Transitivity Denial Is Crackpot Lunacy

At least climate change deniers accept transitivity

A preliminary note: Denying transitivity is a respectable academic position. Much of the harsh wording is as a result of A) My strong sentiments on the matter and B) My finding it funny to refer to philosophical views as “denialism.”

If A>B and B>C then A>C. Right? We’re done here, no further justification needed. What could be more obvious than that? Transitivity science denial is lunacy, absurdity, foolishness, and crackpottery¹.

For those who have been living under a rock² transitivity³ is the notion that if A is morally better than B and B is better than C, then A is better than C. Yet some have taken to denying transitivity—even otherwise serious individuals like Temkin. So aside from outraged squawks, what can us defenders of transitivity muster to defend truth, justice, and all that is good⁴ ⁵. Well, here are several arguments.

First, transitivity is incredibly intuitive⁶.  It seems extremely implausible that A could be morally better than B, which could be better than C, but C could be better than A.  One who prefers A to B, B to C, but C to A, seems to have misunderstood the definition of the word prefer.  

The second objection given by (Huemer) is the money pump objection.  If one prefers B to C, then they should be willing to trade C and something of value for B. If one prefers A to B, then they should be willing to trade B and something of value for A.  If one prefers C to A, then they should be willing to trade A and something of value for C.  If one has all these preferences, we can take everything of value to them, by trading B and something of value for A, C and something of value for B, and C and something of value for A.  We can keep going through these trades until they lose everything of value.  

The Third argument comes from Huemer ,once again⁷.

It relies on two premises.  

1. Dominance: For any states of affairs x1, y1, x2 and y2, if x1 is better than y1 and x2 is better than y2, and there are no significant relationships between any of these states, x1 + x2 is better than y1 + y2.  

2. Asymmetry: If X>Y Y is not better than X.  

The dominance principle can be seen with an example.  Suppose I prefer an apple to an orange and one pair of mittens to another pair of mittens.  If there are no relationships between any of them, then I’d prefer apples and the first pair of mittens to the second pair of mittens and oranges.  

If dominance and asymmetry are true, so is transitivity.  Suppose I prefer A to B, B to C, and C to A.   Then suppose I’m comparing A and B to B and C.  Which would I prefer.  

Well, arranged one way I’d prefer A and B.  After all I prefer A to B and B to C, so arranged that way, I prefer A and B.  

However, arranged a different way I’d prefer B and C.  I prefer C to A and find B equally good to B.  Thus, if we compare 

A to C and B to B we BC > AB, because C>A and B=B.  However, if we compare 

A to B and B to C then we get AB>BC because A>B and B>C.  

A fourth argument for transitivity is the offset argument.  Suppose we accept that 1 year of suffering at intensity 10,000 is less bad than 2 years of suffering at intensity 8,000, which is less bad than 3 years of suffering at intensity 7,000,... which is worse than 1,000,000,000,000,000,000 years of suffering at intensity .0000001.  The person who rejects transitivity thinks that each scenario gets worse than the previous ones, but the last one is better than the first one.  

We can additionally suppose that, rather plausibly, each list of intensities over time has a number of years of pleasure at intensity 10,000 which is sufficiently good that the suffering and the pleasure in conjunction are neutral.  E.G. if the number of years of pleasure required to offset 1 year of suffering at intensity 10,000 is 2, then perhaps the number of years of pleasure to offset 2 years of suffering at intensity 8,000 would be 4.  

Thus, for each list, the number of years of pleasure required to offset would increase over time.  Suppose that the number of years of pleasure required to offset the last scenario is 100,000,000,000.   This would mean that the conjunction of 1,000,000,000,000,000,000 years of suffering at intensity .0000001 and 100,000,000,000 years of pleasure at intensity 10,000 is morally neutral.  Additionally, the conjunction of 1 year of suffering at intensity 10,000 and 2 years of pleasure at intensity 10,000 is morally neutral.  

Thus, if we accept the principle that, if to offset the badness of A one needs something better than they would to offset the badness of B, then A is worse than B, then we’d have to accept transitivity.  If for each bad thing one needs something increasingly good to offset it, then better than must be transitive.  

This is incredibly hard to deny⁸.  If you need something much better to offset 1,000,000,000,000,000,000 years of suffering at intensity .0000001 than to offset 1 year of suffering at intensity 10,000, it’s hard to deny that 1,000,000,000,000,000,000 years of suffering at intensity .0000001 is worse.  

Given that 1,000,000,000,000,000,000 years of suffering at intensity .0000001 + 100,000,000,000 years of pleasure at intensity 10,000 is morally equal to 1 year of suffering at intensity 10,000 + 2 years of pleasure at intensity 10,000, and 100,000,000,000 years of pleasure at intensity 10,000 is clearly better than  2 years of pleasure at intensity 10,000, 1,000,000,000,000,000,000 years of suffering at intensity .0000001 is worse.  

A fifth argument for transitivity is the following.  Suppose we’re deciding between A, B, and C.  A>B, B>C, but C>A, based on our preferences.  Which one should we choose?  On this account, there is no right answer, because each option has a better option that could be chosen.  B is preferable to C, A is preferable to B, but C is preferable to A, so no option that can be chosen is the right option.  This requires rejecting a very plausible principle, which is that if A>B then we should never choose B instead of A.  

So let’s dispel with this transitivity denying lunacy. We’re better when we all accept transitivity then when only some of us do and we’re better when some of us do then when none of us do (thus by transitivity we’re better when we all do then we are when none of us do).

1. Keen readers will note that I am not here describing the breaking of poverty.

2. By which I mean, not reading random obscure philosophy papers.

3. In ethics

4. Keen readers may sense that this article has more bizarre passionate fervor and less detached observation than usual.

5. Keen readers may also notice lots of footnotes.

6. For more on why we should believe intuitive things, see Ethical Intuitionism, by Michael Huemer

7. No, I have not been sponsored.

8. Especially if one has not had their brain polluted by denial of transitivity