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According to the truth-tracking theory of Nozick,

S knows that P iff

(1) P is True,

(2) S believes that P,

(3) If P were not True, S would not believe that P, and

(4) If P were True, S would believe that P

But when explaining the third subjunctive, Nozick limits himself in examining "those worlds in which P holds True that are closest to the actual world, Q also is True." (Q := S would not believe that P)

Why is that so? Why he restrict his two counterfactual tests only to the nearest possible worlds? Is this just a choice or is there any reasoning behind this?

Nozick, Robert, Philosophical Explanations (Cambridge MA: Harvard University Press, 1981), pp. 172-175

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    Because nothing will come out as truth tracking if wild possibilities, like deceitful demons or brains in a vat, are allowed.
    – Conifold
    Nov 11, 2020 at 1:09
  • @Conifold, the skeptic still wins then. Even we incorporate the fourth subjunctive or ways and methods of Nozick, it still cannot address the cartesian demon or a BIV. Ideally, this should be a worry.
    – Abdul Muhaymin
    Nov 11, 2020 at 15:15
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    – J D
    Nov 11, 2020 at 15:32
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    There are two parts to winning: making an argument and getting it listened to. Consider an analogy: someone on the street tells you that you shall suffer eternally unless you pay $XXX and challenges you to refute it. You tell them to get lost. Did they win? It is the second part that skeptical arguments typically fail to meet, only those that can are interesting enough to "win".
    – Conifold
    Nov 12, 2020 at 1:33

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At the time Nozick wrote Philosophical Explanations, the theories of conditionals advanced by David Lewis and Robert Stalnaker were still fairly new. Lewis' book Counterfactuals was published in 1973 and Stalnaker's work was published in a series of papers from about 1968 onwards. Previously there hadn't been any generally accepted account of how counterfactual conditionals worked. Lewis and Stalnaker both drew on Kripke's work in using possible worlds (PW) to explicate the logic of necessity and possibility. They advanced similar accounts, under which a conditional "if A then B" is true when in the closest PW in which A is true, B is also true. There were some differences between them and various complications, but this was the basic notion. Actually, for Stalnaker, it was intended as an account of indicative conditionals as well.

The Lewis and Stalnaker account proved popular, though there are now several others, so Nozick adopted it in order to explain his counterfactual theory of knowledge.

According to Lewis, it is only the closest PW that determines the truth of a counterfactual. If A is false in the actual world, but true in some other PWs, then we use a bunch of rules of thumb to determine which is the closest PW and check whether B is true in that PW. So, for example, "if I hadn't missed my train I would be in London by now" is true if in the closest PW in which my counterpart catches the train they are in London. Since the trains are fairly reliable where I live, this counterfactual comes out true. More distant worlds where weird things happen, or the laws of nature are different, or the history of the world is unlike ours do not contribute to the truth of the counterfactual.

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  • Thanks. So is it safe to say that Nozick lowered the standard of knowledge by passing his counterfactual condition only to the closest possible world!? Cause whenever a Cartesian demon or a BIV gets involved, it seems that both of the counterfactuals fail.
    – Abdul Muhaymin
    Nov 11, 2020 at 15:20
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    @Earmen: This is no problem if these concepts are incoherent, as e.g. Putnam showed analytically.
    – Philip Klöcking ♦
    Nov 11, 2020 at 18:47
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    @Earmen That's really the whole point of Nozick's approach. He wants to say I know I am in Boston, or wherever it is I am, but I don't know that I'm not a brain in a vat, or being deceived by an evil demon. The counterfactuals correctly track the first belief but not the second. An important consequence is that for Nozick knowledge is not closed under known entailment. I can know P, know that P entails Q, knowingly infer Q from P, but still not know Q.
    – Bumble
    Nov 11, 2020 at 22:44
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    @Earmen Indeed, Nozick lowered it too much, but not so much by using the closest worlds as by choosing the particular form of his counterfactual (sensitivity) conditions. "George knows that he has hands, but he doesn’t know that he’s not the handless victim of a Cartesian demon" is what De Rose called an "abominable conjunction" that Nozick's theory endorses, and one big reason why it quickly fell out of favor, see SEP, Sensitivity.
    – Conifold
    Nov 12, 2020 at 1:52

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