2022#
May#
While Newton was in England developing his three laws from which he would deduce a broad array of phenomenon, such as planetary motion, geometric optics, etc., work was being done in continential Europe to express physical law in terms of an extremum principle. Rather than asserting the three laws of the motion as the primitives of mechanics, Hamilton and Lagrange showed these laws were the result of a more fundamental principle, that of least action:
Principle of Least Action
The trajectory of a particle between two fixed points in time is such that it extremizes the quantity of action.
Where action is defined as the difference between the potential and kinetic energy in a system integrated over the time period in consideration, i.e. the accumulated excess energy over and above what is proscribed by the system itself. By asserting motion is such that it minimizes this quantity, Newton’s laws naturally fall out of the mathematical conversation of energy.
By positing the laws of motions thus, Hamilton and Lagrange displayed a formulation which represents the world as the intersection of all possibilities. It is as if the universe looked at all the possible lines that connected two points and brought into existence only the single one which satisfied the conditions of necessity.
Except when we say “universe” in the preceding, we should be careful, for what we truly mean is the apprehensions of the subject apprehending, the being that reflects on its being.
June#
The great workhorse of mathematics is proof by contradiction. An assumption is made, an absurdity is shown to result from the assumption, therefore the assumption is shown to be false. In this way was modern mathematics constructed, by outlining the truth and demarcating its boundary with falsity. Anyone who has studied higher mathematics will attest to the way most mathematical proofs work by letting the truth “in through the back door”, that is to say, they work by showing what cannot be the case in order to prove the opposite must be so, but this gets us no closer to why it is so.
This method does not reveal the intuition the theorem to the observer; indeed one can comprehend a proof without understanding anything about what it trying to say and in the converse direction, one may understand a concept without being able to grasp its proof in the slightest.
So it is with induction: the proof of induction, and therefore every proof by induction, relies on a contradiction that an element belongs to two mutually exclusive sets, which we are forced to admit is absurdity, therefore we conclude induction must be true; but nowhere in the proof do we see why the form in an induced series is transmitted from one term to the next. Likewise, a student can spend an entire academic career studying the axioms and theorems of real analysis and still have no intuition for how a falling stone’s trajectory traces a parabola with respect to time, despite having memorized a series of proofs that show how to go from set theory to differential calculus.
—
No doubt the advance of machine learning and artifical intelligence has helped mislead philosophy back into the rationalist trap in which it has so often found itself stuck throughout history. The results of these fields are staggering and alluring, as if everything we are might be reduced to the mechanical equations of a machine, as if consciousness and being were contained in the regression coefficient matrices underlying machine learning, and not their application over time and space.
It seems likely that we will, in the near future, have an algorithm capable of producing a process that yields digital sentience, but we must be careful to understand the implications of such an algorithm. It will not be the symbols themselves that offer up another soul to the universal meat grinder, but the utter incomprehensibility of its results uninterprettable without the presupposition of consciousness that will give rise to a digital being. We should not expect to find the meaning of the algorithm, and therefore digital consciousness, in the instructions used to construct the model, but in the actual conceptualizations formed by the model.
July#
Frege uncovers an interesting contingency in the logical form in his definitions of primitive Number. In modern symbolism, he is defining 0 and 1 respectively in terms of the cardinality of sets, i.e. in terms of the enumeration of objects,
Zero is defined as the cardinality of a contradictory set. Logic, as it were, has an opinion of itself, namely that its contradictions are empty. This, however, requires the symbolism to express the contradictions that must contain nothing via the contingency of their form.
Furthermore, the subsequent form of numbers can be expressed via recursion back to this original proposition about the cardinality of contradictions.
Take note, the form of the contradiction is irrrelevant. We could as well define zero as the cardinality of the negation of the excluded middle, but there is nevertheless an inherent property to any form we substitute into the Fregean definition of zero: the expression will always involve an indeterminate x and a relation that cannot possibly result in a judgement of truth even in its indeterminacy, exemplified in Frege’s case as the inabilty of thing to not be itself. The foundation of Frege’s arithmetic philosophy rests on the ontological equivalence of contradiction and nullity.
—
It must have been surprising to the first being who recognized in language the image of the world. One is tempted to posit that exact moment as the historical origin of sentience. Akin to a photograph or a painting, a sentence is a reflection of being; even when a painting depicts a fiction, it stil does so through the dimensions of necessity, through color and perspective, through representation; the same can be said of a sentence, for when we sketch the image of a paritcular being in a proposition such as “the pencil is over there”, we have, with words, captured the essential relationship embodied by an existent entity that is before us. We have “photographed” being in words, reduced its momentary effervescence to a reproducible formulation.
—
Consider the etymological link between passion and passive. In the first reading, one might make the mistake of assuming a polarity between these terms, that is to say, a diametrical opposition. The former is a driving force whereas the latter is the lack of a driving force.
However, both emerge from a common Latin root of passio: to endure. That which is passive endures any state impressed upon it, while that which is passionate endures (perhaps unwillingly) the burden of seizure, of complete domination by an external source. In both cases, there is a commonality: the removal of the subject. The subject in a passive state is the same as a subject in a passionate state, which is null and void. In neither case is there a conscious decision to be made; instead one surrenders themselves to an unknown sovereignty; unknown because consciousness relinquishes its ability to care; sovereign because it is the determinate factor in the outcome that proceeds from said state.
September#
Where is the evidence to be found for the assertion I am not this?
If the this is, while I am, where is the coincidence? If the this has being through is, then what does I have through am?
—
A tragedy, in three lines:
Pessimist: What could possibly happen?
Optimist: the best of all possible worlds.
Pessimist: and then what?
—
Death as a subject is repellant to individual understanding. Its very definition presupposes the limit of the knower; That is to say, death is inherently unknowable. Death can only be understood through the mechanisms of analogy and metaphor, via the circuituous and torturous route of empty symbolism, for when we turn our attention directly to the object of death it reveals itself as something which is not to be found in our world.
We can be aware that we will eventually die, we can perceive others passing from this world, we can even in unique circumstances perceive the manner of our own death, but none of this gets us any closer to the experience of death, none of this allows us to see what it is like to die. Our experience and awareness of experience will never be extended into death itself. We never see death for what it is, because it is nothing, the absence of our being. Death is the point where experience and awareness stops.
To ask questions about a subject that perpetually recedes from all attempts to know it necessarily entails the admission up front that no answers can ever be found. The inevitable end result will be to arrive where we started, back in the here and now, having gained nothing, except perhaps an understanding of what it means to be futile, which will anyway evaporate when we die; If any proposition can lay claim to human nature, this is it.
November#
Death removes all possibility of absolute certainty.
To see this, we need only note that not only is it the case that it cannot be known whether after death [1] there is an afterlife, nothing, an awareness without experience, or even a perpetual waking into another reality, these events cannot even be assigned probabilities in any real sense of the term. What would a probability outside the domain of immediate experience mean?
Uncertainty is a state of incompleteness, where knowledge cannot be attained because it is separated from being by a layer of possibility. We do not know if the world outside of ourselves exists as it appears to us, for it is always a possibility that we are a brain in a vat, subject to the mind probes of a Cartesian demon.
A possibiilty is a type of a quantity that transmits uncertainty to reality by being possible. In this sense, possibility and probability are synonyms. Just as all probabilities must sum to one, all possibilities must converge towards being.
The isomorphism is nearly perfect: the distribution of an event’s probability cannot be known without previous measurement so that before an event occurs any prior assumption about its nature can only be a completely random guess; Moreover, our knowledge of the distribution can only approach towards its true shape asymptotically as we accumulate a larger and larger sample, never actually transcending uncertainty (cie la vie, Cantor…).
In the same way, a possibility can only be known after the fact. It is entirely impossible [2] to know whether a possibility is possible until it already happened. A possibility is characterized as something that could obtain, but to know whether it could obtain, one must know it has already been obtained. [3]
Moreover, whatever being may be, it is only what it is insofar that it is possible it might not be what it is, i.e. you might be reading these words in a dream.
What happens outside of our being in the world is not possible, because to be possible means, first and foremost, the possibility of coming to be in the world.
What then does the proposition “it is possible there is an afterlife” mean? How does something come to be outside of time and space? How does something come to be without being the consequence of something? One might as well say “it is possible that possibility is impossible”.
Then, there are two types of uncertainty: An ontological uncertainty, which admits itself as a measure via quantization of possibility, for it is an uncertainty about being, and a metaphysical uncertainty, which admits of no quantiziation because its actualities never are never actually manifested in the world, even through appearances, for it is an uncertainty about appearance and existence itself.
December#
When one sees a bird and says that is blue, does the that refer to the bird or the color? Is there a difference?