The Logical Must: Wittgenstein on Logic

by Penelope Maddy

The Logical Must is an examination of Ludwig Wittgenstein's philosophy of logic, early and late, undertaken from an austere naturalistic perspective Penelope Maddy has called "Second Philosophy." The Second Philosopher is a humble but tireless inquirer who begins her investigation of the world with ordinary perceptual beliefs, moves from there to empirical generalizations, then to deliberate experimentation, and eventually to theory formation and confirmation. She takes this same approach to logical truth, locating its ground in simple worldly structures and our knowledge of it in our basic cognitive machinery, tuned by evolutionary pressures to detect those structures where they occur. In his early work Tractatus Logico-Philosophicus, Wittgenstein also links the logical structure of representation with the structure of the world, but he includes one key unnaturalistic that the sense of our representations must be given prior to-independently of-facts about how the world is. When that assumption is removed, the general outlines of the resulting position come surprisingly close to the Second Philosopher's roughly empirical account. In his later discussions of logic in Philosophical Investigations and Remarks on the Foundations of Mathematics, Wittgenstein also rejects this earlier assumption in favor of a picture that arises in the wake of the famous rule-following considerations. Here Wittgenstein and the Second Philosopher operate in even closer harmony-locating the ground of our logical practices in our interests, our natural inclinations and abilities, and very general features of the world-until the Second Philosopher moves to fill in the account with her empirical investigations of the world and cognition. At this point, Wittgenstein balks, but as a matter of personal animosity rather than philosophical principle.

Genres: Philosophy, Logic

152 pages, Kindle Edition

First published August 1, 2014

About the author

Penelope Maddy is a UCI Distinguished Professor of Logic and Philosophy of Science and of Mathematics at the University of California, Irvine. She is well-known for her influential work in the philosophy of mathematics where she has worked on realism and naturalism.
Maddy received her Ph.D. from Princeton University in 1979.
Her early work, culminating in Realism in Mathematics, tried to defend Kurt Gödel's position that mathematics is a true description of a mind-independent realm that we can access through our intuition. However, she suggested that some mathematical entities are in fact concrete, unlike, notably, Gödel, who assumed all mathematical objects are abstract. She suggested that sets can be causally efficacious, and in fact share all the causal and spatiotemporal properties of their elements. Thus, when I see the three cups on the table in front of me, I also see the set as well. She used recent work in cognitive science and psychology to support this position, pointing out that just as at a certain age we begin to see objects rather than mere sense perceptions, there is also a certain age at which we begin to see sets rather than just objects.
In the 1990s, she moved away from this position, towards a position described in Naturalism in Mathematics. Her "naturalist" position, like Quine's, suggests that since science is our most successful project so far for knowing about the world, philosophers should adopt the methods of science in their own discipline, and especially when discussing science. However, rather than a unified picture of the sciences like Quine's, she has a picture on which mathematics is separate. This way, mathematics is neither supported nor undermined by the needs and goals of science, but is allowed to obey its own criteria. This means that traditional metaphysical and epistemological concerns of the philosophy of mathematics are misplaced. Like Wittgenstein, she suggests that many of these puzzles arise merely because of the application of language outside its proper domain of significance.
Throughout her career, she has been dedicated to understanding and explaining the methods that set theorists use in agreeing on axioms, especially those that go beyond ZFC.

http://en.wikipedia.org/wiki/Penelope...

Reviews

[Ali Reda · Rating 1 out of 5]

This isn't a reading of the Tractaus on its own terms, but a reading through Quine and Mill's Philosophy [a naturalist conception of logic where Logic is derived from the world through experience] despite the fact that the Tractatus itself was against this conception completely. So Maddy completely rejects the a priori necessity of logic and it being transcendental and its metaphysical implications for the world as a whole. And the same applies for her reading of Kant where she rejects the transcendental level in Kant's logic and only keeps the empirical level. So it keeps one wondering why refer to Wittgenstein and Kant in the first place?

[Ben · Rating 4 out of 5]

This is a terse and brief book which will appeal to anyone interested in Wittgenstein, philosophy of logic or Penelope Maddy’s other work. The book peaks in its discussion of the Tractatus and its comparison between Early Wittgenstein and Kant on logic

[Richard · Rating 4 out of 5]

illuminating on connections and differences between kant/tractatus/later wittgenstein, though her substantive views aren't really defended at length in the book