The Problems of Contemporary Philosophy by Paul Livingston & Andrew Cutrofello

Author:Paul Livingston & Andrew Cutrofello
Language: eng
Format: epub
Publisher: Wiley
Published: 2015-10-29T16:00:00+00:00

3.5 Is it possible to refer to the whole of which we are parts?

Philosophers since (at least) Parmenides have considered the possibility of conceiving of or talking about the whole of being. For Parmenides, although it is in a certain sense impossible to speak of or conceive of non-being, there is a basic connection or sameness between thought and the totality of being, which Parmenides considers to be a bounded, homogeneous whole or “one.” In his dialogue Par­menides, Plato derives a series of paradoxes or seemingly contradictory results, in Parmenides’ own voice, from the claim that the “one” of the whole of being exists and can be rationally considered and spoken about. The dialogue famously ends with the aporetic conclusion that “…whether [the] one is or is not, it and the others both are and are not, and both appear and do not appear all things in all ways, both in relation to themselves and in relation to each other” (Plato, 1997: 397 [Parmenides, 166c]).

In the “Transcendental Dialectic” of the Critique of Pure Reason, Kant develops a series of arguments for opposed conclusions, or antinomies, each of which concerns the idea of the totality of the world. For instance, the first antinomy considers whether the world has a beginning in time and an outer bound in space (the thesis) or has always existed and is infinite in extent (the antithesis). Kant argues that while it is impossible to prove either claim directly, it is apparently possible to prove both indirectly by deriving a contradiction from the opposite claim. The resulting contradiction – or apparent contradiction – shows, he thinks, that the dispute must rest on an unwarranted assumption. This assumption is that the phenomenal world, considered as the sum total of temporally given appearances, can be given all at once as a totality. Kant takes this result to confirm his idealist thesis that the world of appearances only exists to the extent that it has actively been synthesized by the operations of a transcendental subject.

By contrast with this, a variety of projects of twentieth-century philosophy have assumed that it is both possible and meaningful to talk assertively about the world as a totality. Wittgenstein's Tractatus, for instance, begins with the statement that “The world is all that is the case.” And recent projects in metaphysics, for instance David Chalmers's Constructing the World (Chalmers, 2012) and Ted Sider's Writing the Book of the World (Sider, 2011) have similarly presupposed or argued for the accessibility of the world as a whole or its underlying structure to our philosophical understanding or analysis.

In the late nineteenth century, Cantor revolutionized philosophical and mathematical thought about totalities by showing that it is mathematically possible to consider certain infinite totalities, such as the totality of all natural numbers (0, 1, 2, 3…) as whole and actually completed (infinite) sets. Additionally, Cantor showed that some infinite sets are (in a strict sense) bigger than others, and that for any set (finite or infinite) the set of all its subsets is bigger (in this sense) than the initial set itself.

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