Logic

Is nothing impossible? Is it just that a lot of things have infinitely small probabilities of occurring?

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(This evening, shortly after reading this, I had dinner at arestaurant in NYC — and there was Mayor Bloomberg at the next table. I heard someone say, "Nothing's impossible after all.")

I'm not sure what an infinitely small probability would be. Perhapsjust a probability of 0? But that sounds like an impossible event. Soperhaps you're asking whether all events have some finite non-zeroprobability of occurring — and whether the events we call "impossible"really just have a very small finite probability.

Philosophershave spent a lot of time trying to figure out what we're actuallysaying when we assign a probability to an event. Are we making someclaim about the world? Or are we making a claim about our degree ofconfidence in some judgment about the world? I won't go into that hereand instead will say a few words about impossibility.

Philosophersoften distinguish between different kinds of impossibilities. Somesituations would conflict with the laws of logic: for instance, thestate of affairs in which I am over thirty years old and not overthirty years old is one that conflicts with the law of logic that saysthat "A and not-A" is false for every statement A. We might say thatthat state of affairs is logically impossible, or impossible relative to the laws of logic.By contrast, some situations conflict only with the laws of physics:for instance the state of affairs in which I am moving faster than thespeed of light is not a possible one according to contemporary physics.It's one that is logically but not physically possible, one that is impossible relative to the laws of physics.Likewise, we might have situations that we would describe as impossiblerelative to the laws of chemistry, and so on. And perhaps, when someonesuggests that your spouse is having an affair you will find yourselfexclaiming that that's impossible, meaning not that such perfidy isinconsistent with the laws of logic or physics, etc., but that it'sincompatible with what you believe to be true about your spouse.

If this is the right way to think about impossibility, then nothing is impossible — tout court. A situation is possible or impossible only relative to certain assumptions. And relative to any given body of assumptions, many situations will be impossible.

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