Probability, Truthlikeness and the Cenk Uygur versus Sam Harris Debate

I became aware of the Young Turks and their main man Cenk Uygur earlier this year. As the months have gone by and I have watched more of their YouTube clips, Uygur’s arrogance, ignorance and general thickheadedness has become more apparent.

One conversation that I found interesting is the one Uygur had with Sam Harris, particularly the following portion, as it involves discussion relevant to truthlikeness and probability:

In this discussion, Harris makes the point that Mormonism is slightly more improbable/absurd than other Christian faiths because it makes the more specific claim that Jesus will return to Jackson County, Missouri rather than the more general claim that he will return to somewhere on Earth.

Now, the first problem with Uygur’s response is that he misrepresents Harris, by saying that it is just as equally unlikely that Jesus will return to Jerusalem as he will return to Missouri. Whether this is the case or not, it deviates from Harris’ point, which concerns the fact that an event occurring with an extra condition is going to be less probable than it occurring without the extra condition. In probability this is captured by the law that for any two propositions A and B, Pr(A & B) ≤ Pr(A).

Cenk, without necessarily understanding Harris’ point, says that both of his outcomes are equally unlikely. Whilst there are exceptional cases where Pr(A & B) = Pr(A), as will be discussed shortly, it is doubtful they apply to this example. But before looking at such cases and a possible charitable interpretation of Uygur’s claim, I want to touch upon another claim that he makes, one which exemplifies his lack of ability to understand or at least acknowledge the concept of degree. To quote Uygur:

That’s the difference between saying that 2+2=5 and 2+2=6; neither one is true so what difference does it make.

Well, it is true that both of those mathematical statements are false. But as someone who studied the concept of truthlikeness in their doctoral thesis, I can strongly say that there is a difference in degree of truthlikeness between these two statements; 2+2=5 is more truthlike than 2+2=6. To further illustrate this point, 2+2=5 and 2+2=1000 are both false, but the former is significantly more truthlike than the latter.

As I said, this is just one example of Uygur ignoring or being unaware of the fact that things can each possess a negative attribute but in unequal quantities. To take an example from another domain, two doctrines can both be morally problematic, with one being more morally problematic than the other.

Now, as mentioned, there is the possibility that Pr(A & B) = Pr(A). When AB or B is a logical tautology are two technical instances. In terms of our example, another instance where the two would be equal would be if the probability of Jesus returning to Missouri was equal to one, which clearly is not the case.

But the other possibility, and the one which could be charitably considered for Uygur’s example, is the case when Pr(A) = 0. To quote Uygur again:

it’s like dividing by zero … it’s equally unlikely that he is going to go to Jerusalem or Missouri.

Setting aside his division by zero disanalogy and apparent failure to appreciate Harris’s general mathematical point given his misrepresentation of Harris with the Jerusalem comparison, perhaps we can say that Uygur’s ultimate point is that since the probability of Jesus returning to Earth is zero, then the probability of him returning to Missouri is the same, zero. But is it rational to assign a probability of zero to Jesus returning to Earth?

According to the thesis of Bayesian regularity, all contingent propositions should be assigned a probability strictly between zero and one. Therefore apart from logical and other necessary falsehoods, no proposition will be assigned a probability of zero. Adoption of this philosophical position on probability would mean that the probability of Jesus returning is not zero and therefore `Missouri’ is less than `Earth’. Regardless though of this position on probability, which has its own issues, it seems reasonable to claim that we cannot assign a probability of zero to such a proposition. Yes it is utterly implausible from an atheistic viewpoint that Jesus will return to Earth in a second coming, but one cannot be absolutely certain of this; one cannot disprove that Jesus will be coming back. Perhaps therefore epistemic humility suggests that the probability of Jesus returning to Earth, whilst extremely small, is not to be assigned a value of zero. In this case, given that Missouri is not the only place that Jesus could return to, the probability of A (Jesus returning) & B (Missouri) is less than the probability of A.

The final point I want to consider is that even if two propositions have a probability of zero, one can be more absurd than the other. Consider the statements (1) there are unicorns somewhere on Earth (2) there are flying pigs somewhere on Earth. Whilst both statements may be assigned a probability of zero in the same sense that Jesus returning would be assigned a probability of zero, statement (1) here is in some sense less absurd than (2). This is because given the world we live in, a possible world in which horses have horns is closer than a world in which pigs have the ability to fly. Perhaps in a somewhat similar way Jesus returning to Missouri could be considered more absurd, even if the probability of a return at all is deemed to be zero. The gist would be something like the more specific you make a claim for which you have no evidence in the first place, the more absurd it becomes.

As discussed earlier, 2+2=5 and 2+2=6 both have a probability of zero but the former is more truthlike than the latter. It is an interesting question whether if (1) Jesus returning somewhere and (2) Jesus returning to Missouri both had a probability of zero and were therefore false, the former would still have more truthlikeness than the latter. For true statements, the more specific or logically stronger its claim the more truthlike it is; this is generally a feature of formal truthlikeness measures, although some accounts have the occasional exception. What about false statements? Is it reasonable to suppose the condition that if ∃x1P(c, x) (e.g. Jesus will return to some one place) is false, then the instantiation P(c, a) (e.g. Jesus will return to Missouri) is less truthlike? Well, off the top of my head it seems like some formal truthlikeness measures (e.g. Tichy/Oddie) will give both statements the same truthlikeness value whilst some will give them different values. This requires more investigation.

In summary:

  1. Given the reasonableness of assigning a minute but non-zero probability to Jesus returning, the probability of him returning to Earth is greater than the probability of him returning specifically to Missouri
  2. Even if Jesus returning to earth were assigned a probability of zero, adding extra conditions can make such a claim less truthlike, further from the real world and more absurd

Either too ignorant or deliberately antagonistic to acknowledge Harris’ point, Cenk misses the mark on this one, like many other things. Subsequent appearances where he claims that Harris is a pseudo intellectual and doesn’t understand probability rile me to no end. This post has been a nice opportunity to vent via analysing this debate with a formal philosophical lens.

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