Thanks for the comments -- and the patience. It would be interesting to see the entire Jacques Maritain pdf, but it's sideways on my screen, and without some computer trick I don't know about, I'll end up at the chiropractors. Maybe I'll figure out a way to read it; it does look interesting.
But what I seem to be seeing -- is that Maritain is offering some schematics -- a graphical layout for the way logic is arranged. That appeals to me, and goes to my own fundamental instinct on this subject -- which is, that if we shift our attention away from the vast confusing pool of "actual observed instances" (the "six million word senses"), and instead, see the empirical ground of definition in context-specific stipulation -- we might reduce the vast teeming complexity and confusion of algebraic semantics to something astonishingly simpler.
For me -- all logic is simply bi-directional: UP the hierarchy of abstraction or DOWN the hierarchy of abstraction. Period. Everything else is a confusing artifact or side-effect of grounding definition in empirical instances, which spawns a bottomless violation of Occam's Razor -- http://en.wikipedia.org/wiki/Occam's_razor -- and causes an explosion of unnecessary and confusingly inconsistent logical definitions. Is the Minsky "frame" concept one of these? The idea of frames as he described it does make a lot of sense, yes. But isn't there a better and simpler and cleaner and stronger way to say the same thing, without introducing an entirely new and distracting concept?
So, for example -- treading cautiously -- I am suspicious of the concept of "abduction". Can't we get rid of that idea, and see it as a special case of induction? Why confuse the heck out of what should be simple by positing a special term in the middle of the process? Generalize the framework, please, and locate these special cases as heuristic conveniences. Yes, it's an interesting point. "Abduction is a guess". Ok, thank you, but isn't all of induction more or less a guess?
http://en.wikipedia.org/wiki/Abductive_reasoning
This was the idea that happened to me, many years ago, working on an undergraduate paper on "The Pre-Socratic Opposites". I saw the opposites as arranged in a circular format, essentially in a hierarchy from center of the circle to the perimeter, and I just flashed that all logical organization is a movement across this grid (see Ramon Lull for suggestive historical precedent). Induction moves from the perimeter towards the center, deduction moves from the center towards the perimeter. Analysis and synthesis are subject to the same polarity. Stare at the idea for a while, and big pool of very simple definitions for the fundamentals of epistemology seems to fall into place.
Is this all a gross and nonsensical oversimplification? Well maybe. But it's looking to me like the great stumbling block in algebraic semantics is this blinding notion of a shared pool of meanings, to which we attempt to assign some enduring stable ontological status -- when, I think we can say around here, it's quite clear that this pool is an endlessly moving target, precisely because all definition actually IS stipulative and intentional, and the dimensionality of its particulars absolutely subject to a high degree of variation due to variations in context-specific motivation -- a variation that destroys any notion that these things have enduring Platonic stability, or can serve as the bedrock for a global semantics. Isn't that what J.S. is telling us over and over again in various ways?
For me, under stipulation, it all looks like this:
Empiricism is at the bottom (right side) of this framework, abstraction and transcendence at the top (left side). Conceptual structure is a kind of “Twenty Questions” taxonomic drill-down (“Is it plant, animal, or mineral”), and all logic simply builds structures moving across this frame.
Of course, we are not making some general/universal claim that every word has one single decomposition map. Wasn’t something like that the fundamental confusion in Wittgenstein? No. The general principle is – every instance of word usage has a context-specific one-use-only decomposition cascade. There are too many implicitly nested dimensions to make this kind of generalization, and their values are all stipulative and driven by motivated choices. The complexity of the cascade quickly becomes explosive. It only works once. But seen that way, as a one-time diamond-cutting process of discrimination and distinction, it IS linear.
Taxonomic structures in the context of working science are consensual stipulations. Some scientific body or group gets together, and hammers out something they can agree on. Is reality absolutely “like that”? Is that distinction they are suggesting “the absolute difference between a dog and a wolf”? No – but their consensus becomes a guiding map for cooperative work, and science as a collaborative process can continue – and changes will no doubt continue to emerge.
Can we do linear dimensional analysis of abstract qualities? Not if we ask a broad question like “What is beauty?” and then try to posit some universal scientific definition. That would be a bottomless argument – perhaps re-enforceable from the “six million word senses”, but still confusing. But if I say something is “beautiful”, and you ask me what I mean by that, and you push hard and I can handle it, we might end up with a very precise this-context-only mathematical definition, where any terms in my ad hoc context-specific I-am-talking-to-you-right-now cascade are given stipulative values that I hope make sense and I hope you understand.
For me – in a general way, all logic and semantics moves across this simple grid, and this framework is the common ground of all natural language, and the general form of “conceptual parsing”. All distinction arises within this space. Why “multiply entities beyond necessity?” Build the details within a common shared framework. That would make life so much easier. And yes, it would be a huge scientific revolution…
Well, it does turn out that generalizing this form in credible algebraic terms is not so easy, and maybe there is some kind of very profound dimensional trick required to fully integrate this framework as a single composite unit – a kind of universal two-sided “holon”, where one side is a unit of abstraction (a genus or “the whole”), and the other side is the composite elements of its definition (the species within the genus or “the parts”). So, the revolution has not really hit us yet. We are still stumbling in a hugely complex noisy space full of transient and conflicting heuristics, because we don’t see or agree upon the general form. So maybe this field needs its own Einstein or Kurt Gödel, to integrate this vast array of interconnected but messy and conflicting definitions into a single composite integral framework, where the large-scale structure appears clearly, and the interconnection of the moving parts can be seen precisely. Until we get there, traditional empiricism will dominate, for very sensible reasons, including the need of working ontologists to pay their mortgages…
***
On the Maritain quote:
[Concluding a review of the classical rules for determining the substitutive value of a term in a proposition:] "This brief survey of the diverse properties of the term in the proposition is instructive in several respects. For if we have really understood that a single term may stand for different things in discourse, even while it keeps the same signification (corresponds to the same concept, and to the same word in the dictionary)--if we have really understood this--then we shall also understand why the necessity of "distinguishing,", i.e., making distinctions, dominates all human discussions.
And it does dominate. As long as abstractions are necessary and inherent in language, and embody multiple alternative interpretations that may not be constrained by the context, confusion in communication will arise. And that confusion has its cost – not only in frustration and wasted time, but in blood. We really need to figure this out. Trying to run a global economy without understanding this – is pretty dumb…
We shall comprehend also why this necessity arises from the specific character of our intelligence: not only because the same word may signify different concepts, but also because words being the material tools, and concepts the immaterial tools, of rational activity the reason may _put the same concept_ and _the same word_ with its signification unchanged _to different uses_.
So, we must probe in a respectful way – in “dialogue” – until meaning is clarified…
We shall also understand how useless it would be to attempt to substitute for the _Logic of ideas_ or of _concepts_, which always supposes the activity of the mind using concepts and words as tools, a logic of written or oral _signs_, so perfect as to dispense with thought and be sufficient unto itself (the _universal characteristic_ of Leibnitz--modern _Logistics_).
Now, do I understand this? Maybe not – but it looks to me like Maritain is saying that an attempt to perfect this process is foolish. Or is he saying that yes, indeed, that perfecting this process does not imply any sort of one-size-fits-all general definition for any particular concept --
Of course, a system of signs more perfect and more rigid than ordinary language may be conceived; but, with the exception of certain limited domains, such as that of algebra, we shall never succeed in completely suppressing the margin of indetermination that subsists around the oral or written sign, and attests to the transcendence of thought over its material symbols
Well, this looks very sensible to me – because clearly there is great potential variation in meaning – and Maritain is probably not talking about stipulation. But is he glossing over important details, that we really need to understand explicitly, when he says, rather poetically, that we “cannot suppress the margin of indetermination” (ie, the inherent ambiguity or multiple-alternative-interpretability) of thought – because we must recognize the “transcendence of thought over its material symbols”?
I’m not sure I understand his meaning, and I have not read enough of this – but this feels like a poetic testament to the sacredness of human communications, which I acknowledge, but see as a bit dangerous, because seeing abstractions as sacramental is in the eye of the beholder, and can instantly lead to war. We can’t go around “transcending” without an explicit map and presuming that others can follow us. They won’t, and they will get confused, and possibly annoyed. We got to articulate the map – no disrespect to transcendence or poetry intended or implied. Let’s just figure this out, make implicit meaning explicit, and then we can relax…
Bruce Schuman
FOCALPOINT: http://focalpoint.us
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-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Paul Tyson
Sent: Thursday, October 23, 2014 8:06 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] "Data/digital Object" Identities
On Thu, 2014-10-23 at 08:46 -0700, Bruce Schuman wrote:
> One of these days, I'll take another crack at the core thesis for a
> general ontology, which is that all these interconnected structures
> can be 100% linearly assembled using ONE primitive mathematical
> element -- which is: distinction. Telling two things apart, by making
> a "cut" in some dimension of similarity we discern (this is
> essentially a modern take on Linnaeus). So, the thesis is: every
> concept in reality is a hierarchical assembly of motivated cuts
> organized in a kind of fractal cascade across levels of abstraction,
> from broad generalizations to specific boundary values in specific
> dimensions. This works, and is true, because the most authentic
> empirical foundation for word meaning is not some huge shared database
> of "6 million word senses" (though we may need such things for machine
> translation of natural language, and we need a common pool of shared
> if approximate word meanings), but the principle of context-specific
> stipulative definition in the actual/empirical context of usage --
> intentionally parsing reality in some specific act of communication,
> such that “the words" used in that act of communication most
> authentically have "the meaning" intended by the speaker -- and it is
> up to the speaker to defend that meaning by "dimensioning" the
> specific values within the implicit undefined abstractions of the
> statement. This is how human beings actually communicate – and when
> the “dialog” or drill-down Q and A does not narrow the bounded ranges
> of possible interpretive confusions, we have failure of communication
> and fights.
For another--perhaps quite divergent--view, emphasizing the importance to communication of distinctions of a different sort, here is a paragraph from Jacques Maritain's Introduction to Logic, p. 75-76.
(Italics in the original delimited by underscores in the quote.)
[Concluding a review of the classical rules for determining the substitutive value of a term in a proposition:] "This brief survey of the diverse properties of the term in the proposition is instructive in several respects. For if we have really understood that a single term may stand for different things in discourse, even while it keeps the same signification (corresponds to the same concept, and to the same word in the dictionary)--if we have really understood this--then we shall also understand why the necessity of "distinguishing,", i.e., making distinctions, dominates all human discussions. We shall comprehend also why this necessity arises from the specific character of our intelligence: not only because the same word may signify different concepts, but also because words being the material tools, and concepts the immaterial tools, of rational activity the reason may _put the same concept_ and _the same word_ with its signification unchanged _to different uses_. We shall also understand how useless it would be to attempt to substitute for the _Logic of ideas_ or of _concepts_, which always supposes the activity of the mind using concepts and words as tools, a logic of written or oral _signs_, so perfect as to dispense with thought and be sufficient unto itself (the _universal characteristic_ of Leibnitz--modern _Logistics_). Of course, a system of signs more perfect and more rigid than ordinary language may be conceived; but, with the exception of certain limited domains, such as that of algebra, we shall never succeed in completely suppressing the margin of indetermination that subsists around the oral or written sign, and attests to the transcendence of thought over its material symbols."
(Online scanned PDF version available at
https://archive.org/details/AnIntroductionToLogic_880.)
Regards,
--Paul
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