The point against the "finitist
response" is also made by Mary Tiles by appealing to the continuum problem.
As Roy Bhaskar remarks: "Any Marxian dialectic will be objectively conditioned, absolutely finitist
and prospectively open (i.e.
From his point of view, the Aristotelian finitist
and differentiated conception of cosmological space as an ensemble of places was useless because it could not be easily represented in a geometric model.
While acknowledging his methodological pronouncements that philosophy is purely therapeutic and produces no theses or theories, they have gone on to interpret him as advancing controversial philosophical doctrines such as a behaviorist theory of understanding or a strict finitist
theory of mathematics.
Wittgenstein's philosophy of mathematics has sometimes been described as finitist
; but, as I shall argue here, his actual and consistent position on the question of the finite and infinite in mathematics and language is already well expressed by a remark in his wartime Notebooks, written down on the eleventh of October, 1914: "Remember that the 'propositions about infinite numbers' are all represented by means of finite signs!" (Wittgenstein 1979, p.
As Christians made an attempt to buttress their revelatory experience of God also on the level of rationality, relying in this action on the rich philosophical heritage of the ancients, there was introduced a kind of clash between finitist
and infinitist elements into the thought structure of the Christian world.
Tait maintains that the chief difficulty for everyone who wishes to understand Hilbert's conception of finitist
mathematics is this: to specify the sense of the provability of general statements about the natural numbers without presupposing infinite totalities.
might deny that the indirect infinite liar is a liar paradox just as he denies that Yablo's variation is a liar.
What it lacks, but the finitist
demands, is a guarantee, stemming from a ground other than belief in the consistency of ZF, that the procedure will terminate.
The Greco-Roman model appears to be marked by the value of reciprocity, by homological, immanentist, finitist
, and politicist concord.