FOM: truth, assertion, commands etc.

[Neil Tennant]

John Mayberry is, I believe, correct in his intuition that assertion
and truth are basic. Most philosophers of language who have studied
other speech acts besides assertion tend to agree on that point. For
each speech act has `fulfilment' or `satisfaction' conditions, for the
appreciation of which a grasp of assertion (hence of truth, as what
assertions aim at) is required.

For example, take the command "Bring it about that p!"  In order to
tell that the command has been carried out, you must be able to tell
*that p* is the case (presumably as a result of actions by your
audience after the command was issued).

If you express the wish "I wish it were the case that p!", then you
can enjoy the pleasant surprise of learning that your wish has been
fulfilled only if you can recognize, subsequently, *that p* is the
case. Indeed, we often speak of wishes "coming true", and of "making
(other people's) wishes come true". 

This locution should indeed be generalized across all speech acts. To
make a command true would be to make true the embedded "core content"
p. But in English we prefer to speak of "carrying out" the command, or
"granting" the wish, or "realizing" someone's worst fear. These are
all cases of making true the core content involved.

It is not at all surprising that in mathematics we often express the
argumentative status of an assumption "for the sake of argument" by
means of a "command" whose execution would "make it true". When I say
"Now drop the perpendicular from C to AB, and call it AD", I do so
with the background knowledge (from an axiom or a previously proved
lemma) that from any point C off any line AB there is exactly one
perpendicular to AB. What I am doing is performing an existential
elimination (and exploiting a uniqueness condition, as can be seen
from the use of the definite article "the", rather than the indefinite
article "a"). In the context of a diagram under construction (whether
on the page or in the mind's eye), carrying out the command produces a
*witness* to the existential in question, and therefore *makes it
true* that there is a unique perpendicular *within the diagram*. When
we continue to reason "about the `perpendicular' AD" from A to BC, the
phrase AD is the name-like parameter in the subordinate proof for an
existential elimination.

The same is happening with the use of the "optative" mood rather than
the "imperative" mood in the expression of assumptions for the sake of
argument. I might just as well say "Let AD be the perpendicular from A
to BC" in the foregoing example. 

Of course, this account needs to be fine-tuned to take care of the
case where the assumption is made in the course of a reductio ad
absurdum argument. In that case one is dealing with "hypothetical
truth", and saying that it could be conferred on the new assumption
(in the diagram under construction) if all the current assumptions
could themselves be true. This still brings out the primacy of the
declarative mood and of truth.

It would be interesting to know what `take' people like Jon Barwise
and his group at Indiana have on these matters, since they have spent
a lot of time studying diagrammatic reasoning.

Neil Tennant