Right. So, if we follow the framework of classical logic, "verifiable" and
"falsifiable" are just two (overlapping) special cases of a much wider
notion of "meaningful". Atomic propositions are both verifiable and
falsifiable, because they can be checked directly ("in principle" that
is... we may not be able to visit the core of the Earth to check its
temperature on a given day, but we can treat this as an atomic fact
anyway... if we like.) Existential statements (There exists x such that...)
are verifiable, but not always falsifiable. If the Flying Spaghetti Monster
exists, then we could prove it by finding him/her. But if not, we may never
know. Universal statements (For all x, ...) are falsifiable, but not
verifiable. If we find one counterexample, it is disproven; however, we can
find all the examples we like, yet never prove it for certain. Popper
concentrated on these kinds of statements, because they are the kind most
relevant to scientists; scientists typically want universal laws.
If we stack quantifiers ("For all x, there exists y such that..." "There
exists x such that for all y..."), we get apparently meaningful statements
which *might* never be verified or falsified. Many of the important
theorems or open conjectures in mathematics have this form. (For all
integers, there exists a unique prime factorization. For all maps, there
exists a 4-coloring. For all even whole numbers, there exists a
representation as the sum of two primes.)
Of course, the positivists thought that all mathematical statements would
turn out to be verifiable! But, alas, it's not the case!
But, these days, Positivist ideas and Popper's "opposite" ideas get rolled
together. My impression is that modern-day self-styled positivists are
mostly falsificationist, but their core idea is more that scientific
theories are only meaningfully different insofar as they make different
predictions (so, in particular, a theory which doesn't make specific
predictions is not meaningfully different from no theory at all).
My perspective is, AGI systems should be able to address as meaningful any
concept which humans find to be meaningful. The goal, then, is different
from these kinds of theories. With humans, we need to limit the scope to
keep people "scientific"... and that is the goal of positivist or popperian
theories. With AGI, we need to first understand the scope in order to have
a starting point... so we require a rather more ambitious epistemology!
Best,
Abram
On Thu, Jun 21, 2012 at 1:32 PM, Jim Bromer <[email protected]> wrote:
> This issue of the verifiability of a proposition is related to AGI (of
> course.) In order to be able to use a proposition effectively one has to
> verify that it is meaningful in the first place. Furthermore, you have to
> make sure that it is not dull witted (like proving a statement by inferring
> it from a direct contradiction.) So a proposition has to have some kind of
> interpretation that would make it meaningful and not completely insipid or
> directly contradictory. Next it needs to be related to the subject matter
> that it is supposed to be supporting or be integrated with. The concept of
> "meaningful" does seem to coincide with "relevant". But how do we write a
> program to create meaningful and relevant propositions when the very fabric
> of knowledge is being generated. There is always the possibility that if
> the knowledge that had been generated previously was meaningful then there
> would be no way out of the program just generating a lot more meaningless
> propositions.
>
> Finally the system has to be able to generate or find some propositions
> that will help it achieve some goal. This aspect of meaningful and
> relevant is another complexity.
> Jim
> *AGI* | Archives <https://www.listbox.com/member/archive/303/=now>
> <https://www.listbox.com/member/archive/rss/303/7190161-766c6f07> |
> Modify<https://www.listbox.com/member/?&;>Your Subscription
> <http://www.listbox.com>
>
--
Abram Demski
http://lo-tho.blogspot.com/
-------------------------------------------
AGI
Archives: https://www.listbox.com/member/archive/303/=now
RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-c97d2393
Modify Your Subscription:
https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-2484a968
Powered by Listbox: http://www.listbox.com
