Zigzag Philosophy

[Annette Fazzari]

Ive encountered the term zigzag theory while randomly clicking my way through the internet. It is given here. I haven't been able to find a clear explanation of what constitutes a zigzag theory. Here, it is said that they have to do with non-Cantorian sets, which, as I understand, are sets that fail to satisfy Cantor's theorem. The article also says that New Foundations is a zigzag theory, but I don't see that it says why exactly that is so. I have gone through the Wikipedia article on New Foundations, and there's nothing about zigzags in it.

In the zigzag theory, we start from the suggestion that propositional functions determine classes when they are fairly simple, and only fail to do so when they are complicated and recondite. If this is the case, it cannot be bigness that makes a class go wrong; for such propositional functions as "$x$ is not a man" have an exemplary simplicity, and are yet satisfied by all but a finite number of entites. In this theory, as well as in the theory of limitation of size, we define a predicative propositional function as one which determines a class (or a relation, if it contains two variables); thus in the zigzag theory the negation of a predicative function is always predicative. In other words, given any class $u$, all the terms which are not members of $u$ form a class which may be called the class not-$u$.

The zigzag theory, in some form or other, is that assumed in the definitions of cardinal and ordinal numbers as classes of classes (if numbers are supposed to be entities). For all these classes of classes, if they are legitimate, must contain as many members as there are entities altogether; hence, if bigness makes classes go wrong, as we suppose in the "limitation of size" theory, cardinals and ordinals so defined will be illegitimate classes.

Nozick's other work involved ethics, decision theory, philosophy of mind, metaphysics and epistemology. His final work before his death, Invariances (2001), introduced his theory of evolutionary cosmology, by which he argues invariances, and hence objectivity itself, emerged through evolution across possible worlds.[4]

Nozick was born in Brooklyn to a family of Jewish descent. His mother was born Sophie Cohen, and his father was a Jew from a Russian shtetl who had been born with the name Cohen and who ran a small business.[5]

At one point, Nozick joined the Young People's Socialist League, and at Columbia University he founded the local chapter of the Student League for Industrial Democracy. He began to move away from socialist ideals when exposed to Friedrich Hayek's The Constitution of Liberty, claiming he "was pulled into libertarianism reluctantly" when he found himself unable to form satisfactory responses to libertarian arguments.[6]

After receiving his undergraduate degree in 1959, he married Barbara Fierer. They had two children, Emily and David. The Nozicks eventually divorced; Nozick later married the poet Gjertrud Schnackenberg.

Nozick's first book, Anarchy, State, and Utopia (1974), argues that only a minimal state limited to the functions of protection against "force, fraud, theft, and administering courts of law" can be justified, as any more extensive state would violate people's individual rights.[8]

Nozick believed that a distribution of goods is just when brought about by free exchange among consenting adults, trading from a baseline position where the principles of entitlement theory are upheld. In one example, Nozick uses the example of basketball player Wilt Chamberlain to show that even when large inequalities subsequently emerge from the processes of free transfer (i.e. paying extra money just to watch Wilt Chamberlain play), the resulting distributions are just so long as all consenting parties have freely consented to such exchanges.

Anarchy, State, and Utopia is often contrasted to John Rawls's A Theory of Justice in popular academic discourse, as it challenged the partial conclusion of Rawls's difference principle, that "social and economic inequalities are to be arranged so that they are to be of greatest benefit to the least-advantaged members of society".

Nozick's philosophy also claims a heritage from John Locke's Second Treatise on Government and seeks to ground itself upon a natural law doctrine, but breaks distinctly with Locke on issues of self-ownership by attempting to secularize its claims. Nozick also appealed to the second formulation of Immanuel Kant's categorical imperative: that people should be treated as an end in themselves, not merely as a means to an end. Nozick terms this the 'separateness of persons', saying that "there is no social entity...there are only individual people", and that we ought to "respect and take account of the fact that [each individual] is a separate person".[9]

Most controversially, Nozick argued that consistent application of libertarian self-ownership would allow for consensual, non-coercive enslavement contracts between adults. He rejected the notion of inalienable rights advanced by Locke and most contemporary capitalist-oriented libertarian academics, writing in Anarchy, State, and Utopia that the typical notion of a "free system" would allow individuals to voluntarily enter into non-coercive slave contracts.[10][11][12][13]

Early sections of Anarchy, State, and Utopia, akin to the introduction of A Theory of Justice, see Nozick implicitly join Rawls's attempts to discredit utilitarianism. Nozick's case differs somewhat in that it mainly targets hedonism and relies on a variety of separate intuition pumps, although both works draw from Kantian principles.

There are also substantial puzzles when we ask what matters other than how people's experiences feel "from the inside." Suppose there were an experience machine that would give you any experience you desired. Superduper neuropsychologists could stimulate your brain so that you would think and feel you were writing a great novel, or making a friend, or reading an interesting book. All the time you would be floating in a tank, with electrodes attached to your brain. Should you plug into this machine for life, preprogramming your life's experiences?[15]

Nozick claims that life in an experience machine would have no value, and provides several explanations as to why this might be, including (but not limited to): the want to do certain things, and not just have the experience of doing them; the want to actually become a certain sort of person; and that plugging into an experience machine limits us to a man-made reality.

Another intuition pump Nozick proposes is the utility monster, a thought experiment designed to show that average utilitarianism could lead to a situation where the needs of the vast majority were sacrificed for one individual. In his exploration of deontological ethics and animal rights, Nozick coins the phrase "utilitarianism for animals, Kantianism for people", wherein the separateness of individual humans is acknowledged but the only moral metric assigned to animals is that of maximising pleasure:

Before introducing the utility monster, Nozick raises a hypothetical scenario where someone might, "by some strange causal connection", kill 10,000 unowned cows to die painlessly by snapping their fingers, asking whether it would be morally wrong to do so.[17] On the calculus of pleasure that "utilitarianism for animals, Kantianism for people" uses, assuming the death of these cows could be used to provide pleasure for humans in some way, then the (painless) deaths of the cows would be morally permissible as it has no negative impact upon the utilitarian equation.

Nozick later explicitly raises the example of utility monsters to "embarrass [utilitarian theory]": since humans benefit from the mass sacrifice and consumption of animals, and also possess the ability to kill them painlessly (i.e., without any negative effect on the utilitarian calculation of net pleasure), it is permissible humans to maximise their consumption of meat so long as they derive pleasure from it. Nozick takes issue with this as it makes animals "too subordinate" to humans, counter to his view that animals ought to "count for something"[18]a.

Nozick's third and fourth conditions are counterfactuals. He called this the "tracking theory" of knowledge. Nozick believed the counterfactual conditionals bring out an important aspect of our intuitive grasp of knowledge: For any given fact, the believer's method (M) must reliably track the truth despite varying relevant conditions. In this way, Nozick's theory is similar to reliabilism. Due to certain counterexamples that could otherwise be raised against these counterfactual conditions, Nozick specified that:

A major feature of Nozick's theory of knowledge is his rejection of the principle of deductive closure. This principle states that if S knows X and S knows that X implies Y, then S knows Y. Nozick's truth tracking conditions do not allow for the principle of deductive closure.

The Examined Life (1989), aimed towards a more general audience, explores themes of love, the impact of death, questions of faith, the nature of reality, and the meaning of life. The book takes its name from the quote by Socrates, that "the unexamined life is not worth living". In it, Nozick attempts to find meaning in everyday experiences, and considers how we might come to feel "more real".[21] In this pursuit, Nozick discusses the death of his father, reappraises the experience machine, and proposes "the matrix of reality" as a means of understanding how individuals might better connect with reality in their own lives.[22]

The Nature of Rationality (1993) presents a theory of practical reason that attempts to embellish classical decision theory. In this work, Nozick grapples with Newcomb's problem and the Prisoner's Dilemma, and introduces the concept of symbolic utility to explain how actions might symbolize certain ideas, rather than being carried out to maximize expected utility in the future.

3a8082e126