It is normal to think that a disjunctive proposition that is true is grounded in each of its true disjuncts.

This may be false. Let *p* be the proposition that 2+2=4. Let *q* be the infinite disjunction *p* or (*p* or (*p* or ...)). Then *q* is its own second disjunct. Moreover, *q* is true. But surely what *q* is grounded in is not *q* itself but *p*.

For the same reason, it does not appear correct to say that a conjunction is always partly grounded in at least one of its conjuncts. For instance, take the infinite conjunction: *p* and (*p* and (*p* and ...)). The second conjunct is the conjunction itself, but it does not seem that this conjunction is even partly grounded in itself.

When I came up with the disjunction example today, I thought that I could weaken the disjunctive grounding principle to say that a disjunction is grounded in at least one of its disjuncts. But even that is not clear to me right now. For perhaps we could construct a complex infinite disjunction such that each disjunct is the disjunction itself. But I am less sure that such a disjunction really does exist.

On reflection, I wonder if my examples work. Maybe there is no disjunctive proposition *p* or (*p* or (*p* or ...)), but only the disjunctive proposition ...(((*p* or *p*) or *p*) or *p*).... In other words, the direction of the infinite nesting may matter. The difference is that the latter disjunctive proposition has a starting point: we take *p* and disjoin *p* to it infinitely often. The former one does not.

Another interesting case is: "2+2=4 or the proposition expressed by this sentence is true."

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