What Is A Logic? Just A Piece Of Mind

I would propose that a logic is anything which can be modelled with a piece and parcel of brain.

I will show, surprisingly enough, that this is a further step in Cartesian Logic.

At first sight, it may look as if I were answering a riddle, by further mysteries. Indeed, but with mysteries which can be subjected to experimental inquiry (now or tomorrow).

What is a brain? A type of Quantum Computer! And what is Computing, and the Quantum? Well, works in progress. There is something called Quantum Logic, but it does not necessarily defines the world, as exactly what Quantum Physics is, is still obscure.

In practice? Logic is what works, a set of rules to go from a set A of statements to a set B of statements.

In this perspective, Medieval logic did not decline. Instead it transmutated into mathematics.

 The teaching of Logic or Dialetics from a collection of scientific, philosophical and poetic writings, French, 13th century; Bibliotheque Sainte-Genevieve, Paris, France. The 13th century was a time of extreme intellectual activity in Europe, superior to anything else in the world, centered 800 miles around Paris. In particular the heliocentric system was proposed by Buridan, after he overthrew Aristotelian Physics, by inventing and discovering inertia.

The teaching of Logic or Dialetics from a collection of scientific, philosophical and poetic writings, French, 13th century; Bibliotheque Sainte-Genevieve, Paris, France. The 13th century was a time of extreme intellectual activity in Europe, superior to anything else in the world, centered 800 miles around Paris. In particular the heliocentric system was proposed by Buridan, after he overthrew Aristotelian Physics, by inventing and discovering inertia.

An article in Aeon, “The Rise And Fall And Rise Of Logic”,


Reflects on the importance on the history of the notion of logic:

Reflecting on the history of logic forces us to reflect on what it means to be a reasonable cognitive agent, to think properly. Is it to engage in discussions with others? Is it to think for ourselves? Is it to perform calculations?

In the Critique of Pure Reason (1781), Immanuel Kant stated that no progress in logic had been made since Aristotle. He therefore concludes that the logic of his time had reached the point of completion. There was no more work to be done. Two hundred years later, after the astonishing developments in the 19th and 20th centuries, with the mathematisation of logic at the hands of thinkers such as George Boole, Gottlob Frege, Bertrand Russell, Alfred Tarski and Kurt Gödel, it’s clear that Kant was dead wrong. But he was also wrong in thinking that there had been no progress since Aristotle up to his time. According to A History of Formal Logic (1961) by the distinguished J M Bocheński, the golden periods for logic were the ancient Greek period, the medieval scholastic period, and the mathematical period of the 19th and 20th centuries. (Throughout this piece, the focus is on the logical traditions that emerged against the background of ancient Greek logic. So Indian and Chinese logic are not included, but medieval Arabic logic is.)”

The old racist Prussian, Kant, a fascist, enslaving cog in the imperial machine turned false philosopher was unsurprisingly incorrect.

The author of the referenced article, Catarina Dutilh Novaes, is professor of philosophy and the Rosalind Franklin fellow in the Department of Theoretical Philosophy at the University of Groningen in the Netherlands. Her work focuses on the philosophy of logic and mathematics, and she is broadly interested in philosophy of mind and science. Her latest book is The Cambridge Companion to Medieval Logic (2016).

She attributes the decline of logic, in the post-medieval period known as the Renaissance and the Enlightenment, to the rise of printed books, self-study and the independent thinker. She rolls out Descartes, and his break from formal logic:

Catarina writes: “Another reason logic gradually lost its prominence in the modern period was the abandonment of predominantly dialectical modes of intellectual enquiry. A passage by René Descartes – yes, the fellow who built a whole philosophical system while sitting on his own by the fireplace in a dressing gown – represents this shift in a particularly poignant way.”

Speaking of how the education of a young pupil should proceed, in Principles of Philosophy (1644) René Descartes writes:

After that, he should study logic. I do not mean the logic of the Schools, for this is strictly speaking nothing but a dialectic which teaches ways of expounding to others what one already knows or even of holding forth without judgment about things one does not know. Such logic corrupts good sense rather than increasing it. I mean instead the kind of logic which teaches us to direct our reason with a view to discovering the truths of which we are ignorant.

Catarina adds: “Descartes hits the nail on the head when he claims that the logic of the Schools (scholastic logic) is not really a logic of discovery. Its chief purpose is justification and exposition.”

Instead, Descartes claims and I claim that a new sort of logic arose: Medieval Logic transmuted itself into mathematics (Descartes does not say this, but he means it). And mathematics is not really logical in the strictest sense. As it has too many rules to be strictly logical.

Buridan, a great logician who studied well the Liar Paradox (which gave the Incompleteness Theorems) had students such as (bishop) Oresme, who demonstrated what, it turned out, were the first practical theorems in calculus (more than 2 centuries before the formal invention of calculus by Fermat, and Fermat’s discovery of the Fundamental Theorem of Calculus, that integration and differentiation are inverse to each other).

For example, under the influence of Buridan and then Oresme, graphs and later equations themselves were invented. So logic became mathematics. That was blatant by the time Descartes invented Algebraic Geometry. Algebraic Geometry gave ways to deduce, to go from a set A to a set B, using a completely new method never seen before.

In turn, by the Nineteenth Century, mathematical methods contributed to old questions in Logic (the most striking being the use of Cantor Diagonalization to show incompleteness, thanks to the Liar Paradox, self-referential method.

In this spirit, not only Set Theory, naive or not, but Category Theory can be viewed as types of logic. So is, of course, computer science. Logic is whatever enables to deduce. Thus even poetry is a form of logic.

Logic is everywhere there is mental activity, and it is never complete.

If logic is just pieces of brain, then what? Well, some progress in pure logic can be made, just paying attention to how the brain works. The brain works sequentially, temporally, with local linear logics (axonal and dendritic systems). The brain tends to be deprived of contradictions (but not always, and nothing infuriates people more, than to be exposed to their own contradictions and gaps in… logic). Also all these pieces of brain, these logics, are not just temporally ordered, but finite.

As we try to use logic to look forward, as a bunch of monkeys messing up our space rock, it is important to realize that what logic is, has not been properly defined, let alone circumscribed. Indeed, if, surprise, surprise, logic has not been properly defined, let alone circumscribed, much more is logically possible than people suspect!

Patrice Ayme’



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13 Responses to “What Is A Logic? Just A Piece Of Mind”

  1. brodix Says:


    Then again, don’t overthink logic. Focusing on the details distracts from a broader, general perspective.
    Mathematicians don’t always make the best philosophers and philosophers don’t necessarily make the best politicians. Though one would think being well trained in formal logic would make one all that much better at philosophy. As well studying philosophy would be useful for persuasion. Yes, they are useful and often necessary, but as part of a foundation, not as a mold.
    The term “common sense” probably better describes the ability to balance information to the circumstance.
    There is a reason why the people in charge of armies are called “General” and “Specialist” is one grade above private.

    • Gmax Says:

      Methinks that was a point Patrice was making, that logic was very general and the illustration is about teaching logic from poetry, and that’s also Patrice’s conclusion. So I don’t know why you think Patrice ‘overthinks’

    • Patrice Ayme Says:

      Looks like I did not make myself clear enough. My point was a GMax said: logic is much more general than generally conceived. Philosophers and politicians? Great politicians were always philosophers of some sort, even Genghis Khan. Napoleon was a terrible politician, because he was a terrible philosopher. Washington was an excellent politician (for his ilk) precisely because he was so terrible… Generalities in this area are hopeless…
      Obama was terrible, because he was precisely not much of a philosopher, although much of one… as a puppet…

      • brodix Says:

        I guess I was addressing the evolution of philosophy and the article in Aeon. I’m a bit ADD and so is my logic.

        • Patrice Ayme Says:

          Well, I share the blame, as I realized meanwhile I could have got clearer. I have written something more to make myself clearer (to my horror, it explains a bit, and makes explicit things Heidegger tried to say…)

  2. Gmax Says:

    Buridan is 14th century, not 13th… otherwise I think you are right that mathematics replaced logic

  3. Paul Handover Says:

    Must stop reading your blog last thing at night!

    I feel uncertain about what I am about to write, but here goes! That is that logic must be a train of thoughts, or ideas, or writing that sits on a foundation of deductive reasoning.

    And with that, I’m turning off the bedside lamp!

    • Patrice Ayme Says:

      Goodnight Paul! Logic, described formally in the most general way, is pretty much anything that can be depicted by a countable code. However, in the brain, it’s something much more general.

  4. Marcio Bueno Says:

    This blog is amazing. I don’t remember how I stuck here, but since then, I truly love it.
    I love these thoughts deeply. They are mine, also. And, as known after social media success, nothing is better then meet people who think like us. And I love lavender smell and rosé as well.
    And I hate Kant, since my grad years.

    Thank you Patrice.

    • Patrice Ayme Says:

      Hello Marcio, welcome, and plenty of thanks for your compliments! Your comments should now be published immediately (if the electronics works, and there are not too many links).
      Thanks for hating Kant. Eichmann and other Nazis used Kant to justify their crimes (‘under orders’). Unfortunately some German physicists (often rather Nazi) claimed Kant helped with modern physics. That’s not true… Although, in a twist, one must admit Kant was not just a scientist, but an excellent one (for his thesis he proposed galaxies were what they are, stars together, in an “island universe”)

      Kant’s thought the dim, tiny, ‘nebulous’ “nebulae” were themselves external galaxies, as Wright had proposed for the Milky Way… “Island universes” — similar to the Milky Way. He wrote:

      “It is far more natural and conceivable to regard them as being not such enormous single stars but systems of many, whose distance presents them in such a narrow space that the light, which is individually imperceptible from each of them, reaches us on account of their immense multitude in a uniform pale glimmer. Their analogy with the stellar system in which we find ourselves, their shape, which is just what it ought to be according to our theory, the feebleness of their light which demands a presupposed infinite distance: all this is in perfect harmony with the view that these elliptical figures are just universes and, so to speak, Milky Ways, like those whose constitution we have just unfolded.”

      So Kant was clever. That makes him all the more terrible, as an enslaving racist…

      Hoping to hear from you soon,

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