Steve Newcomb schrieb:
> Ingvar Johansson <ingvar.johansson@xxxxxxxxxxxxxxxxxxxxxx> writes:
>
>> (2) Is it merely your subjective opinion that mathematics is grounded in
>> itself?
>>
>
> Nah. But for the sake of the question you're developing here, let's
> stipulate that it is indeed merely my subjective opinion.
>
>
>> (3) If it is merely your subjective opinion, is then your opinion an
>> opinion *about a fact* or an opinion about something else?
>>
>
> I'm having trouble following your question. You seem to be making a
> distinction between opinion and fact (which is a useful thing to do),
> but you haven't characterized the distinction. (01)
O.K., now I will try. There is a class of entities such as perceptions,
opinions, assertions, statements, and propositions that can be
characterized by saying that (normally) they have *aboutness*
(alternatively, *directedness* or *intentionality*). There is another
class of entities that can be characterized by saying that they lack
this feature of *aboutness*. To this class belongs: (i) kinds of
concrete things such as atoms, molecules, and macrolevel material
things, as well as kinds of abstract entities such as sets and
mathematical numbers; (ii) properties such as mass, volume, shape, and
being a prime number; (iii) obtaining states of affairs constituted by
the kind of things and properties mentioned in (i) and (ii). This
distinction makes it possible to say that *opinions can be about
entities that are not themselves opinions*; but, of course, there can be
opinions about opinions, too. (02)
What is perplexing to many people is that if there is *aboutness*, then
this aboutness must be *about something that exists*. But this is not
always the case. If I assert "there is a beer in the fridge", I have
made an assertion that is true or false, and which (assuming we are in
the same apartment) you can go and check. If there is a beer, my
assertion is true, and it is about the beer and the fridge. If there is
no beer, my assertion is false, and it is about the fridge but not about
a beer. Nonetheless, my assertion has - no doubt! - *aboutness towards a
beer*. The aboutness of an assertion is logically prior to the latter's
truth-value. (03)
The ontological-semantic point made above must not be conflated with our
epistemological predicament. We can never be literally *absolutely sure*
whether or not there is a beer in the fridge; for instance, you may
hallucinate that there is a beer even though there is none. But this
epistemological point cannot possibly cancel the ontological-semantic
point, since the latter is a presupposition for asking questions such as
"can we know this?". (04)
I think I need a beer,
Ingvar (05)
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