Curling heresies, pt. iii

Now it gets fun.

3. It is not possible that another team won more head-to-head matches than Bob's team.

If Bob's team won the round-robin tournament, then this statement is true. If you want to get picky about tie-breaking procedures, we can stipulate that the tie-breaking procedures used in the tournament were such that no team could win the most head-to-head matches without also winning the tournament.

So what might Alice believe about Statement #3? It might help to consider #3 together with its opposite:

4. It is possible that another team won more head-to-head matches than Bob's team.

As I say,

(#1 is true) => (#3 is true)
(#1 is true) => (#4 is false)

But these implications are both objective, or logical, or factual. The question is whether these logical implications imply

(belief that #1 is true) => (belief that #3 is true)
(belief that #1 is true) => (belief that #4 is false)

My contention is that they do not.

Wait, I'll go further: My contention is that the contention that they do not is not contentious. It's the common experience of humanity. Anyone who has ever mistaken someone on the street for someone else, anyone who has ever added a column of numbers incorrectly, has held contradictory beliefs ("beliefs" used here in the broad sense of things you assert through knowledge, faith, or opinion).

To hold contradictory beliefs is not itself contradictory, at least not necessarily. Given the three bases by which I might assert something -- knowledge, faith, and opinion -- the only combination of contradictory assertions I cannot make is of two things I know (since what I know is necessarily true and truths cannot contradict each other). Since what I assert by faith and what I assert by opinion is not necessarily true, I am not necessarily doing anything impossible in asserting something by faith or opinion that is objectively contradictory to something else I assert.

It might help to point out the distinction I'm implying with the term "objectively contradictory." I can assert two contradictory things, but only if I don't think they're contradictory. If I know, believe by faith, or opine that they are contradictory, I cannot rationally assert them both.

Next step is to actually try to answer the question of what Alice might believe about Statement #3.

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