This book is about a certain kind of limit; not the limits of physical endeavours like running a mile, but the limits of the mind. I will call them limits of thought, though 'thought', here, should be understood in its objective, Fregean, sense, as concerning the contents of our intensional states, not our subjective consciousness. One might also describe them as conceptual limits, since they concern the limits of our concepts. Whatever one calls them, by the end of the book I will have given a precise structural characterisation of the limits in question, in the shape of the Inclosure Schema. For the present, some examples will suffice to indicate what I have in mind: the limit of what can be expressed; the limit of what can be described or conceived; the limit of what can be known; the limit of iteration of some operation or other, the infinite in its mathematical sense.

Limits of this kind provide boundaries beyond which certain conceptual processes (describing, knowing, iterating, etc.) cannot go; a sort of conceptual ne plus ultra. The thesis of the book is that such limits are dialetheic; that is, that they are the subject, or locus, of true contradictions. The contradiction, in each case, is simply to the effect that the conceptual processes in question do cross these boundaries. Thus, the limits of thought are boundaries which cannot be crossed, but yet which are crossed.

In each of the cases, there is a totality (of all things expressible, describable, etc.) and an appropriate operation that generates an object that is both within and without the totality. I will call these situations Closure and Transcendence, respectively. In general, the arguments both for Closure and for Transcendence use some form of self-reference, a method that is both venerable and powerful. Closure is usually established by reflecting on the conceptual practice in question. In a polemical context this can appear as an ad hominem argument. Arguments for Transcendence are of more varied kinds; often they involve applying a theory to itself. Some of them are more technical; a paradigm of these is diagonalisation, a technique familiar from the logical paradoxes. This construction is precisely a boundary-tearing heuristic which, given any boundary of a suitable kind, can be applied to violate it.

see here and here for dialetheism. he goes from Aristotle to Berkeley, then Kant's noumena and antimonies leading into Hegel. from Hegel, he goes into Cantor, set theory, and the paradoxes. he ends with language by going from Frege to Wittgenstein and then Derrida.

the second edition has a little more

Crow posted:
hahaha in a stalinist nation, a janitor IS a high level bureaucrat! Oh what a free and equal state we lost..

If only Marxist revolutionary Leon Trotsky could see what has become of his great-grandson, David Axelrod.

The 49-year-old Russian émigré to Israel has adorned his modest living room with a singular-framed photograph: a bird’s-eye view of Jerusalem with the Dome of the Rock — Islam’s third-holiest shrine — digitally replaced with an image of an imagined Third Jewish Temple.

He named his 10-year-old son, Baruch Meir, after two of Israel’s most notorious Jewish figures: Baruch Goldstein, who gunned down 29 Muslims at prayers in Hebron in 1994, and Rabbi Meir Kahane, whose ultra-nationalist political party was outlawed by Israel some years prior.

And he has served three terms in jail, he said, on counts of attacking Arabs and setting fire to a mosque, charges that he denies.

discipline posted:
I went to the grave of Karl Marx and this creepy old dude came up to me and started showing me pictures of his great granddaughter, pictures he had cut out from newspapers and kept in his wallet

karl marx's? could it by chance be the guy who wrote this? http://archive.newsmax.com/archives/articles/2005/2/24/173151.shtml

its really funny

e: oh boy, the guy who wrote this http://en.wikipedia.org/wiki/Lev_Navrozov

Edited by Crow (Feb. 1, 2012 22:02:45)