤dal as waves. Waves are quantum likelihood omnistributionings which, in Quantonics, we m¤dal using fuzzons. QLOs are n¤n~negative!

Who says?

Kyburg and Smokler in their Studies in Subjective Probability, "...probability is a non negative, additive set function, with a maximum probability value normalized to unity..." That's similar to saying "quantum reality is a n¤n negational reality," and "quantum reality is an animate, EIMA, c¤mplementary reality."

We take slight quantum~exception to our Kyburg-Smokler quote since, classical, ideal unity and ideal nullification (zero) do not 'exist' in quantum reality.

There is n¤ 'physical' way of manufacturing a classically mathematical 'one' or a 'zero' ihn quantum reality. For relevant examples see: point, line, circle, One is Only, and our Hamiltonian Quaternion. Quantum reality is a n¤n mechanical reality.

In classical reality it is possible since any symbol/symbol is 'one' and any symbol minus symbol is 'zero' Those ideal mechanical, formal operations are simply impossible in any absolute flux-based quantum reality. They only work in a reality which may be conveniently, conventionally, mechanically, formally "stopped."

Doug - 11Aug2005.

Sophism 2 - 

No proposition is negative, therefore some proposition is negative.

Negatives are subjective. See Bergson's negation is subjective.

Sophism 3 - 

Every man is running, therefore a donkey is running.

Use two contexts here.

Sophism 4 - 

I say a man is a donkey.

Thus our speaker is a donkey.

Doug extracts this following detail example from Quantonics' 2003 News:

"Allow us to offer an example which is as real as we can make it.

"Classical Aristotelian syllogistic predication says (identity, contradiction, and excluded-middle):

  • A is A
  • A is not B
  • A is not both A and not A

"Allow us to make them classically real:

  • chicken is chicken
  • chicken is not human
  • chicken is not both chicken and human

"Allow us to make them quantum real:

  • chicken issi b¤th chicken amd human

"Aghast you ast, "How can our quantum script possibly be describing quantum reality? That's just plain nuts!"

"A chicken's DNA is ~86% human! A human is, based on intracellular DNA mapping only, 0.86 chicken! Expressed as phenomes humans and chickens classically appear hugely "di fferent," but genetically they differ by only 14%, regardless what classical fundamentalists say. Apes match humans even more closely, genetically. Humans share at least some genetic (bionon) SP¤Vs with all known Earth life emerqants."

Extension added and refined 13-14Mar2004 - Doug.

Sophism 5 - 

Whatever Socrates is hearing Plato is saying. 

Use two contexts here. (Re: two; i.e., implication of two or more; multiple.)

Sophism 6 - 

It is true to say that a man is an animal.

See our separate both True and False contexts.

Sophism 7 - 

Every proposition is false.

Thus this proposition is false, but it's true.
Need double context here.

Classical negation of 'every' appears empty,
implying again that classical negation is subjective.

Sophism 8 - 

What Plato is saying is false.

When? Need two contexts, at least.
Implied temporal recurrence.

Sophism 9 - 

What Socrates is saying is true. 

Ditto 8.

Sophism 10 - 

There are the same number of true and false propositions.

Which classically implies that there are not the same
number of true and false propositions. I.e., ideal
classical negation of this sophism 10 'exists' which
says it is not true. Need at least two contexts.

Classical logic is illogical... Why? Classical reality
does n¤t exist.

Notice how our quantum exegeses of this sophism also answer Mitch's June, 2005 question number three.

Classical logic is illogical because dialectic is 'illogical:' i.e., it contradicts itself!

Syllogistic logic is sillygistic 'logic.' Classical "Real Logic," is an oxymoron! Heraclitus calls classical dialectic, "mere toys."

See Quantonics' Bases of Judgment, judge, logic, reality, reason, science, truth, think, understand, uncertain, ...

Under Bases of Judgment pay close attention to SOM's dialectical bases in yellow background cells, near page bottom. Start at page bottom and work up. Doug.

Doug - 13Sep2005.

Sophism 11 - 

What I am saying is false.

Then it's true, too. Two contexts.
Implied temporal recurrence.

Sophism 12 - 

God exists and some conjunction is false.

Then God exists and some conjunction is true.
Two contexts.

Other possibilities for interpretation here,
e.g., God does not exist and some conjunction
is true/false.

Sophism 13 - 

Socrates knows the proposition written on the wall to be doubtful to him.

Doubt is subjective negation. Doubt is 'Mu.'
Doubt is tertium non datur.
Doubt begs an included-middle.
Doubt begs uncertainty.
Doubt offers n¤ binary alternative
denial AKA Sheffer stroke.

Sophism 14 - 

Either Socrates is sitting or the disjunction written on the wall is doubtful to Plato.

Classical either/or dichotomy with
implied temporal recurrence.
Negation is subjective. At least two contexts.
See doubt above in sophism 13.

Sophism 15 - 

Someone is doubting a proposition.

Someone is not doubting a proposition.
Implied temporal recurrence. Two contexts.
See doubt above in sophism 13.

Sophism 16 - 

You are going to answer in the negative.

When? Past/future dichotomy. Classical cause-effect.
Negation is subjective. Multiple temporal contexts,
at least one is uncertain.

Sophism 17 - 

You are going to throw me into the water.

When? Past/future dichotomy.
Classical cause-effect. Multiple temporal contexts,
at least one is uncertain.

Sophism 18 - 

Socrates wants to eat.

When? Past/future dichotomy.
Multiple temporal contexts apparently uncertain.

Sophism 19 - 

Socrates is cursing Plato.

When? Past/future dichotomy. Negation is subjective.
Multiple temporal contexts, unlimited and recurring.

Sophism 20 -

Socrates wishes Plato harm.

When? Past/future dichotomy. Classical cause-effect.
Negation is subjective. Multiple temporal contexts,
apparently recurring.

Hughes interprets and translates Buridan's original, technical Latin. Hughes makes it clear translation from technical Latin to English is difficult, and certainly subject to judgment and one's own perspicacity of context in Buridan's 14th century. It is very easy to misinterpret Buridan's original meaning. Some technical Latin terms have no English equivalent. So when Hughes shows us his translation of Buridan's twenty sophisms from Sophismata, he wants us to be mindful he was rigorous, but "What I tried to do with this material, however, is simply to assemble a version that seemed to me to make the best philosophical sense at each point." P. 31.

Hughes' own warning carries within it another perhaps unintended warning. His statement tells us he presumed to know, "...the best philosophical sense."

In his 33 page Introduction, Hughes distills Buridan's own, 'Theory of the Meaning of Truth.' We condensed his introduction into four lists:

  1. Outline of Hughes' Description of Buridan's Theory of the Meaning of the Truth
  2. A list of Buridan's explicit assumptions for his theory,
  3. Your Reviewer's contrived list of Buridan's implicit assumptions, and
  4. A list of Buridan's definitions.

Our first list is simply an outline of many technical features of Buridan's 'Theory of the Meaning of the Truth.' This list should help those who are new to Buridan to establish an expedient footing from which to grow.

Our second list of explicit assumptions shows both Buridan's and Hughes' nearly pure classical philosophical sense. This list is important for our review endeavor to compare their explicit assumptions to our list of explicit assumptions for a new philosophy, new ontology, and new logic for millennium III.

Your reviewer contrived a third list of implicit assumptions to help the reader begin departure from Buridan's classical realm. Here you may begin to experience some unease, either because Buridan's implicit assumptions depart from your own classical repertoire, or because you begin to fathom some problems in any classical realm. Again, we wish to use this list to compare to our proposed new way of thinking.


We want to remind you no matter what our endeavor, our results depend on our assumptions. Classical dialecticians made one overriding assumption. It affected all their subsequent results: they assumed classical reality! They presumed to know reality, and they presumed it is classical.

In this review, we are assuming too. We presume a quantum reality!

What likelihood is quantum reality real? In your reviewer's opinion, practically zero. Why? Because your reviewer assumes Homo sapiens possess finite intellect and our universe (multiverse) is a source of infinite potential knowledge. But how much better is a Homo sapiens-conceived quantum reality than a Homo sapiens-conceived classical reality? Vastly, almost immeasurably better. We are evolving our perception of reality, and we are making progress. But we always must keep in mind any ultimate knowledge of reality is beyond Homo sapiens' (and we presume our immediate evolutionary successors', e.g., Neo sapiens') reach. Some many Planck iterations from now, someone will look at our assumptions and declare their inadequacy.

Just remember our claims about a new logic in a new quantum reality derive from our own explicit and implicit assumptions too.

Our fourth list of definitions consists of quotes of definitions we found in Hughes' text. Where terms are undefined, we supply our own definitions and attempt to retain a classical purist's perspective.

After Hughes' Introduction, he proceeds to quote his translation of Buridan's solutions to Buridan's twenty sophisms.

Buridan concludes his twenty sophisms are all false and Hughes agrees, but Buridan's results still cause discomfort. His results look good on first surface perspective. When one looks at them classically; however, they appear less well conceived compared to a newer, more general perspective.

In this review, we intend to show you sophisms were perceived by Buridan, his predecessors, and his successors as problems, even insolubles. We want to show you apparently none of this ilk of dialecticians saw sophisms as cautionary compasses pointing to basic, wrong philosophical assumptions underlying Aristotelian logic and its successors.

Our goal is to show you, our reader-assessor, our crippled SOM (Subject-Object Metaphysics' Western classical) logical thinking may be cured. We can show you how Buridan, Hughes, et al., are wrong. They are wrong at their very foundations. We no longer must be SOM thinkers. SOMthink is passé. A cure lies in our acceptance of new ways of thinking, many of which we disclose in this review.

One way we choose to show you a cure for SOMthink is to disclose our own explicit assumptions and our own definitions. Then we will compare Buridan's assumptions to ours and comment on many glaring differences, one assumption at a time. We hope our following three lists accomplish a cure:

  1. A list of Reviewer's explicit assumptions
  2. A list of Reviewer's definitions (Latest update 27Jul2010 - Doug.)
  3. A list comparing Buridan-Reviewer assumptions

That wraps up this part of our review for now. Watch for changes here. We will gradually add analyses of Hughes' comments on each of Buridan's sophisms. As we do, Buridan's list of 20 sophisms at top of this page will turn into links.

If you have not, be sure to see other relevant links in our table, next to our graphic of a new reality, on our parent page of this child.

Thank you for reading.

Many truths to you,


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Doug Renselle
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©Quantonics, Inc., 1998-2016 Rev. 27Jul2010 PDR Created: 17Dec1998 PDR
(28May2001 rev - Correct a plural possessive typographical error.)
(15Dec2001 rev - Add top of page frame-breaker.)
(20Jan2003 rev - Provide a general description of our Quantonic approach to 'solving' classical sophisms under Sophism 1.)
(20Jan2003 rev - Provide tentatives for sophisms 2-20.)
(28Jan2003 rev - Add donkey link to sophism 4.)
(13-14Mar2004 rev - Extend sophism 4 with a real example from our 2003 News.)
(18Jul2004 rev - Add link to QELR of 'judge.' Reset legacy red text update markings.)
(4Nov2004 rev - Update reviewer explicit assumptions.)
(11Aug2005 rev - Update comments to 'sophism 1.')
(13Sep2005 rev - Update comments to 'sophism 10;' nexus to Mitch's June, 2005 question 3.)
(7Nov2005 rev - Update 'Alethic Sophisms.')
(16Dec2005 rev - Mark revisions to list of "Buridan's Definitions.")
(16Oct2006 rev - Reset legacy red text.)
(10Nov2007 rev - Reformat slightly.)
(14Mar2009 rev - Update logic comparisons page.)
(23May2010 rev - Add commentary to comparisons re: 'entail false conclusions.')
(27Jul2010 rev - Why quantum~uncertainty is 'not' absolute.)