Brian:
> In formal logic, whether approached from philosophy
> or, as in my case, from mathematics, it is not an
> assumption;
No, it wouldn't be an "assumption" to a strict
Logic priest :) However, clearly you can see that
existence is fundamentally an assumption that is
required to make Logic work. So, yes, it's sadly an
assumption, making Logic merely a philosophy or
religion one may choose to live by, like any other.
However, my way of looking at Logic outside of the
sphere of Logic does not matter much to the results
born from our perceptions of Logic here on a forum
devoted to the religion of Logic since we are all
expected to be Her devout followers and She has
a strict code of law :)
> as I said, and meant quite literally, it's a matter
> of definition.
More or less, yes, but I think you're being too
narrow-minded if you think that existence, and
subsequently Logic, is not fundamentally an unprovable
assumption. I respect Logic but She is what She is.
> The terms are defined in such a way that no entity
> is both.
In your usage of the terms. Of course, I have sinned
and have been using my own definitions. I admit that
I must repent for this. I will offer a computer
program to my local temple of Athena today.
> Indeed, having taught many students who habitually
> confused validity of inference with truth of
> conclusion, I'd say that the distinction is
> not just useful, but also a prerequisite to clear
> thinking.
Yes, I understand your point and agree. However, I
don't see how this has a bearing on how I assessed
your hypothetical example. Read below.
> The fact that the premises are false tells you
> nothing about the truth or falsity of the
> conclusion.
Yes, but Brian, you're using "true" and "false" in
absolute terms like any good Boolean citizen. I
use them in relative terms. The conclusions I make
are *never* written in stone. I adapt to the realities
I discover along the way. This is why you are having
issues with what you perceive incorrectly to be
stern, unwavering conclusions that you *think* I'm
making. Most often it seems, people on this Forum
still think that I make unchanging conclusions and
yet my views have clearly changed over the years. Odd.
Now, based on the scenario in your previous post, I
would have _temporarily_ concluded (and only
_temporarily_, pending new and contadicting facts)
that it is "more likely" that the conclusion is a
false one.
If I since discovered that the statements were more
relatively true than I first thought, then I would
see that the conclusion too is more relatively true
than I had assessed in the first iteration of my
examination.
> You are not logically entitled to conclude that the
> conclusion is relatively untrue, [...]
We are entitled to make conclusions to all statements
that we come across... otherwise we aren't thinking.
:) The key is that the conclusions one makes can only
ever be temporary and non-final. The conclusions must
be based on the relative facts available at the time.
Again, in the previous example, the available relative
facts that I had told me that a giraffe does not have
the qualities described. Ergo, the statement was
relatively false and all subsequent conclusions based
on it are also relatively false. I then would await
to see the day when the initial statement is true
(which would probably require nothing short of a
voyage into parallel universes to make it so). Rather
than hold my breath, I would continue on searching
for more profitable conclusions.
> All you can legitimately conclude is that the
> argument, despite its impeccable inference, offers
> zero support the conclusion;
Yes. However, until it does offer support, there is
no need to revisit the claim. It remains most
relatively false until then and irrelevant to me.
> the conclusion itself may nevertheless be true,
> [...]
Exactly. However, possibility is irrelevant. Only
probability is relevant. It is probably untrue,
therefore it is irrelevant (for now, until there
are new facts showing otherwise).
> To put it another way, the falsity of the premises
> entitles you to dismiss the argument, but not its
> conclusion per se.
Until such time as facts show otherwise, revisiting
an invalid conclusion would be highly inefficient.
So too is the need for a distinction between validity
and falsity because all conclusions may be temporary.
Nothing is absolute... well, almost nothing, hehehe.
> Of course, if the flawed argument was the only
> evidence offered for the conclusion, the latter is
> now back to ground zero, which might well put it
> behind one or more competing hypotheses.
Which is precisely the comparative Logic that I
ascribe to. So we come to the same conclusions but
describe the thinking process differently.
= gLeN
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