Buddha said:
You do understand that the apple in your left hand and the apple in your right hand are existentially two different apples - and that their degree of similarity is relative to a pre-established, epistemic standard, right? And that the apple in your left hand + the apple in your right hand does not equal 2 absolutely, existentially similar apples. it equals two epistemically similar apples.
I’m objecting to your use of the words “exactly” and “absolutely” in what I perceive to be a disembodied, non-contextual sense.
- I did not say anything about identical qualitative sameness between the two apples. Similarity and conceptual standards are objective or factual, that means it is more than “epistemic”. We cognitively isolate “existential” facts to serve as standards. This is what makes them _objective…_The epistemic nature of essence for Oism is not a repudiation of the factual nature of similarity…
This is a theme for you as I’ll show. I mentioned to you before that similarity is not a matter of “strict identity” here:
http://forum.objectivismonline.com/index.php?showtopic=27504#entry327051
- The very concept “1” is derived from bodies or _entities. _There is no context where an concrete entity is not an instance of _“1”…_And in the context of numbers one omits all the measurements of the units one is counting…
ITOE said:
AR: In a certain sense the measurements omitted from the concept of numbers are the easiest to perceive. What you omit are the measurements of any existents which you count. The concept “number” pertains to a relationship of existents viewed as units—that is, existents which have certain similarities and which you classify as members of one group. So when you form the concept of a number, you form an abstraction which you implicitly declare to be applicable to any existents which you care to consider as units. It can be actual existents, or it can be parts of an existent, as an inch is a part of a certain length. You can measure things by regarding certain attributes as broken up into units—of <ioe2_197> length, for instance, or of weight. Or you can count entities. You can count ten oranges, ten bananas, ten automobiles, or ten men; the abstraction “ten” remains the same, denoting a certain number of entities viewed as members of a certain group according to certain similarities.
Therefore, what is it that you retain? The relationship. What do you omit? All the measurements of whichever units you are denoting or counting by means of the concept of any given number.
Here the omission of measurements is perceived almost at its clearest. And I even give the example in the book—it’s an expression I have heard, I did not originate it—that an animal can perceive two oranges and two potatoes but cannot conceive of the concept “two.” And right there you can see what the mechanics are: the abstraction retains the numerical relationship, but omits the measurements of the particulars, of the kind of entities which you are counting.
Buddha said:
The statement: 1+1=2 (per Post #91) is completely different from the statement: 1 apple + 1 apple = 2 apples (per post #93). You incorrectly believe that they are interchangeable.
Yes they are interchangeable because they are symbols used to convey the meaning I chose them for. Remember that I said that I suspected that you don’t “understand what I’m asking” in post 91, so the second is simply me clarifying what I meant in 91.
We can restate this intended meaning as: 1 entity + 1 entity =2 entities.
One of the reasons I asked this question is to see how deep the rabbit hole goes for your skepticism of measurement, absolutes, correspondence and universals. I didn’t recall these past comments at the time:
Except for fairly mundane statements which can only be proven by ostensive definitions (the building exists) we never reach a point where we have “absolute” knowledge of anything. Propositions are limited, finite and contextual and, most importantly, made by individuals. […]
see the “problem” of induction as having to do with measurement. […]No two existents are ever EXACTLY identical and neither are two causes or two effects. Each moment in the Universe is unique and never to be repeated. Everything is in a constant state of change. There are no Universals.
In any inductive statement, you must explicitly (or implicitly) state the degree of similarity that you are expecting to
observe. […]The essential demarcation between Objectivism and other philosophies is not A is A, or the Law or Non-Contradiction. It’s the Validity of the Senses as the basis for individual objective knowledge. […]
Objectivism is not concerned with Truth! and Ultimate Reality!
Objectivist epistemology says that an individual, based on evidence provided by his senses, and through the application of reason, non-contradiction and non-evasion, is capable of obtaining objectively knowledge. That’s pretty much it. It doesn’t’ say that you will at some point be omniscient or infallible or will reach a point where there is nothing more to learned or no new light can be shed on an old subject […]
You are under the impression that Objectivism leads one to an “absolute” understanding of anything. This is not what Objectivism claims. […]
There will never be a “Theory of Everything”. To even attempt to do so is to fundamentally misunderstand what knowledge is.
Edit 3: When I make a recording of a symphony, the recording is not equal to, or interchangeable with, the live performance. But the recording was made by a QUANTIFIALBE exchange of mechanical/electromagnetic energy ( minus entropy’s share, of course). This is also true for ideas
The equivocation I mentioned earlier is concerning concepts like " absolute" being packaged into discussions about, measurement, objectivity, exactness, identicalness, and in particular the law of Identity (as has happened in this thread with Andie.)
A is A-the LOI as such, is a separate matter from essence and essentiality. The whole equivocation of "A=A with “A-ness” in this thread is misguided. You mentioned this to Andie in #88 and went right to differentiating objectivity from “theories of everything”.
The law of Identity doesn’t tell us what anything is in particular and certainly not what something is essentially…but likewise identification doesn’t imply exhaustive knowledge-omniscience either.
This post is an example of the way you bring objectivity and uniqueness - _ particularity _ into a discussion about what you see as a denial of what you seem to think of as as the limited nature of knowledge or the repudiation of the uniqueness of particulars :
You are equating the Law of Identity with the (cognitive) Method of Identification. It is wrong to equate them. Identity does NOT equal Identification. A single, human mind will never exhaustively understand what “dog-ness” is. To a single, unique human mind, “dog-ness” will always remain open ended, and subject to revision/clarification/expansion.
However, this does not mean that what a single, human mind knows is not objective. The knowledge can be said to be Objective to the degree that the individual has integrated, to the best of his ability and experience, what he knows to be true, while rejecting contradictions and evasive thinking. […]
Notice the way you differentiate identity from identification here. The law of Identity does not say anything qualitative about any existent except that none will have and not have the qualities that is possesses. Simply put, contradictions do not exist mind independently.
Identity is not a synonym for omniscience or exhaustive knowledge of an existents qualities. In several places in this forum you make this kind of differentiation and then immediately begin discussing objectivity and individuality. But objectivity has nothing to do with the notion that knowledge is final or exhaustive and similarity has nothing to do with exact sameness or Leibnitz’s “identity of identicals” . Why package them together so often as if omniscience-“exhaustive knowledge” is a foil for objectivity?
I have wondered why you always make this type of comment about objectivity and Individuality following repudiations of absolutes, and “Truth” etc.
Example:http://forum.objectivismonline.com/index.php?showtopic=27665&page=2#entry327837
I wonder if the reason for this repeated type of statement from you is contained in this comment:
The essential demarcation between Objectivism and other philosophies is not A is A, or the Law or Non-Contradiction.
It seems you don’t accept the Oist claim that the Primacy of Existence as a corollary if the LOI is the central them to all of Objectivism. You rather see the reliability of the senses as the essence of Oism and some kind of cornerstone for individuality that somehow serves as a type of bulwark against what you think are claims to omniscience .
The “1 entity+1 entity” question was a rhetorical device to get at the implicit confusion in your qualitative comments about essences or similarity between particulars. (2x8 D fir, Drawing vs things drawn ,etc.) But there is another reason which I will get to later.
But the objectivity of the senses is in fact_ _the absolute foundation for exact correspondence for Ms. Rand !
There is an entire discussion in ITOE on this topic of _ exact correspondence _ in the section title " Exact Measurement and Continuity":
Ms. Rand Said :
if you are able to measure it, and you are able to grasp relationships by means of measurement which you didn’t invent, that is exactness. And if you are able to grasp that maybe some milli-milli-parts of a millimeter are not correct and you are not able to bring it to a greater precision, who grasped that? You did. Therefore, your concept is correct, does correspond to reality, and it is reality that you have been consulting in discovering that perhaps you can’t measure submicroscopic quantities. […] when we speak of measurement, we begin with a perceptually given unit, and that unit is absolute and exact [within the context of our means of perception]. Then conceptually we may refine our methods and we may measure such things as milliseconds and a part of a subatomic particle, which we can’t do perceptually. But the standard of these measurements, the base from which conceptual complications may later be derived, is that which we perceive directly on the perceptual level; that is what measurement means, that is its base. Therefore, when I say that for measurement there has to be a unit of measurement, I mean that even when you take a submicroscopic, conceptual type of measurement, that type ultimately has to be reduced back to our standard of measurement, which is the perceptually given, and nothing more or less.
With scientific development you might discover that, microscopically, the edge of this piece of paper is ragged and has tiny mountain peaks and valleys. That is not relevant to your [macroscopic] process of measurement, because you had to use the perceptual method as a start in order to get to your microscopic instruments of measurement. […]
if you say it is so much measured by a ruler, or it is something else measured by some fancy apparatus, you have complied with the requirement of absolute correspondence to reality.
More later…