Tag Archives: Philosophy

Incompleteness: The Proof and Paradox of Kurt Godel by Rebecca Goldstein

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This is the story of Kurt Godel, considered to be the greatest logician since Aristotle and the second greatest mind of the 20th century after Einstein. The book includes discussion of the Vienna Circle, whose meetings Godel sometimes attended; Godel’s differences with Wittgenstein, whose views impressed the Vienna Circle but not Godel; and Godel’s friendship with Einstein, when both of them were at the Institute for Advanced Studies in Princeton.

Godel is most famous for proving that that any formal system that is rich enough to contain arithmetic or number theory must contain a true statement that can neither be proven nor disproven, in other words, that such a system is necessarily incomplete. A corollary of the incompleteness theorem is that any such system cannot be proven to be consistent within the system itself. Goldstein suggests that the incompleteness theorem demonstrates that there is a mathematical reality beyond the reach of any human-made formal system.

Goldstein steps through the proof of incompleteness, but I didn’t or couldn’t follow the whole proof.  The proof seems to rely on the strange consequences that result from sentences that refer to themselves, such as “This sentence is false”. Russell ruled out such sentences in his Theory of Types, and that seems like a good idea to me. It may be arbitrary, but it seems right to say that sentences that refer to themselves and sets that contain themselves should not be allowed in any formal system, given the paradoxical results that follow.  (5/11/10)

Saving God: Religion After Idolatry by Mark Johnston

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Johnston tries to determine what God would really be, not the God necessarily worshiped by Judaism, Christianity or Islam. He develops the idea of the actual Highest One as “the outpouring of Existence Itself by way of its exemplification in ordinary existents for the sake of the self-disclosure of Existence Itself”. The teleological “for the sake of” is difficult to understand, which Johnston acknowledges, since he is suggesting a completely naturalistic view of existence. His view is panentheistic: God is wholly constituted by the natural realm.

Johnston’s argument leads to an extended discussion of how existence presents itself to us, how we are samplers of Presence, not producers of Presence. He rejects the idea that we perceive the world via representations in our minds. Perception is of the world itself. He concludes by suggesting that we survive death by identifying ourselves with the people who live on after us, an idea that must be discussed at much greater length in his slightly more recent book “Surviving Death”.  (5/7/10)

Mind and World by John McDowell

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This is a serious work of philosophy that deserves more than one reading. McDowell says that he is trying to overcome the philosophical tendency “to oscillate between a pair of unsatisfying positions: on one side a coherentism that threatens to disconnect thought from reality, and on the other side a vain appeal to the Given”. He suggests that in order to escape this oscillation, “we need to recognize that experiences themselves…combine receptivity and spontaneity”. Kant distinguished between the receptivity involved in receiving sense impressions and the spontaneity involved in rational thought. 

One way of describing McDowell’s position is that experience always involves the application of concepts. Experience, therefore, exposes us to nature (the realm of law) while standing in rational relations to beliefs and judgments (the normative space of reasons). According to McDowell, this dual aspect of experiences allows us to find a resting place between the two unsatisfactory positions referred to above. As we mature and learn to speak a language, we acquire the ability to use concepts. This is a completely natural process, what he calls “naturalized platonism”, as opposed to an otherworldly “rampant platonism”.  (3/31/10)

Lust by Simon Blackburn

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This is one of a series on the Seven Deadly Sins, but may differ from other books in the series, since the author defends what is supposed to be sinful. Blackburn defines “lust” as “the enthusiastic desire, the desire that infuses the body, for sexual activity and its pleasures for their own sake”.

He endorses Hobbes’s explanation of this pleasure: “LUST…is a sensual pleasure, but not only that; there is in it also a delight of the mind: for it consisteth of two appetites together, to please, and to be pleased; and the delight men take in delighting, is not sensual, but a pleasure or joy of the mind”.

Blackburn contrasts this view with that of Aristophanes: sexual desire is “the hopeless attempt to regain a total unity, a fusion of self and other”. Dryden translates Lucretius on the impossibility of attaining this goal: “They grip, they squeeze, their humid tongues they dart; As each would force their way to t’other’s heart; In vain, they only cruise about the coast; For bodies cannot pierce, nor be in bodies lost”.

On the other hand, a Hobbesian unity is attainable between sexual partners sometimes, much like musicians who create a unified performance.

This is a playful but serious book. Blackburn concludes that “lust best flourishes when it is unencumbered by bad philosophy and ideology, by falsities, by controls, by distortions, by corruptions and perversions and suspicions, which prevent its freedom of flow”. (3/22/10)

Being Good: A Short Introduction to Ethics by Simon Blackburn

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It is rather short, and not as satisfying as Blackburn’s Truth. The book is divided into three parts. The first deals with seven threats to ethics, such as the Death of God, Relativism and Determinism. The second deals with some ethical ideas, such as Utilitarianism and Rights. And the third discusses possible foundations for ethics, like those offered by Kant and Rawls.

Blackburn is skeptical about providing a rational foundation for ethics, somehow “built into the order of things”, but argues that it is good enough that, as social beings, we can share an ethical framework based on sympathy for each other. This framework allows us to reason about ethics, but only within that framework.  (3/19/10)