In the ancient mathematics, “space” was a geometric abstraction of the three-dimensional space observed in the everyday life. Axiomatic method had been the main research tool since Euclid (about 300 BC). The method of coordinates (analytic geometry) was adopted by René Descartes in 1637. At that time geometric theorems were treated as an absolute objective truth knowable through intuition and reason, similar to objects of natural science; and axioms were treated as obvious implications of definitions.

The first axiomatic treatments and those which caused the greatest stir (those of arithmetic by Dedekind and Peano, those of Euclidean geometry by Hilbert) dealt with univalent theories, i.e., theories which are entirely determined by their complete system of axioms; for this reason they could not be applied to any theory except the one from which they had been extracted (quite contrary to what we have seen, for instance, for the theory of groups). If the same had been true for all other structures, the reproach of sterility brought against the axiomatic method, would have been fully justified.*

Bourbaki - “The Architecture of Mathematics" (1950), p. 230

* There also occurred, especially at the beginning of axiomatics, a whole crop of monster-structures, entirely without applications; their sole merit was that of showing the exact bearing of each axiom, by observing what happened if one omitted or changed it. There was of course a temptation to conclude that these were the only results that could be expected from the axiomatic method.

Capitalism is indeed an axiomatic, because it has no laws but immanent ones. It would like for us to believe that it confronts the limits of the Universe, the extreme limit of resources and energy. But all it confronts are its own limits (the periodic depreciation of existing capital); all it repels or displaces are its own limits (the formation of new capital, in new industries with a high profit rate). […] And it does both at once: capitalism confronts its own limits and simultaneously displaces them, setting them down again farther along.
—  Deleuze and Guattari, A Thousand Plateaus, “7000 B.C.: Apparatus of Capture,” 463
Split Decisions (i)

In Split Decisions: How and Why to Take a Break from Feminism, Janet Halley extracts from feminism three axioms, which she labels m / f (“there are two genders”, male and female), m > f (the male is placed in a position of dominance with respect to the female), and “carrying a brief for” the female (seeking to identify and redress the wrongs produced as a result of gender inequality). Halley’s argument is that it is sometimes useful to suspend one or more of these axioms, in order to “see around corners” that the feminist axiomatic introduces into our view of the world.

For example, we may sometimes want to suspend, if only temporarily, our assumption that binary genderism is essential to the way gender is practised and experienced (even by those who refuse, or find it impossible to accomodate themselves within, a binary-gendered “world of men and women”). One argument for doing so would be that the experience and practise of gender dissenters already prefigures and realises - if only locally and precariously - a world that is not a “world of men and women”. The global consistency of gender, its thoroughgoing structural power, meets its limit at the point where gender-alternative “spaces” are able to come into being. Thinking according to the feminist axiomatic will tend to frame such spaces as exceptional enclaves, endangered (and perhaps inevitably doomed) reservations of utopian possibility that remain ultimately subject to the heteronomy of the law of gender. The gamble Halley proposes is that thinking that suspends the feminist axiomatic might be better able to think in accord with the experience that such spaces embody and preserve, an experience of already-realised, this-worldly autonomy.

Feminists have understood that binary genderism is “the law”, and framed their analysis accordingly; but this analysis may founder when it encounters the social fact of “outlaw” existence. There is sometimes a conflict between two antinomianisms, one apocalyptic (there will come a time when the entire system of gender will be overthrown) and the other insurgent (the law of gender is murderously oppressive, and in order to live at all it is necessary and possible to live outside this law). Apocalyptic antinomianism maintains a strategic “pessimism of the intellect”, constantly spying-out the ruses and deceptions of the law (radical feminists have been prone to seeing trans activists, for example, as infiltrators or unwitting shock troops of a patriarchal backlash). Insurgent antonomianism embodies an “optimism of the will”, a belief that meaningful autonomy is possible, that a good life can be lived in (and indeed explicitly against) a bad world.

With respect to gender, trans (or more generally gender-dissenting) politics could be considered “non-feminist” (non-standard with respect to the axioms of feminism) without thereby being “anti-feminist”; and indeed the categories of “cissexism” and “transmisogny” generated by trans politics may be said to constitute a powerful extension to the conceptual armoury of feminism.


The highway code contains quite a lot of inconsistencies. Every time I notice contradicting traffic signs, I’m being reminded of Gödels incompleteness theorems. Although they apply to “mathematical” systems, we can more or less interpret the highway code as an axiomatic system. Gödel’s theorems then say one of the following possibilities has to occur:

  • There exist situations in traffic where the highway code requests contradictory behavior; the system is inconsistent.
  • There exist problematic situations in traffic (such as who has right of way) where the highway code offers no help. Particular solutions “outside the box” are needed to solve this particular situations; the system is incomplete.

Perhaps one would think that including particular solutions to the system would eventually complete it, but then again, this cannot be done without introducing inconsistencies; every axiomatic system is doomed to be incomplete or inconsistent.

So if you’re ever being pulled over by a cop, blame Gödel :)

Another Project Fear attacks Scottish civil society as anti-semitic and urges Scottish Jews to leave for Israel/Palestine

It is an axiom of political Zionism that Jews can not live safely anywhere outside Israel and those who do so are inferior to those who emigrate to Israel (olim) to take part in the Zionist project of dispossession of the native Palestinian people. The original European project to colonise Palestine makes no sense unless one accepts as axiomatic, ie so obviously true as to require no need for any proof, the notion that Jews can not live safely among non-Jews. Zionist assertions, thus, often need no proof in the eyes of their authors. 

The Israel Times attacks Scottish civil society as anti-semitic, tries to implicate all Scottish Jews in Israeli crimes, and urges Scottish Jews to get ready to leave for Israel. 
Most Scottish Jews seem to enjoy life in Scotland. Photo below: Rabbi Mendel Jacobswith kosher Scotland's official Jewish tartan. According to Rabbi Mendel, “The Jewish people have been an integral part of Scottish Culture for more than 300 years, with the first Jew recorded in Edinburgh in 1691. In Scotland, the Jews were never persecuted and there were no pogroms, no Holocaust, no national or state sponsored antisemitic laws. When England was burning and exiling its Jews in the Middle Ages, Scotland provided a safe haven from English and European anti-Semitism. “
Anti-Zionism is a duty; anti-semitism is a species of racism as ugly as islamophobia and equally deserving of condemnation.

The Transposed Heads. Thomas Mann. New York: Alfred A. Knopf. 1941. First edition. Original dust jacket. 

Mann retells the Indian legend from a metaphysical, yet ironic viewpoint. He strongly reacts to the axiomatic assumption that there is a dichotomy between spirit and life, mind and body. He, like many 20th century writers, felt the necessity of reshuffling the present scale of values and meanings by constantly juxtaposing them with older ones.

Pieter Bruegel the Elder’s painting The Fall of the Rebel Angels shows us there really is a force to subtraction: you subtract from an angel until you end up with a demon. If you download an image of the painting onto your computer, or better yet see in hanging in the Royal Museum of Arts in Antwerp, you will notice how the rebel angels fall from heaven at the top left of the canvas to hell at the bottom right. Their wings are first subtracted for the lesser wings of bats and dragons. Toward the earth they are reduced to moths, frogs, and other soft things. They are driven together by the golden angels of heaven armed with effulgent discs, lances, and swords, whose task it is to sanitize our world. You will see how the rebel angels continue to change their form as they are driven into a sea, whose opening is an obscure drainpipe. They lose their legs, wings, all hope of surfacing and become fish, squid, spawn, and seeds of trees never to be planted. Underwater they continue to be subtracted from their former selves until they are at last incorporeal and see-through at the bottom.

J M Ledgard, Submergence. Minneapolis, 2013. pbk, 5-6

Axiomatization may also give ready answers to new questions when a novel interpretation of primitive concepts is discovered. As an illustration, consider the concept of a commodity, which had meant traditionally a good or a service whose physical properties and whose delivery date and location are specified. In the case of an uncertain environment, Arrow (1953) added to those characteristics of a commodity the event in which delivery will take place. In this manner one obtains, without any change in the form of the model, a theory of uncertainty in which all the results of the theory of certainty are available (Debreu [1959], Chapter 7).
—  Debreu - “Economic Theory in the Mathematical Mode,” p. 98

viridian-sun said:

idea: autochthon got out of his exile much sooner - just after the empress got established. autochthonia, with its superior champions and technology conquered realm at ease, and now, the autochthonian dominion spans the whole of creation (which is much larger than it was post baloran crusade because reality engines are /trivial/ for everyone enlightened by Axiomatic essence to build. basically solars start to exalt in steampunk/cyberpunk creation.


"This is shit," I tell myself with each sentence I write. The cursor hits like a finger incessantly jabbing at my sternum, my throat. "This is really, really, shit. Stop. Please. Read more. You need to read more."

I abandon the fucking thing, mid-paragraph, our hero’s motivations to be forever unexplored, and exit the word processor. No, I don’t want to save. Yes, I’m aware that any changes I’ve made will be lost. That we will never be more than what we are is axiomatic.

I open the browser, pull down the bookmarked list of lit mags, pick one at random. Scan the front page, select a punchy sounding title, open the story in a new tab. I glance at the right. The thumb is one-tenth the size of the scrollbar, more or less. Perfect. Shouldn’t take too long.

I make it a few sentences before saying, “You should be writing.”



In order to be back, one first had to be gone. 

That seemed simple enough—axiomatic even—and it was. At least under most circumstances. The real trouble came when there was no way to articulate (much less rationalize) where someone had gone, and that made it difficult to understand how they could be back. That sort of circle of twisted inferences would be dizzying for any one, even any genius, but for someone with a white-knuckled grip on demonstrable facts and logical reasoning…it was nearly impossible. 

Few people would think it an unfair stretch to call Seto Kaiba ‘notoriously stubborn’, oppositional, or even defiant. While he could certainly be all those things, he did eventually have to admit that even he couldn’t change facts by ignoring them. And at this point ignoring them was what he would have to do if he were going to remain committed to his prior worldview—unfortunately that wasn’t an option, so now he had to understand.

The logistics had been easy enough. It had taken little effort to track down this “pharaoh.” Even in his head the term was laced with some level of disbelief and derision. Maybe he would try to avoid that leaking into his speech. But just maybe. Seto gave a mental shrug at the relative merits of that thought as he settled in to wait, leaning slightly against a streetlamp. He hadn’t given any indication of his coming, and so he was content to wait as long as necessary—a tall, thin figure in a slim-cut suit, ice blue eyes trained unblinkingly on the cafe door.

This is a title.

Quick question:

If axiomatic principles are to be established before a set can be logically deduced to its completeness, then the set of logical deduction must rely on entirely topological concepts other than the original principles that have been assumed before deduction has been done upon the set. Other than from an entirely pragmatic viewpoint there can surely be no rules for applying such foundational knowledge, then coherency cannot be or perhaps rather should not be a factor. However, if it is not so then all pragmatic functions are redundant as coherency implies direct functional control and therefore to be pragmatic it must first be coherent. However, coherency cannot be found within a foundational set until the complete logical deductive process is complete. Unless I am mistaken, the order of which these effects occur is irrelevant as if they were not so, the set could not be completed. Moreover if this is so, could we theoretically extrapolate from this logical set to a less profound yet more common set such as experience?

Words I Love

For no reasons beyond a passion for language, I have decided to make a list of words that I enjoy. To give this list some form, I’ve decided to list 3 words per letter of the alphabet. Feel free to copy me or ignore me, as this is quite nerdy but (to me) also fun.

A: Axiomatic, Anarchy, Altruism

B: Bohemian, Bell, Brusque

C: Cerulean, Cityscape, Countenance

D: Dendrochronology, Demesne, Descend

E: Elusive, Enigmatic, Elven

F: Fixation, Fog, Frost

G: Gale, Grievous, Globe

H: Helm, Hirsute, Harridan

I: Indigenous, Idiomatic, Irrelevant

J: Jasper, Jape, Jurisdiction 

K: Knit, Knot, Kale (That was a hard one!)

L: Lyrical, Luminous, Lunar

M: Malevolent, Melody, Matrilineal

N: Nascent, Notation, Nihilism

O: Oligarchy, Opalescent, Orbit

P: Pallid, Phantasm, Prescription

Q: Quiescent, Queer, Quake

R: Retroactive, Rune, Rime

S: Serpentine, Sylvan, Savannah

T: Temporal, Travesty, Transgress 

U: Usurp, Undulate, Ululation

V: Vanguard, Vexation, Venom

W: Wellspring, Weave, Wax

X: Xenolinguistics, Xylophone, ?

Y: Yield, Yule, Yew

Z: Zoological, Zoroastrianism, Zygote

I was defeated by the letter ‘X’.