One Man’s Modus Ponens is Another Man’s Modus Tollens

Sometimes you hear this expression “one man’s modus ponens is another man’s modus tollens” (hereafter MPMT) from philosophers and others. Here’s my understanding of it.

Modus Ponens and Modus Tollens are argument forms. Arguments are attempts to support a claim with reasons or evidence. The reasons/evidence are the premises, the claim being supported is the conclusion. Conclusions are often indicated by the keyword therefore.

Modus Ponens:
(1) If A, then B
(2) A
(3) Therefore, B

Example:
If today is Monday, then tomorrow is Tuesday.
Today is Monday.
Therefore, tomorrow is Tuesday.

Modus Tollens:
(1) If A, then B
(2) Not B
(3) Therefore, Not A

Example:
If today is Monday, then tomorrow is Tuesday.
Tomorrow is not Tuesday.
Therefore, today is not Monday.

Now for MPMT. It occurs when there are disagreeing parties. The first offers modus ponens. The opponent agrees with the first premise, but disagrees with the conclusion, and therefore, with the second premise.

It’s form:
Modus Ponens
(1) If A, then B
(2) A
(3) Therefore, B

Opposing Modus Tollens
(1) If A, then B
(2′) Not B
(3′) Therefore, Not A

The result is an battle between (2) and (2′). The first thinks that there is more behind A than Not B. The second thinks there is more behind Not B then A.

Here’s more of a real life example:

Conservative Modus Ponens:
(1) If freedom is more valuable than equality, then the government shouldn’t redistribute wealth.
(2) Freedom is more valuable than equality.
(3) Therefore, the government shouldn’t redistribute wealth.

Liberal Modus Tollens:
(1) If freedom is more valuable than equality, then the government shouldn’t redistribute wealth.
(2′) The government should redistribute wealth.
(3′) Therefore, freedom is not more valuable than equality.

These arguments agree on (1). The idea is that freedom and equality conflict at points. (Example, tall men have an unequal share of dating opportunities. To make things equal, we’d have to force women to consider short men equally. To make everyone equal regarding income, we’d have to prevent some people from earning and keeping more.) They disagree on which of these two have the most behind it: That freedom is more valuable than equality, or that the government should redistribute wealth.