Adding Structure To Logic


Basic logic, any logic, works with axioms and a “universe”. And “logic”, the logos, is just a discourse. Even with a logos, there is then the question of what is meant by a “proof”. “Proof Theory” is itself a… science… That is a body of knowledge deduced from a logic. That’s why there is such a field as metalogic.
https://en.wikipedia.org/wiki/Proof_theory

Last, but not least. IMHO, the basic set-up of logic is not finished. I share this opinion with some top logicians, who are suspicious that some gigantic piece is missed in the entire setup of logic, any logic. My own suggestion is to introduce time and causality in any logic… And prevent time reversal! In other words, I propose to introduce what is called in set theory a well-ordering. That would immediately short out problems such as self-reference (“Liar paradox”).

In conventional logical systems, all propositions are equal (except, not really as Godel showed with a number of construction from the infinity axiom). In my vision of the universe, time is pretty much absolute, and not relative (even in the Special Theory of Relativity, Time is LOCALLY absolute, at the very least as a well-ordering… as the theory rests on light clocks… In other words, I am not trying, or succeeding to contradict Special Relativity, in which I believe…)

In support to this, the spirit of the Incompleteness Theorems a la Godel. Godel showed the theoretical existence (through Cantor’s Diagonal Process) of “Godel Numbers” which although they could not be computed (!) encoded propositions which had to be decided, true or false, as new axioms. Thus there is, in any mathematics sophisticated enough for basic arithmetic, a hierarchy in the axiomatics according to the order of appearance of said axioms. (Right, the whole thing is to some extent silly, as these axioms cannot be shown…) I simply propose to establish the hierarchy from the start, as a meta-axiom. Then a number would be attributed to any proposition. Proposition with higher numbers could not change propositions with lower numbers.

To my knowledge, this simple ordering scheme for any logic has not been suggested anywhere (an order given by the arrows is somewhat implicit in Category Theory, and makes its strength, IMHO). The meta feelings leading my proposal are the importance of the Time Arrow, and also the importance of Hierarchies (life itself is a hierarchy, from simple life forms, like viruses, to extremely sophisticated ones, like yours truly…) Hierarchies take time to develop, so both concepts are related. Many of the problems and contradictions and shortcoming of modern logic comes from problem with hierarchies (hence Russell-Whitehead “Theory of Types”)… Instead of getting hierarchies to contradict logic, I integrate them right away… From time and significance (see below).

Some may say… so what? Who cares about fundamental logic? Not so simple. Any serious logic works with axioms, rules of deduction (which are themselves axioms), and a universe endowed with semantics. To all of this, I add a time ordering… But one also can add a SIGNIFICANCE ordering (in the universe attached to the logic). Now this has direct consequences on a theory of truth.

And since I want to create a Department of Truth, as a fourth branch of government, in particular to help the Judicial, Legislative and Executive Branches with a COGNITIVE BRANCH, it better be about something establishable in a more rigorous way… Than we had it so far.

Patrice Ayme

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5 Responses to “Adding Structure To Logic”

  1. brodix Says:

    Patrice,
    To add a few points about time and the construct of math;
    Consider that math is reductionist. We distill logic down to its most stable components and patterns. Yet that is top down descriptive, not bottom up explanatory. Like boiling a body down to its most stable features and you have the skeleton, not the egg from which it emerged. Epicycles were brilliant math, as description of our view of the cosmos, but the crystalline spheres were lousy physics, as explanation.
    How do you construct math upward, out of nothing?
    Consider that three dimensions really are a mapping device. The xyz coordinate system, like longitude, latitude and altitude. If you remove all physical properties from space, you have the non-physical qualities of infinity and equilibrium. Infinity, as there is nothing to bound it and equilibrium is implicit to SR, because the frame with the fastest clock and longest ruler would be closest to the equilibrium of the vacuum. The unmoving void of absolute zero.
    So space is the absolute and the infinite.
    What fills space is this dynamic we refer to as energy, which is always fluctuating and changing. Creating time, as well as temperature, pressure, color, sound. Frequencies and amplitudes. Time is frequency, events are amplitude.
    As these mobile organisms, we have this sequential process of perception, in order to navigate, then as humanity, we have narrative based culture, from sharing stories. So we experience time as the point of the present, moving past to future. Physics codifies it as measures of duration.
    The reality is that change turns future to past. Tomorrow becomes yesterday, because the earth turns. Duration is the present, as the events come and go.
    There is no literal dimension of time, because the past is consumed by the present, to inform and drive it. Causality and conservation of energy. Cause becomes effect.
    Energy is “conserved,” because it is the present, not some dimensionless point between past and future.
    So energy, as process, goes past to future, while the patterns generated go future to past.
    Think of a wave; As the energy radiates out, eventually toward infinity, the patterns, the ripples, settle back toward equilibrium. Both effectively entropic.
    Consider that galaxies are energy radiating out, as order coalesces in.
    In a factory, the product goes start to finish, while the production line goes the other way, consuming material and expelling product, like a wave passing through water, that rises and falls.
    Lives go birth to death, while life moves onto the next generation, shedding the old.
    Consciousness goes past to future, while the perceptions, emotions and thoughts go future to past.
    Suggesting consciousness functions as an energy, always pushing the forms it manifests and encounters. Though it is our digestive, respiratory and circulatory systems processing the energy, feeding the flame, while the central nervous system sorts and orders the patterns precipitating out. Motor and steering.
    So time is a function of the effect and measure of action, thus is variable to what is being measured. Every action is its own clock.
    Though organisms have to synchronize their various clocks, while ecosystems harmonize, as each organism fills a niche in the larger space.
    It is just that as communities function as social organisms, there is a need toward a monoculture, so anyone not synchronized with the herd will be ostracized/cancelled. Though in the growth side this tends to draw everyone toward the center, while in the downside, as the organism loses contact with the ecosystem, it starts alienating the fringes, creating more negative feedback.
    As for galaxies, if this relationship between energy and form is total, the place to look for the additional gravitational effect is further out the spectrum, from mass. Essentially that mass is an effect of gravity, not the other way around and this process of inward curvature starts all the way out where photons and waves start to emerge from the light, given that energy and the information it expresses are not synonymous. So the bending of the light is not caused by gravity, but is gravity.
    Then consider that multispectrum light “packets” do redshift over distance, as the higher frequencies dissipate faster, so we are sampling a wave front, not individual photons, traveling billions of years and the process of quantization is a function of the information falling back in, not the energy expanding out.
    It is just that as our central nervous system is designed for processing information, our thought process sees reality from its top down position and so it’s information all the way down, rather than the energy all the way up and out, generating this downward flow of information. The ripples.
    Like a camera taking a picture, we can only see/process static forms, or it would be a whiteout of overwhelming light, like leaving the shutter on open.
    Though we are constantly bathed in enormous amounts of light and process much of the information subconsciously, as all those fluctuations, errant thoughts, emotional contacts, etc, we get from our environment and the other creatures in it.
    Yet the “scientific method” only accepts the most distilled and stable perceptions, so only a tiny fraction is accepted as “real.”
    Thoughts are like a cresting wave. The energy has expressed its complete and final form, yet immediately receding, leaving only the abstractions of order. While emotions and intuition sense the energy and force of the wave starting to build, or receding. Not clear and precise, but unrelenting, carrying us, not just flashing in our minds.
    There is no form to the void, only structures and patterns left in the wake of the energy.
    A bit of my cosmology….

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  2. kathw Says:

    Couldn’t agree more – our democracy needs a COGNITIVE BRANCH to discern what is true/significant/constructive in our ongoing evolution. Esp. in a highly polarized milieu, governance needs a reliable, objective way to separate the signal and the noise to achieve consensus.

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  3. De Brunet d'Ambiallet Says:

    Great. But what’s the differnce with the numerotation used by Godel?

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  4. Ian Miller Says:

    Good luck getting politicians to tell the truth. An always truthful politician seems to me to approach being an oxymoron. I also think that we should not draw conclusions based on a proposition that is self-contradictory because perforce it has to be false in some way.

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    • Patrice Ayme Says:

      Politics is unavoidable, and it should determine truth, for civilization to survive. Professional politicians should be unlawful, though, because their electioneering depends, per force, on lies.

      Institutions of democracy found in the most democratic Greek City States (or even Republican Rome!) have to be reinstituted…

      Having a DEPARTMENT OF TRUTH, and TRUTH AS AN INDEPENDENT BRANCH of government would be useful.

      What proposition is false???…

      Liked by 1 person

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