Accepting Rand's definition of axioms, I have little prob with your basic argument. Rand's ID of what I call the 'fundamental to philosophy, existence, and life' axioms are, strictly speaking, contextual, as I see all axioms as being. Granted, outside of her fundamental ones, there is no other context; but, she never said (or implied) that she ID'd the ONLY 'axioms' around. Some axioms of a given territory are dependent on (if not derivative from) truths (axioms or not) in other areas. Epistemology has it's own, but dependent upon the Metaphysical ones...as I see things, anyway. Then there's Ethical ones, and Political ones, non? Each has it's own subject-'axioms' relative to the subject's contexts. --- Her definitional use of the term 'axiom' gives much leeway in it's application, methinks, and your 'gap'-filling (as NB might call it) I find to be very useful.
However, ID'ing something derivative, or at least less basic, as an 'axiom' and otoh, talking about implications of an axiom are two different things; the implication may, or may not be a sub-'axiom,' though, corollary it may also be.
Re the grasped concept of existence thereby implying grasping the concept time, I'll admit is getting a bit too deep for me to untangle, though I'll venture to say that until one attempts to consciously measure time (via [or is it merely synonomous with, as Ed argues?] any periodic motion), one is not consciously aware of 'time' being implied from one's awareness of existence per se. --- Pre-conscious 'awareness' I'll not get into.
Re the concept 'space' being implied, I think there may be a good argument there, but, not the one you gave. There's something a bit...glib...about it, no offense. But I agree: such is an 'implication' in the action.
Generally, re Rand's careful wording in defining 'axiom,' I have little problem with it, though, after years, find myself still a bit unclear re the whole idea of 'a consciousness doing X implies the fact of Y.' A 2nd party's awareness of such, I can see; but the act itself, per se? Some analysis re the very term 'implies' seems another 'gap' that could be usefully filled.
Re your view as time not being ontological (existential?), I'm of mixed minds on this, fer sure. Without such, where is any meaning in Al's Relativity theories (re space-time physical dimensions) other than as mere conceptual-models, or heuristically-mathematical tools? Otoh, Lewis Little's theory itself seems to dispense with the necessity of 'fields,' ergo modifies drastically not only QM theory interpretations but Relativity's as well. Gotta admit, at this point, I flip a coin.
Your remarks on Rand's remarks are well put, (can't believe I forgot them; I've read her non-fiction enough times), but, as above, I'm still not sure about the concept 'time.' Consider: in a sense, such may be argued as applying to the consciousness of...well...any being, terrestrial or otherwise, all the way down to fish and maybe some insects, non? Still, food-for-thought.
Also, your later quoting of Rand re the act of grasping does help clarify some things.
Re your even later argument that to argue "X is blue" implies nothing about 'space,' I must take issue with. X's 'blueness' is of course irrelevent to any implication about 'space.' Referring to X as having a characteristic/attribute unpossessed by concepts, however isn't, non? Even if it's established later (how?) that X does not exist.
Your distinction re 'background' of the 3 primaries vs the others Fred brings up is right on. However, methinks that Fred wasn't introducing the delineated new ones as being as primary/fundamental as the main 3 (though I may be incorrect there.) I saw his argument as arguing that the new 3 are inherently implied by the 1st 3 and that they applied just as much as the 'primaries' to any non-mental entity, whether one was conscious of such or not. (Thanx for the ITOE ref re 'time;' still workin' on that baby.)
Re her reference to Causality as a 'Law' and not (that you remember) an actual 'axiom,' sad to say I also don't clearly remember. However, remember her definition of 'axiom,' and my above argument about context. As soon as the idea of 'change' enters the picture of existence, I'd have to say we're using an axiom here. However, apart from that, I agree: to speak about existence per se does not seem to imply anything about change, per se. Down that line, this is where the concept of 'time' might then be implied (or would it be 'applied'?). Hmmm...
Yeah, I've always had a problem with the phrase "logically prior to" as well. And anyone who sees worthwhile similarities between Rand and Descartes is missing something there.
Could you explain what you mean by "obtains" re what you see as "a problem" re "consciousness?" I'm lost there. The last time I heard/read "obtains" used in logical argumentation was in my college math-logic (which I call conjunction-logic) class...years ago, and considered it a pre-PC euphemism re the terms 'fact/truth.' ("holds" is another one.) But, maybe you mean something more...ontological?
Your conclusion that "Rand has done little more than replicate [I love that word since Blade Runner 1st used 'replicant'; it's synonomous with duplicate, but...definitely has more pizzazz] Descartes' cogito" methinks is a bit...off. More accurately, your argument for it is.
You argue that re Rand's argument-premises being a statement and a mental act, both being aspects of consciousness, (actually, I only see 1 there) that, therefore "In that case the 'something' of the conclusion 'something exists' must also be consciousness." I, uh, missed your 2nd premise in that argument of yours. --- Consider: we can say that a dog is 'aware' of X; I'd say that all Rand's statements re PRIMARY axioms apply thereby merely by considering the meaning of consciousness. Such does not imply that a dog is aware THAT they have awareness; they merely act from it, but do not know how to use it. --- Methinks you jumped to a conclusion re Descartes and Rand (and overlooked non-human consciousness.)
I sorta see why you regard Rand's "primary axiom" (existence exists) as being "logically dependent on a particular theory of mind"...but...not quite. She never delineated what you call a 'theory.' She merely referred to the concept "consciousness" and it's performance of an action ("Grasping": hmmm...back to change/action/and time again. What a hall of mirrors this subject seems to become.) There's no 'theory' framework for "Existence exists" to depend upon that I see in her argument. Any 'theory' would fall more into Philosophical-Psychology (or, just the latter) and thereby is either derived from, or at least delimited by, her basic axioms; they'd not be the base (hence: 'axioms') for what she's arguing.
True, her view of a human-consciousness was (conceptually-speaking) tabula rasa, opening the door to her idea of concept-formation (and thereby, volition) but such is neither a theory (so much as a single tenet of several competing theories) nor an inherently 'logically prior' necessity of presumably deriving that, therefore, "existence exists." The latter is stated as, per se, irrelevent to the existence of any consciousness, n'est pas? It's the action performed by a consciousness ('consciously' as such, or not) that all else, if not derived, is built upon.
Otherwise, your posts have been...thought-provoking.
Your argument re the status of 'axiomatic concepts' makes me think you are working from a different definition than us Randites work from. If NO empiric base is relevent thereby, then we're all talking in the framework of mere Rationalism, non?
Could you clarify, please? Uh, more diplomatically than your last post, please?
(Edited by John Dailey on 8/08, 4:50pm)