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A binary number can be represented by any sequence of bits (binary digits), which in turn may be represented by any mechanism capable of being in two mutually exclusive states.
The modern binary number system was fully documented by Gottfried Leibniz in the 17th century in his article . Leibniz's system uses 0 and 1, like the modern binary numeral system. As a Sinophile, Leibniz was aware of the I Ching and noted with fascination how its hexagrams correspond to the binary numbers from 0 to 111111, and concluded that this mapping was evidence of major Chinese accomplishments in the sort of philosophical mathematics he admired.[6]
This paradigmatic opposition at the root of thought. Need we go into details? Us/them, up/down, good/bad, 1/0, I/You, subject/object, and so on.
These types of oppositions appear to be a fundamental requisite in human thought, for whilst no such oppositions can be identified in nature, as far as humans are concerned, they seem to be a necessary condition to ground knowledge on and to give order to our worlds of complexity.
The dichotomy code no doubt stems from some essential principle common to all species of a type. The need to identify friend or foe; that which you can mate with, or eat, or not. And because we have developed a larger range of codes to draw upon - such as those stemming from spoken language - we can surrender upon the world a greater range of fabricated oppositions.
At this junction, we could speculate that it is only when absorbed in the code of language, say, that humans are able to conceive of such bizarre (using the adjective in a very rhetorical manner) oppositions like God/Mankind, Natural/Unnatural, Mind/Body, Heaven/Hell, and so on. That we as a race come to believe in such oppositions, not just as a theoretical device we use, a tool which aids the ordering of our experiences, but as actually existing out-there, perhaps demonstrates less their truth and more the force and bewitchment our language codes cast upon us. Again, rhetorically, did not men and women believe for almost two-thousand years that the ancient Greek split-up opposition of fire and water, earth and air was the underlying nature to all reality?
The / (bar) placed between the oppositions should not always indicate any clear and fixed dichotomy. As if there were a clearly defined division between the concepts we have mindfully projected onto the world. As if there is The Good and The Bad, The Truth and The Untruth. If we start unpacking many of our binaries, I imagine we will realise that the subtle / is itself an essential feature to our oppositions, giving sense to them, acting as the silent guardian to the bounds, preventing too much trespassing or straying from the opposition.
Then, again, maybe that little / acts in the fashion those clever Zen dudes conceived their world. The / is Mu, that essential space indicating that the entire opposition system as stemming from our language codes and then projected onto the world, is intrinsically incoherent, or worse, meaningless.
As Pirsig wrote some years ago when reflecting on the standard binary code of 1/0, "...it's stated over and over again that computer circuits exhibit only two states, a voltage for "one" and a voltage for "zero." That's silly! Any computer-electronics technician knows otherwise. Try to find a voltage representing one or zero when the power is off! The circuits are in a mu state."
Perhaps all our oppositions, by virtue of that /, have this state of offness, containing the promise to reside forever in the world of Mu.
Thanks for a great post.
Perhaps all our oppositions, by virtue of that /, have this state of offness, containing the promise to reside forever in the world of Mu.
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What's fascinating to me is that this binary tendency is so strong in us that even if we think about the opposite of the binary tendency, we are still within the binary framework. Binary versus Fuzzy, for instance. I sincerely wonder if can avoid thinking in these terms. Obviously we can become self-conscious about it, and dodge some of the negative consequences. But perhaps the human form of life will always experience reality in such terms, and one might add that the notion of a reality outside human experience still resides within human experience. We are crawling on the inner surface of a hollow sphere. The limits of our language/self are the limits of our reality?? I do generally feel this way, but I don't want to come off too strong or maniacal on the point.
A vulgar-empiricist walks into a bar and insists that her narratives, discourses, twists and turns of phrases are not narratives at all. "No." She claims. "My narratives relate to truth and reality and what really happens, or happened. And I oppose what I am doing with myth and fiction, and that dodgy continental stuff and the tripe spilling from eastern philosophy. Indeed, what I come up with is sharp, critical, so much ever more true and real."
and those which have no need to relate to the reader for they refer to events, causal properties, brute facts.
When Saussure argued that a language or code is one based on differentiality, something Derrida jumped on, he meant that a language's elements are not defined by their content, but by contrast - our binary conversation - with other elements within the same system.
For Saussure the language we happen to use is an inheritance from the past, it is an always-already given. The relationship between signifier and signified is not a matter for the individual to decide, and to this extent, the individual has no power to alter the sign or code in any respect once it has been firmly established within the linguistic community.
Another important design feature in Saussure's linguistic critique is language's essential arbitrariness. The letter S, for example, has no connection with the sound it happens to denote, or again, there is nothing legish about the word leg. In principle, then, although a sign may be motivated or determined to a certain extent, such as needing a given combination of sounds which conform to the existing system, any signifier could have represented any signified. No doubt Saussure would have agreed with Plato's Cratylus when he claimed that "no one is able to persuade me that the correctness of names is determined by anything besides convention and agreement."
If language is essentially arbitrary, then according to the argument, the categories the sign-system happens to depict are also arbitrary and thus, our linguistic categories are not the consequence of some predefined structure of reality, some big T truth, The Truth of Reality, but actually constructed by the sign system, the code itself. In other words, the Saussurean understanding of language, our fundamental way of intelligibly cognisising the world, not only lies parallel to reality, but actively constructs the categories of that reality :shocked:
I think you'd enjoy this Reconstructo
5.471
The general propositional form is the essence of a proposition.
from 5.47
One could say that the sole logical constant was what all propositions, by their very nature, had in common with one another.
from 5.4541
The solutions to the problems of logic must be simple, since they set the standards for simplicity...a realm subject to law: Simplex sigillum veri.
from 5.44
..The proposition '~~p' is not about negation, as if negation were an object: on the other hand, the possibility of negation is already written into affirmation. (emphasis mine)
from 5.2341
(Negation reverses the sense of a proposition)