Excellent questions, Doug.
The simple answer to your questions about "foundation" is
that all of the concepts used in the axioms are axiomatic
concepts. Ayn Rand devotes a whole chapter of "Introduction
to Objectivist Epistemology" to axiomatic concepts, and I think
the beginning of that chapter is the best _expression_ of what
axiomatic concepts are. I quote
Axioms are usually considered to be propositions
identifying a fundamental, self-evident truth. But
explicit propositions as such are not primaries.
They are made of concepts. The base of man's
knowledge -- of all other concepts, all axioms,
propositions and thought -- consists of axiomatic
concepts.
An axiomatic concept is the identification of a
primary fact of reality, which cannot be analyzed,
i.e., reduced to other facts or broken into component
parts. It is implicit in all facts and in all knowledge.
It is the fundamentally given and directly perceived
or experienced, which requires no proof or explanation,
but on which all proofs and explanations rest.
The strange thing about axiomatic concepts is that they
are so general and so abstract that they are hard to describe,
and at the same time they are the "foundation" that all our
simpler concepts depend on. If the axiomatic concepts
were not "true", our simpler concepts would not be "true".
After that good beginning, Rand says a lot of things
about the most general axiomatic concepts:
Existence, Identity, Consciousness
That's when it gets really hard to understand, and I
personally think that the propositions in the rest
of that chapter are not expressed correctly. First,
there are meaningful relations between the axiomatic
concepts which are not mentioned. Second,
I think Rand was intuitively using an axiomatic
concept to name an axiom, and her failure to
explicitly recognize that fact was the main source of
confusion.
This answer is already getting so long, I am going to
post the English versions of the axioms on my website.
I will do that ASAP. But I will say two more things here.
The basic notation that I use
proposition name :: proposition
was not used by Ayn Rand. As I said, I think she was
intuitively naming axioms without realizing it.
The March 26 version of the Objectivist Axioms is
my first attempt to capture the content of Harry Binswanger's
new book, "How We Know". I'm already beginning to have some
second thoughts about the exact wording. For example, I said
Identification :: at view { concept := I do identify od existent done; };
which in English is
in the view context
a concept is the result of I identify an existent
1) I am thinking of changing "identify" to "conceive".
2) That's not what Ayn Rand said. She used Identification at a different
level of abstraction. Her famous definition is
Knowledge is the identification of a fact(s) of reality,
reached either by perceptual observation or by a process
of reason based on perceptual observation.
Ignoring the last phrase for now, my mKR translation is
Identification :: knowledge := I do identify od existent done;
Dick McCullough
Context Knowledge Systems
mKE and the mKR language
mKR/mKE tutorial> Date: Thu, 3 Apr 2014 02:23:00 -0400
> From: doug@xxxxxxxxxx
> To: rhm@xxxxxxxxxxxxx; ontolog-forum@xxxxxxxxxxxxxxxx
> CC: kr-language@xxxxxxxxxxxxxxx
> Subject: Re: [ontolog-forum] mKR proof of correctness
>
> On Thu, April 3, 2014 01:14, Richard H. McCullough wrote:
>
> > The Objectivist Axioms describe the epistemology of man --
> > how he perceives and conceives the external world.
>
> Could you state them in plain English, please? If you are using
> terms in non-standard ways, could you define them in plain English,
> as well?
>
> > They are the foundation of all man's languages and knowledge.
>
> If they are the foundation, they must predate. Obviously, people didn't
> know these axioms before language was invented, much less before
> knowledge existed. So you must mean something else by "foundation".
>
> Could you re-state the intent of the previous sentence in terms that
> could be understood by someone not well versed in Ayn Rand?
>
> Thanks!
>
> -- doug foxvog
>
>
> > Dick McCullough
> >
> > Context Knowledge Systems
> >
> > mKE and the mKR language
> >
> > mKR/mKE tutorial
> >
> >> Subject: Re: mKR proof of correctness
> >> From: phayes@xxxxxxx
> >> Date: Wed, 2 Apr 2014 22:21:15 -0500
> >> CC: ontolog-forum@xxxxxxxxxxxxxxxx; sowa@xxxxxxxxxxx;
> >> kr-language@xxxxxxxxxxxxxxx; rslatimer@xxxxxxx;
> >> dkelley@xxxxxxxxxxxxxxxx; wthomas@xxxxxxxxxxxxxxxx
> >> To: rhm@xxxxxxxxxxxxx; rhmccullough@xxxxxxxxx
> >>
> >>
> >> On Apr 2, 2014, at 5:10 PM, Richard H. McCullough
> >> <rhmccullough@xxxxxxxxx> wrote:
> >>
> >> > John
> >> >
> >> > I don't want there to be any doubt about what I'm saying,
> >> > so I'm devoting one extra email to this topic.
> >> >
> >> > The mKR language is proved semantically correct
> >> > because the mKR run-time system guarantees
> >> > that the Objectivist Axioms are satisfied.
> >>
> >> I actually laughed out loud when I read this. First, I have no idea what
> >> you mean by proving a language to be semantically correct, but claiming
> >> anything semantic **because some axioms are present** misses the entire
> >> point of having semantics in the first place, which is to connect formal
> >> sentences with claims about the actual world. Then again there is your
> >> conflation of semantics with a 'run-time system', which I take it means
> >> a system that performs inferences. But without an independent semantics,
> >> how d
> oes one know that these inferences are valid or complete? The
> >> general problem of proving that a program is correct is still open, of
> >> course, but any approach to even defining what this means requires that
> >> the language of the program has some kind of separate semantics. If the
> >> run-time system *Is* the semantics then 'correctness' is trivial to
> >> prove - the program does what the program does - but also trivially
> >> meaningless. But the final howler here is the idea that Ayn Rand's
> >> thoughts might have anything, even the shred of a remotest connection,
> >> to do with correctness, in any sense of that word.
> >>
> >> IF your notation had a semantic theory that would enable an objective
> >> check to be made on its validity, and IF you could then show that those
> >> axioms were satisfied AND that your run-time system preserved truth (or
> >> whatever your semantics calls it), then you might reasonably claim that
> >> mKE had a property that one might call Randianicity: conformity to the
> >> thoughts of Ayn Rand. But to call this property "semantic correctness"
> >> is simply farcical.
> >>
> >> Pat Hayes
> >>
> >>
> >> >
> >> > Dick McCullough
> >> > Context Knowledge Systems
> >> > mKE and the mKR language
> >> > mKR/mKE tutorial
> >>
> >> -------------------------
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> >>
> >>
> >>
> >>
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