Flagg

I'd love to see a Logical Positivist account for the uniformity of nature. I've been harping the New Atheists about this for a long time.

Has anyone heard this argument? It is a favorite of Calvinists, the Christian denomination that denies free will to the sovereign choice of God. The juice of the argument is that it supposedly proves the Christian God by the impossibility of the contrary, by stating that without God, one cannot prove anything. The reasoning for it goes that God must be the source for the laws of logic (Identity, Non-Contradiction, Excluded Middle, etc.) since an atheistic worldview cannot account for the laws of logic at all. Morality and the problem of induction are also introduced as supposed proofs for God's existence, since they claim atheism cannot account for moral laws, nor can it count on the reliance of future events based on past experience.

Of course, Objectivism has an account for this, but I have not really seen anyone confront it directly. Thoughts?

Been reading Gordon Clark lately, eh? Or, much worse yet, John W. Robbins?

Bill P

Clark was a hoot. I think this is used more on the Van Tillian side of things, though, but I haven't really run up against a Clarkian before.

Has anyone heard this argument? It is a favorite of Calvinists, the Christian denomination that denies free will to the sovereign choice of God. The juice of the argument is that it supposedly proves the Christian God by the impossibility of the contrary, by stating that without God, one cannot prove anything. The reasoning for it goes that God must be the source for the laws of logic (Identity, Non-Contradiction, Excluded Middle, etc.) since an atheistic worldview cannot account for the laws of logic at all. Morality and the problem of induction are also introduced as supposed proofs for God's existence, since they claim atheism cannot account for moral laws, nor can it count on the reliance of future events based on past experience.

Of course, Objectivism has an account for this, but I have not really seen anyone confront it directly. Thoughts?

Maybe there is supernatural being who questions whether or not 'existence exists', does he exist?

This is a stolen concept. I did not say "maybe" and I did not say "supernatural being."

Let's take this to the personal level: You (GS) have to exist in order to question whether existence exits.

If you (GS) don't exist, you can't say anything, much less question something specific. That is where existence an axiomatic concept instead of an assumption.

I do agree that your "maybe" and your "supernatural being" are assumptions. I do not agree that your existence is an assumption, at least not so long as you post here. smile.gif

... there is only "to the best of our knowledge right now"

In relation to what? What determines best and worst? What standard do you use to make this measurement?

Thought I'd better start a new thread. After considering this some more it seems to me that the statement "existence exists" means existence is undefinable. So we must accept this term and move on but I cannot do this. Let me ask you this, do atoms exist? Do quarks exist? Do tachyons exist? All of a sudden 'exists' is not so cut and dried is it? No, this term 'exist' or 'existence' is way too vague to be axiomatic. In fact, what does this phrase even mean? It's almost as if you are defining 'existence' with the word 'exists' which amounts to saying nothing.

Not quite. The first axiom is better stated "Something is." Now, in this order of precedence, it is implicit what "is" i.e. "exists" means, but this is not explicitly outlined until later down the axiomatic chain. To exist means to have an identity, a nature, a set of quantifiable qualities. So putting it all together, it means that there exists identity or identities, as opposed to no identity or identities. Rand's presentation is rough, admittedly, but the fact of the matter is that it is axiomatically valid.

1. If solipsism is true, then everything that begins to exist has a cause, and this cause must be my perceptions or by an internal faculty able to cause perceptions.

No. You cannot prove that everything that begins to exist has a cause, so that invalidates the argument. There are more points in your list that won't work, but that isn't important as the first point already fails.

Actually, I can prove that everything that begins to exist has a cause under the assumption of solipsism, for, if not, then a causeless percept necessarily has no ties to my consciousness (or else my consciousness would cause its existence, refuting the objection). Since it has no ties to my consciousness, it exists independently of my consciousness even if its existence is coterminal with the existence of my consciousness. This refutes solipsism, since something exists indepedently of my consciousness. So under the assumption of solipsism, everything that begins to exist must have a cause by the impossibility of the contrary. So my argument still stands.

You see consciousness as something embedded in an external reality. Not so the solipsist, to him his consciousness is the equivalent of reality, it is axiomatic, just as existence is axiomatic for Rand. Saying to him that his consciousness causes something is meaningless to him, just as it is meaningless to say that reality "causes" something. Everything he observes he considers to be part of his consciousness, just as we everything that we observe consider to be part of reality. You may find this a silly position to take, but it is logically unassailable.

The proof proper does not assume that consciousness is a member of external reality, because that would be begging the question in favor of my conclusion. And for the solipsist, consciousness is the whole of reality, yes. But if the solipsist is consistent, he will discover that his position logically collapses, as I demonstrate above. The proof I gave was assuming the case of solipsism and reaching a contradiction.

1. If solipsism is true, then everything that begins to exist has a cause, and this cause must be my perceptions or by an internal faculty able to cause perceptions.

2. The first state of my perceptions began to exist.

3. Therefore, my perceptions must have a cause.

4. (From 1) This cause must be my internal faculty that is able to cause perceptions to begin to exist.

5. My internal faculty that causes perceptions must have a content.

6. This content itself began to exist.

7. Therefore, this content has a cause.

8. This cause cannot be itself and cannot be from perceptions.

9. Therefore, solipsism is false.

Ridicule is an appropriate response to such a position. Entirely appropriate.

And I mean the connotations tied to delusional, if somebody is serious about their solipsism.

Bill P

No need for anyone to be serious about it. I just refuted it in logical format, so it cannot be considered because it leads to inevitable logical collapse.

By the way, if one does not accept my view of causation, and asserts that things may still begin to exist without a cause whatever their definition of cause may be (the loosest form is that "a causes b" means "not-a entails not-b"), then the solipsism assumption renders this impossible - if, assuming solipsism, a percept A began to exist uncaused, then there is necessarily no connection between it and my consciousness. At most, A can only have the property of being coterminal with my consciousness, since if it had dependence on my consciousness, then my consciousness causes its existence continuously even if it began to exist uncaused. But even if A simply is coterminal with my consciousness, this means that the fact that it has no necessary dependence on my consciousness entails that it must exist independently of my consciousness, refuting solipsism. So under the assumption of solipsism, everything in the content of my consciousness must be caused by my consciousness, including their first state at their beginning, entailing my consciousness caused their beginning to exist. The argument thus still follows.

Now, under A-time theory, everything that begins to exist has a cause

Why? That we often find causes for events doesn't mean that this always must be the case. That is the fallacy of induction. So your argument has already been derailed at this point, no need to read further...

Good point; you do have to accept the Randian state-state nature of causation as I have written it, but supposing you are right - let's define cause as "a causes b means that not-a entails not-b." This is the generally accepted view of causation.

Curiously, my argument still follows from this definition.

Name one event within time that does not have a cause under the definition of "cause" I just gave.

Put the proof in my original post, so future pages can have it ready for commentary.

But there is no way you can prove that, solipsism is unfalsifiable. It's interesting that Rand was in fact defending a solipsist viewpoint when she said: "I will not die, it's the world that will end."

Peikoff, in a recent radio program, pointed out that her statement came from a poet named Badger Clark, called The Westerner. The statement itself doesn't actually appear in Clark's poem, although "the world began when I was born" does - and in the context of the poem, this means that what previously existed before his birth (and what will exist after death) is by definition irrelevant to one's existence, unless one's concern for the future of something one experiences while alive is itself a value. Rand further clarified in that same interview that we won't wake up at some point after death and say "woah, how terrible it is that I'm a corpse!" That's what she meant - not that solipsism is the case.

Anyway, my absolute disproof will follow this post, and you can put that worry that we all could just be in your head to rest. ;)

Solipsism is the view that only I exist, i.e. only my consciousness and the contents of my consciousness exist.

I've formulated an argument that proves with absolute certainty that solipsism is false, but I wanted to know everyone else's take on the subject before I present my own take. Thoughts? EDIT: I put it here so it can be viewed on future pages.

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My proof of the impossibility of solipsism, and therefore of the absolute certainty of the existence of an outside world, is taken by assuming solipsism as to not beg the question, and demonstrating how such a position leads to logical collapse. The following is reprinted from my blog. Looking forward to comments and criticism!

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A Logically Absolute Proof of the Existence of a World Outside My Mind

One of my philosophy professors, Dr. Stewart, used to pose hilariously to his classes the scenario of killing himself to end all of existence by pointing his forefinger to his head, hand in a gun-shape, and screaming "STOP OR I'LL KILL YOU ALL!"

Throughout almost all of professional philosophy, the question of whether one can absolutely verify the existence of a world outside our consciousness has been considered open and perhaps even unanswerable for thousands of years. Indeed, an absolute proof of the impossibility of solipsism by a professional philosopher would throw the philosophical community - or, more likely, bring that professional under extreme ridicule, since many philosophers (unlike Dr. Stewart, who regards it as a thoughtful joke) enjoy hanging this over the heads of others as a verification of the old canard that "you can't prove anything!" A proof is long overdue, and since professional philosophers cannot afford the risk of giving an irrefutable one, I thought I would present one myself.

For those of you unfamiliar with the A-time theory/B-time theory split, a brief explanation is necessary here before my disproof is given. A-time theorists, to paraphrase Dr. Craig, hold that things and events aren't equally real - only the present is metaphysically true; the past is no longer the case and the future will be the case, but it is absolutely true from every vantage in the universe that they are not currently the case. Only the present is such.

B-time theorists hold that there exists a point of reference by which the past, present, and future as experienced illusory by men all are true metaphysically. They are ordered by a temporal relation "before" and "after," where "a is before b" means simply that the truth of b requires the truth of a, but that the truth of a does not require the truth of b (simultaneous occurrence would require both).

To illustrate the difference more clearly, A-time theorists simply state that the universe exists in the temporal progression of one state to another. Thus, the notion of "x begins to exist," loosely, is that x exists over a timespan of finite measure. Yesterday has happened; tomorrow will happen; today is happening. B-time theorists hold that something's temporal existence (i.e. the whole of "yesterday") is simply extended finitely, exactly like a ball is finitely extended in space, when the universe as a whole is taken under consideration. This is what I think is usually meant by referring to time as "the fourth dimension."

That we perceive the "A-theory" of time is granted by the B-time theorist, but the B-time theorist states that this is due to our role as part of the universe, and that ultimately, this is, as stated previously, an illusion, as from the perspective of the entire universe all the past, present, and future simply exists in terms of ordered extensions in a dimension of space representing temporality. Thus, nothing begins to exist, even if its existence is finite in the time-dimension; it is simply finite in time-extension and no more begins to exist by virtue of this fact than a yardstick begins to exist by virtue that it has edges.

Note that if solipsism is true, then A-time theory is absolutely true, since the fact that we perceive a progression of events means that this is exactly the case, due to no other outside point of perception being at all possible. Therefore, all of our perceptions began to exist.

Now, under A-time theory, everything that begins to exist has a cause (under B-time theory, it needen't have a cause; it just *is*). A "cause" is the action of one entity upon another entity with the "effect" being the result of this action in accordance to the nature of the interaction of these entities. The nature of a bat and the nature of a ball, for example, entail that if the ball is hit by the bat, it goes flying, all things in context being fairly granted. Since "nothing" has no properties, i.e. no identity, and thus does not exist, then everything that begins to exist in A-time theory must be caused by other things or must be caused by itself, and that action must occur before the effect or in simultaneous relation to the effect (i.e. quantum entanglement).

Given solipsism, first note that I must begin to exist, because my perceptions are in motion and because this motion has not always been occurring. Thus, I have a cause, and if solipsism is true, I must have caused myself to begin to exist. This leaves three possibilities: I caused myself to begin to exist before I began to exist, a contradiction; or, that I caused myself to begin to exist at a later state of my existence, which would entail that the effect precedes the cause, an impossibility by definition; or, most plausibly, that I caused myself to begin to exist simultaneous to the moment of my beginning.

The latter statement is all that's left for solipsism at this point, so refuting it renders solipsism literally impossible. Note first that since my perceptions themselves began to exist, they must have a cause (they can't exist as "brute fact," as people positing solipsism love to say, since A-time theory is absolutely true under solipsism and thus it is absolutely certain they must have a cause). This cause must either be due to other perceptions, or due to a creative ability inherent in myself. At the moment when I began, my first perceptions cannot have been caused by previous perceptions, or else it was not the first moment when I began. Therefore, my creative faculty must have (simultaneously with my beginning) caused them to begin to exist. Furthermore, my creative force must itself begin to exist with a content with which to create, since it would otherwise be empty (as I have not perceived at the moment of my beginning) and thus would lack any means of creative power, since there would be nothing by which it has means to create - even God has an idea of what He creates if we presume theism and creation out of nothing on that account. So, I must begin to exist with some preconceived notions of what I cause to exist at my beginning. Therefore, these notions must themselves have a cause.

Since no other outside force (evolutionary processes, a nasty god, etc.) exist to supply these notions, and since these notions cause the perceptions to begin to exist (and thus, by logical precedence, cannot caused by these perceptions), we have nothing left to supply their necessary cause. Therefore, I could not have caused myself to begin to exist simultaneously at the beginning of my existence.

Therefore, we have nothing left to supply the necessary cause of the self under the assumption of solipsism. But this is a logical contradiction.

Therefore, an outside world exists absolutely, 100%, objectively, irrefutably, and inarguably exists by the impossibility of the contrary. So quit positing that it could possibly be "all in your head". =P

It would imply that every concrete can be placed in concept classes whose linear measures are not only ordinal-scale, but interval- or ratio-scale as well[43].

From what I gather, you're implying the "other direction" in this post and thus grounding the theory like Newton did gravity. Kinda scary...

Very good job on this paper, and a fun read! It's great that you identified your fallacy at the end here, but I would add the following: how could neurological analysis deny an epistemic process? Perhaps electric pathways lighting up in the structures of our brains may cross specific memories just over the places that link their essentials and omit consideration of their particulars ...

The measure values required for Rand's theory need not be interval units. As Rand realized, merely ordinal measurement suffices for her measurement-omission scheme (1966, 33). I say that the magnitude structure captured by ordinal measurement is the minimal structure implied for metaphysics if, as I supposed at the outset, all concretes fall under one or more concepts for which Rand's measurement-omission analysis holds. What is the magnitude structure captured by ordinal measurements?

Just a bunch of lines with concrete points of constant separation of otherwise unimportant unit length separating the ordered points in the imagined graph, partially ordered. "Cubes" in Rn, in other words. That's my guess, let's see how silly I look at the end of this thing.

The magnitude structure affording merely ordinal measurement is a linear order whose automorphisms are the order-automorphisms of (same-order subsets of) the real numbers in their natural order. Such a magnitude structure affords characterization by a lattice (a type of partially ordered set) formed of sets and subsets of possible Dedekind-cuts of its linear order. This linear order might be scattered or dense; ordinal measurement is possible in either case[25].

Why not just a poset? Why the need to allow for Dedekind cuts and the like? Is this to establish limit points for orderings? I don't quite understand why it can't be modeled by a poset as I explained above.

The magnitude structure affording merely ordinal-scale measurement affords metrics. Each of the three scales adduced above to capture degrees of hardness bears a metric defined by the absolute values of those scales' numerical differences. A magnitude structure affording a (separable) metric belongs to the topological category known as a (separable) uniformity. Topologies that are uniformities in this sense are Hausdorff topologies, but they need not be compact nor (topologically) connected[26]. The topological character of the magnitude structure entailed for all concretes by Rand's measurement-omission theory of concepts is the character of a uniformity.

Hausdorff space is immediate here, of course. I suppose this alleviates the headache of Dedekind cutting and the imposing thundercloud of denseness above, but I guess I don't know what's going on with the previous example at all. Are you asserting that this particular structure presupposes a declared (discrete point) choice of scale, while the above structure does not presuppose that? If so, why does selecting this choice of scale alleviate the headache from the above structure, and how does the above's non-choice of metric entail the possibility of Dedekind cutting and denseness, etc., while this does not?

The magnitude structure entailed by Rand's theory has the algebraic character of a lattice, which has more structure than a partially ordered set (or a directed set) and less than a group (or a semi-group). In terms of the mathematical categories, Rand's magnitude structure for metaphysics is a hybrid of two: the algebraic category of a lattice and the topological category of a uniformity. Rand's structure belongs to the hybrid we should designate as a uniform topological lattice.

OK - the only reason why I think you're asserting this is that the lattice represents the ordinal order-structure for both a ratio and a length-related original conceptual structure, whereas the simpler uniform topo represents the concepts that are relational like the scratching rocks, where ratio and length do not apply. Is this correct?

Concerning multidimensional magnitude structures of concept classes, I concluded in the preceding subsection that Rand's theory entails neither affine nor absolute structure. What is entailed: concept classes with a 2D or 3D magnitude structure will have the structure of at least an ordered, distance geometry[27]. Significantly, it is implied that planes and spaces concretely realizable will have at least that much structure.

Probably only "plane" and "space" themselves fit in accordance with the minima indicated in the last sentence. Correct?

Whichever concept is considered as an instance of the superordinate concept, not only will that subordinate concept and its instances stand as a substitution instance of the superordinate, each instance of the subordinate will have some particular measure value along a specific dimension. And that particular value is suspended for the concept, thence for the superordinate concept.

So the subordinate part is omitted in measurement, allowing the superordinate to act according to its given precedent in context since the subordinate is unimportant? This would seem to cure the problem for practical consideration, but in general, is it still possible for this odd crossover category (math sense) to really be clear on the concrete level?

Analytically, identity precedes similarity[28]. For purposes of her theory of concepts and concept classes, Rand defined similarity to be "the relationship between two or more existents which possess the same characteristic(s), but in different measure or degree" (1966, 13). I concur. Occasions of scratch-hardness are similar to each other because they are all occasions of scratch-hardness, exhibiting that hardness in various measurable degrees. This much accords with Rand's definition and use of similarity in the theory of concepts.

Right.

To say that ball shapes are more like one another than they are like cup shapes is to say something beyond what is claimed in saying: Shapes that balls have are themselves and not something else, such as shapes that cups have.

The latter deals with the identity of the perceptual, while the former the identity of the relevant concepts.

But such an employment of Rand's conception of similarity as sameness of some characteristic, but difference in measure, is incorrect in application to the comparative similarities of the various strengths of solids, thence to their superordinate concept strength of a solid.

Right, because strength involves different measure methodology (linear, relational, ordinal) while shape involves only one linking measure for its subordinate concepts.

. . . . There is no single, common measure of property of a solid that all specific properties of solids have in common. Rand supposed in error that there were, for she supposed it always the case that there is some same, common measurable dimension supporting the conceptual common denominator for any superordinate concept (1966, 23)[29]. That supposition is here rejected, and measurement-omission analysis of superordinate concepts is here corrected in this respect.

Understood.

So I should amend Rand's definition of similarity as follows: Similarity is the relationship between two or more existents possessing the same characteristic(s), but in different measurable degree or in different measurable form.

Why not just chuck the different measurements? They are, after all, measurements to omit; the difference in unit or form is not essential to the quality you abstracted.

The corresponding definition of concepts would be: Concepts are mental integrations of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted or with the particular measurable forms of their common distinguishing characteristic(s) omitted.

Well, you need to do this or else you won't be able to conceptualize the Law of Identity, right? I mean, I suppose that's gotta be the "top of the tower," probably isolated from everything else.

Every concrete falls under both sorts of concept.

In other words, concretes have extension in space and degree (whatever measure this may mean) of density, to put it very broadly.

What is the magnitude relation under which all concretes must stand such that conceptual rendition of them is possible? They must stand in the relation of a uniform topological lattice, at least one-dimensional. This is the magnitude structure implied for metaphysics, for all existence, by the theory of concepts in Rand's epistemology. The same magnitude structure is implied by that theory with my friendly amendment.

Good.

Universals as (abstractions that are) concepts are concept classes with their linear measure values omitted. If the concept is a superordinate, then the linear measurable form might also be omitted, that is, be allowed to vary across acceptable forms. Universals as collections of potential concept-class members are recurrences on a linear order with their measurement values in place[32]. For either sense of the term universals, they are an objective relation between an identifying subject and particulars spanned by those universals (Rand 1966, 7, 29–30, 53-54; 1965, 18; 1957, 1041).

(Continued below)

Good job, but by what standard do we judge "acceptable" forms?

Applied to concept units in their substitution sense, measurement omission means release of the particular identities of the class members so they may be treated indifferently for further conceptual cognitive purposes[7]. This is the same indifference at work in the order-indifference principle of counting. The number of items in a collection may be ascertained by counting them in any order. Comprehension of counting and count number requires comprehension of that indifference.

That\'s correct. As I mentioned with my own thoughts on the conceptualization of the Law of Identity, omission may include more than mathematical quantifiables.

The release of particular identity for making items into concept-class substitution units is a constant and necessary part of Rand\'s measurement-omission recipe. But this part is not peculiar to Rand\'s scheme. What is novel in Rand\'s theory is the idea that in the release of particular identity, the release of which-particular-one, there is also a suspension of particular measure values along a common dimension.

Correct.

But the numbers have intrinsic character—even or odd, whole or fraction, rational or irrational, analytic or transcendental—quite independently of our choices, such as choice of number base.

That\'s right; a rational being with six total fingers who utilized base-six would count a basket of 100 bananas in a different way, but the set of his target of counting would correspond one-to-one with mine, should I be counting the same bananas (in base-10). The fact that the numbers are different due to the choice of bases is a nonessential epistemological difference for that very reason.

Affordance of Ratio or Interval Measures

Shapes must possess such pairs of magnitudes in some measure but may possess them in any measure.

Not zero-measure. Can\'t count a square, or a line segment, or a point, as a cube.

Observe that Rand\'s measurement-omission theory does not entail what number of dimensions for the magnitude relations among concretes is appropriate for the concept. Length requires 1D, shape requires 2D. Rand\'s theory works for any dimensionality and does not entail what the dimensionality must be, except to say that it must be at least 1D. Observe also that the conception of linearity to be applied here to each dimension is not the more particular linearity familiar from analytic coordinate geometry or from abstract vector spaces. It is merely the linearity of a linear order[9].

This is correct. And my above sentence cures the headache the former part of this quote posits.

That is a numerical rule of combination appropriate to concatenations of the concrete magnitude structure in the case of length.

Wouldn't this just be Rn, n = number of qualities to quanitfy?

The magnitude structure of the concretes falling under the concept length also affords ratios that are independent of our choice of elementary unit. The ratio of the span of my left hand, thumb-to-pinky, to my height is simply the number it is, regardless of whether we make those two measurements using sixteenths of an inch as elementary unit or millimeters as elementary unit.

This is correct.

Grades can be concatenated, although the proper mathematical reflection of this concatenation is not simple addition[11].

Grades depend on trigonometry, which presupposes its ultimate origin in a right triangle, meaning it\'s a ratio corresponding with the proper function acting on the angle in question. Its precedent is thus a fraction, which is multiplication, which may be extended - definitely or indefinitely depending on the numbers in question - to summation of integers.

Finest objectivity requires measurement scales appropriate to the magnitude structures to which they are applied. What does appropriate mean in this context? It means that all of the mathematical structure of the measurement scale is needed to capture the concept-class magnitude structure of concretes under consideration. It means as well that all the magnitude structure pertinent to the concept class is describable in terms of the mathematical structure of the measurement scale[12].

Precisely. That\'s my whole issue with the Teleological Argument for the Existence of God, by the way, when they harp on the \"smallness\" of certain constants. The units, of course, are not relational to their everyday application, and thus will appear to be quite precise when they may not have been such at all.

If one uses a different scale for one quantifiable, though - even within reason - won't that bunk the shape of the entire concept here?

What is the magnitude structure of concretes that is appropriately reflected by ratio-scale characterization? It is a magnitude structure whose automorphisms are translations[13]. Translations are transformations of value-points (i.e., points, which may be assigned numerical values) of the magnitude structure (the ordered relational structure of the concept-class concretes) that shift them all by the same amount, altering no intervals between them.

This means: since a ratio is independent of specific measurement, it is crystalline and unchangeable. Much easier to work with than that length-scale structure above that's all amorphous.

What about concretes involving both length- and ratio-scale characteristics, such as a sauna, for instance?

Physical temperature, certain aspects of sensory qualities, and certain aspects of utility rankings are examples of concretes whose magnitude structures afford what are now called interval measures, but evidently do not afford ratio measures[16]. The magnitude structure underlying the concept class temperature affords only an interval scale of measure. Such magnitude structures do not afford concatenations, unlike the natures of length or mass, but they do afford ordering of differences of degree, and they afford composition of adjacent difference-intervals[17].

Right; such things are not extended in space, yes - it makes sense such things fit under interval scale. What is a "composition of adjacent difference-intervals?"

Such magnitude structures do not afford ratios of degrees that are independent of choice of unit, but they afford ratios of difference-intervals that are independent of choice of unit and choice of zero-point[18]. Ratio scales have one free parameter, requiring we select the unit, such as yard or meter. These scales are said to be 1-point unique. Interval scales have two free parameters, requiring we select the unit, such as ˚F or ˚C, and requiring we select the zero-point, such as the freezing point of an equally portioned mixture of salt and ice or the freezing point of pure ice. These scales are said to be 2-point unique[19].

Two points to consider here:

(1) Again - what about concepts entailing both ratio and length? How are those constructed?

(2) Ratio may be used for temperature if the relation of the relative thickness and motion of the particles comprising an object are compared with later states of thickness (or thinness!) and motion of particles.

The magnitude structure of concretes affording interval-scale characterization is one whose automorphisms are fixed-point collineations, preeminently stretches[20]. Stretches are transformations of the value-points of a magnitude structure such that one point remains fixed and the intervals from that point to all others are altered by a single ratio.

Isn\'t this a contraction? And wouldn\'t this only apply to a change of a single unit potentially, i.e. could someone mess with one scale of one quantity in your storage set of concepts and have the concept-structure all damaged as a result, unlike what is possible for ratio structures?

Rand\'s measurement-omission analysis of concepts and concept classes applies perfectly well to cases in which the measurement scale appropriate to the pertinent magnitude structure of concretes is interval scale. The temperature attribute of a solid or fluid must exist in some measure, but may exist in any measure[21].

Right. But if it is not interval scale, then one can structure it under the assumption that there's one anyway.

An analogous conclusion obtains for multidimensional magnitude structures of concept classes. Rand\'s theory does not entail that all 2D or 3D magnitude structures have not only order structure, but affine structure, as Euclidean and Minkowskian geometry have[22]. That is, Rand\'s theory does not entail that multidimensional magnitude structures of concept classes afford a metric definable from a norm (a measure on vector structure)[23].

Why would such a structure be necessary, metaphysically? I don't see how it would relate to something like brain storage, since we're talking about objects more than likely to exceed 3-D. I understand the mathematical interest in it, though.

Won't affine structure only apply to those structures constructed from ratio relations?

Rand's system relies on three propositions taken as axioms[2]. (E) Existence exists. (I) Existence is identity. (C ) Consciousness is identification. Rand's set of axioms conveys the fundamental dependence of consciousness on existence. Existence is and is as it is independently of consciousness, whereas consciousness is dependent on existence and characters of existence (Rand 1957, 1015–16; 1966, 29, 55–59; 1969, 228, 240–41, 249–50).

First of all, the order of precedence of the term "existence exists" is ill-defined without the proceeding notion that defines what existence is in the first place. I tend to work from two axioms: (I) Identity exists; (II) Consciousness (identification) exists.

As part of the meaning of (I), Rand contended (Im): All concretes, whether physical or mental, have measurable relations to other concretes (1966, 7–8, 29–33, 39; 1969, 139–40, 189, 199–200, 277–79)[3]. Every concrete thing—whether an entity, attribute, relation, event, motion, locomotion, action, or activity of consciousness—is measurable (Rand 1966, 7, 11–17, 25, 29–33; 1969, 184–87, 223–25).

Right, but relational measurement itself has an identity, which isn't up in the chain yet. That's why I use what I listed above. B)

All concretes can be placed within some concept class(es). All concretes can be placed under concepts.

That's tautological, since you've already shown "concretes" is a concept that sweeps over reality completely, i.e. implicitly you have shown that the axiomatic concept of the Law of Identity applies to all.

Suppose you were a disembodied mind (OK, pretend you have some means inherent to your mind) in a universe where all that existed other than you was a proton. Then the only conclusion you can discern from recognizing the proton and recognizing that you are conscious of it is: both have an identity. They meet at no specific quality other than the fact that they have quantifiable quality, since no points of specific quality exist between the identity of your mind and the identity of the proton. But here you make an omission of sorts even though no similar concretes allow you a "ratio" - you omit all specifics, because there is no perceived similarity between the proton (an object of mass) and your mind (an abstract particular, so to speak), and you cannot go further in your omissions than that. What you are left with is the only concept possible: that to be is to be something, or more specifically, that to be is to have qualities.

Such mathematical structure obtaining in all concrete reality is metaphysical structure. It is structure beyond logical structure; constraint on possibility beyond logical constraint. Yet it is structure ranging as widely as logical structure through all the sciences and common experience.

It is not beyond logical constraint - it serves as the very basis for that notion. Existence is identity.

The minimum measurement and suspension powers required of the conceptual faculty by Rand's theory of concepts calls for neuronal computational implementation. Is such implementation possible, plausible, actual? This is a topic for the future, bounty beyond the present study.

Well, since we both understand mathematics, I'll venture to say "yes" ;)

Hope this guy comes back, or I'm about to blow quite a bit of time

I hope to dig into this further in the future, Neil. It would be interesting to figure out which philosophers Rand was taking to be conceptualists (concept nominalists). Ockham (and pals)? The British empiricists? Contemporaries such as Goodman and Quine?

Biggest compliment I saw her give was to Witty, whose theory of concepts is somewhat similar to Rand's - she said it was a perfect description on how a mind out of focus operated. I think it was too harsh of a judgment, though.

Thank you all for your replies.

What I am getting is this: We have evolved in this universe (the only one we have) and we are well adapted to the local planetary conditions. Therefore it is possible for us not only to survive, but with wit, luck and pluck, even flourish. There is nothing inherent (currently) in the physical environment that wants to kill us dead. Of course this could change quickly if an asteroid the size of Texas slams into Earth. But this is not News. This has been well known long before Rand. My problem with Rand's statement is that it cannot be taken literally. But that is my Asperger Self manifesting.

Ba'al Chatzaf

This is the explanation why the "Universe" (i.e. the context of one's life) ought to be expected as benevolent, rather than malevolent. Obviously there are many exceptions, such as the malevolent universe of the Soviet Union during the Cold War or in the country of Iran nowadays.

I agree that the Universe just is - calling it malevolent or benevolent is an error of category, sort of like saying the Universe is hungry. But this is not what is intended. The anthropomorphic notion really means that, as you said, we have evolved to survive rather than to die - if the "Universe" of our lives was malevolent, we wouldn't exist as a species.

I, too, have problems with using "arbitrary" as a metaphysical/epistemological cognitive classification. I only find room for it in normative abstractions and acts based on value judgments. To admit the existence of arbitrary (as a sort of non-existence) is like admitting the existence of nothing.

"Arbitrary" is fine as a metaphysical/epistemological statement IMO. In practice (and I think LP himself said this recently, oddly enough) I take it to mean a statement about a truth in reality for which there is no evidence provided at all either for or against its existence, whether in the sense of being testable via science or being inferred by the logic which presupposes the SM.

Oddly enough, I had the fortune to talk to the (Objectivist-friendly!) atheist Dr. Richard Carrier before his debate with my friend Dr. William Lane Craig on the Resurrection, and we talked about this very notion. He stated that when one makes such an assertion one assumes a 50/50 probability without evidence for or against, and then adjusts accordingly to validity (or likely validity) of arguments for the notion's veracity/falsehood. For instance, with the Resurrection, the fact that the Sanhedrin had a tradition to bury the crucified to avoid defiling the land coupled with the tradition of burying blasphemers in common graves makes the probability of Jesus being buried in a fresh tomb of the high-ranking Josephus historically less than fifty percent.

However, the proposition "Christ rose from the dead" is not arbitrary, since Christian apologists present evidence that would support such an assertion and render any contrary explanation less probable. Likewise, the assertion "there exists a planet between Earth and Mars the size and weight of Jupiter" can be rendered either highly improbable or, if gravitational pulls are properly calculated, absolutely disprovable, since such a proposed entity is scientifically testable.

However, the oft-misused atheistic assertion that "a flying plate of spaghetti in deep space is responsible for all of existence" is arbitrary, and cannot be granted a 50/50 probability - at least even the Christian god can be logically analyzed since His supposed word is available, making a even just a fuzzy notion of probability applicable, but for the spaghetti that has no means of supposed independent revelation and is ill-defined inherently, the statement cannot even be placed on the probability scale. If it could, then I could generate propositions ad infinitum just by changing the content of food on the plate, until it is very likely one of them exists!

This is what I mean by "arbitrary," at least. It steals an already-known concept and misuses it in a way where it can't be tested scientifically or logically. It's the adult equivalent of how my old friend Eric who lived around the block always claimed he had the newest Nintendo game that I wanted to play, but that his mother kept it "hidden under his bed" because he always happened to get in trouble at all the right moments.

Epistemologically, arbitrary is to values like nothing is to existence. But values are necessary to the concept of arbitrary. That makes sense to me. Arbitrary pertains to choice.

True.

On a cognitive level, saying that arbitrary is a manner of anti-concept formation is really weird. That means we can speculate without choosing (i.e. without value judgments). I can't make sense of that.

It seems more of a stolen concept than an anti-concept.

I, as you, find the metaphysical/epistemological theories to which you allude wrong. But I don't find them arbitrary. They were developed on purpose and there is a rationale behind them. I find the need to shock others (by claiming that common sense things do not exist, which seems to be the addiction of modern philosophy) arbitrary. You can be just as wrong with it as without it. So I have some fun with it.

"Common sense things"? Do you mean claiming such things like "the external world doesn't exist"? I actually developed an absolute proof that it does, and I've been waiting for a Calvinist to ask me to do so - but no luck so far! I'd love to have an Objectivist take a look at it.

Aren't discussions of the "arbitrary" arbitrary? If not, then please integrate them with scientific metodology.

--Brant

This is a category error. If you think scientific methodology comprises the whole of epistemology, though, have fun with your logical positivism

Self reference is a characteristic of some philosophical axioms. As you point out, existence is one of these. I.E. something exists. To deny the axiom is to assert it. This in turn rests on the most basic assumption of all, to wit, the law of non-contradiction. This is as close to an a priori true and necessary proposition as we will ever get. It is required to establish the axiomatic character of some philosophic assumptions.

Correct.

There are other assumptions we make that do not have this character. For example, the laws of thermodynamics. Denying a law of thermodynamics does not automatically produce a logical contradiction, yet all our our observations (so far) support the laws of thermodynamics. To put it another way, the laws of thermodynamics are NOT self evident. They are true a posteriori based on observations and have not yet been empirically falsified. A similar remark holds for the well known conservation laws of physics.

Ba'al Chatzaf

Correct. Doing so would actually commit the logical fallacy of affirming the consequent, but I think there exists valid arguments via Bayesian probability that increase the likelihood of correspondence for these theorems, sometimes to absurd heights. B)

Of course, you can have scientific theorems which are logically provable - if I recall correctly, Newton mathematically proved that an object (of mass) experiences gravity toward another mass then it is affected by an inverse-square force - and that if an object (of mass) experiences an inverse-square proportional force in relation to another mass, then such an object must be experiencing gravity. Whatever gravity is at its core, the effects at the level of science corresponding to what could be known during Newton's time are 100% airtight.

As Ayn so effectively put it, judge and be ready to be judged as the obverse of judge not lest you be judged.

Well, that was the whole issue with Rand - even LP stated on a recent show that Miss Rand made errors in her personal judgments. Heck, if she were alive today and I told her who I've befriended recently, she'd toss me down the stairs and lock the door behind me - and that's before I would present the points of difference between my philosophy and Objectivism.

Flagg:

Well put. You raised an interesting question. My father was 35 years with the NYFD, an arson investigator and retired as a Deputy Chief. Before I was born, he was on his way to work standing on the platform of the Flushing lines first stop.

A stranger fainted or became unsteady and feel onto the track unconscious. My father and another gentleman jumped down and attempted to get the man to safety.

As they were doing this, a train began to pull into the last stop.

My father got up and ran towards the train and was waving his arms and obviously he was not killed. He was given a medal and had an article in the Daily News and it was no big deal.

He and I had discussed this one and he said that it seemed like a reasonably good risk, he felt that he could always jump out of the way of the train which was slowing down.

I agree.

However, had he been killed...?

Adam

Had he been killed, he'd have gone knowing that, unfortunately, what he assessed to be a negligible risk actually realized. But the presupposition is there - he chose to take a risk conducive to saving a stranger, whom he can (rightly!) do no more than presume is a worthy member of the society in which he chooses to live. Using the "Godwin's Law" rule to contrast this as above - supposing the guy was Hitler instead; your father would be in the right to let him get whacked by the train, unless he assessed that doing so would put a vast number of people on or near the train at risk of injury or death.

I actually am a stormchaser myself - part of the reason is the joy in the days where our hard work preparing a forecast and traveling long distances pays off with some good footage, but the other part touches on the ontologically selfish "altruism" that Christopher touched upon earlier. I empathize with tornado victims because my maternal grandmother was one, and I recognize that many such victims may be innocently subject to such a disaster (i.e. subject without the ability to choose a course of proper action) without the timely warnings that chasers and spotters relay to emergency managers and weather services. So even though I could have chosen a safer hobby that reaped rewards for preparation, the latter portion makes stormchasing part of who I am, and I understand the risk inherent in my hobby/service.

My question about the Iranian journalists applies to actual real circumstances of two people in Iran. This is not a litmus test, this is a real question in which people chose different behaviors. We're observing the aftermath, but you've dismissed it out-of-hand. The goal of both these men was to stand against the government. However, is it better to stand up for your freedoms and go to jail (like Nelson Mandella perhaps?), or to tell untruths for a year, stay out of jail , but lose credibility with Iranians who might have otherwise been more supportive of your cause? Very very valid question, ver very real question, set in the real world.

Why would otherwise sympathetic Iranians be opposed to your lying to a hostile government to escape jail time? I would suppose they are not so sympathetic to your cause in the first place if they behave in this manner. And with this same presupposition, what use is it to martyr (or semi-martyr via indeterminate jail time) yourself for people who would have qualms with your lying to a government blatantly opposing inherent rights? Neither solution seems to work here.

Let's look at the real issue involved: What is the best way for an individual to stand against an aggressive government and improve the chances of bringing down that government, perhaps risking self in the process?

Depends on the context. If a core of people who value what you value and who are ready to risk their lives to improve their situation exist, and if you value these people enough to stay in comparison to whatever risk factor is attached to possible escape for you and your friends instead, then the solution is to use all of your means to determine how to best retaliate against the government. Because the government there is overtly opposed to recognizing any of your rights, the proper course of moral action - should you choose to stay - is to enact as much disruption and violence that you can while balancing the risk to you and your supporters.

What should Iranians living in Iran to do?

Seek willing outside help, gather internally via grassroots methodology, and use the resultant recourses to either violently disrupt, or if enough people are available, violently overthrow the oppressing government with extreme prejudice.

Many intelligent ones just leave the country. If you don't have a solution that works from the inside, then you're hardly in a position to argue that Iranian citizens are responsible for their government.

The citizens are responsible either because of complacency or, most likely, because they actually support the regime. Those who do not fit into such categories ought to either organize for violent revolution, beg for a sympathetic country to engage in overt war or at least aid for an internal assassination and overthrow, or leave the country - whatever the situation entails. My Muslim step-uncle, Ali, escaped Iran because most of the people there were either complacent or supportive, as I mentioned before, and he saw them rightly as worthless. When he escaped in the eighties, all the best minds were slipping out with him. It continues today, but the size of the group is negligible. My uncle was actually hoping for a full-scale invasion on the part of the U.S. with a military takeover a la Japan after the War (and this was before 9/11), but I'm not sure if I'd go that far.

If I lived there and there existed no opportunity for revolution or escape, and no hope in the foreseeable future, then I would make the most of life while being prepared to do what I can to take out as many as I could before they succeed in making me disappear in the dark of night.

I will conclude with your definition of altruism, which I also think is good: "sacrifice of one’s own self-interest for the sake of another person(s)." Even though we can both agree this is true, the act of fulfilling one's self-interest aroused through empathy will be experientially perceived as: sacrificing one's own [ego-attributed] self interest for the sake of another person(s) [as we perceive through empathic experience]. Thus, the chronic miscommunication between philosophical assertion and perceived experience is revealed.

Christopher

I have a challenge for you. Apply all your fancy verbiage to a soldier who falls on a grenade to save his buddies.

Ba'al Chatzaf

You know, I've never been able to figure you out during all my lurking around this place. One minute you could make a very insightful and interesting post, and the next you could turn around and blatantly insult and troll someone who is generally trying to help and explain a point of view in a calm, rational manner, as Christopher took the time to do here. I know you like to stir the pot, and that's fine (and encouraged), but this is not the way to do it. Get back to the style you're successful at conveying here and give Hyde a rest, eh?

The solution, by the way, is that his action is conducive to his chosen obligation to subject himself to potentially life-ending action so long as the end result is better for the armed forces than if he had not. Besides, even if he wasn't in the army, the situation would call for this action if he knew he was the only means by which his friends (who are values to him) will survive. To make sense of this, suppose instead of friends he was surrounded by Hitler, Goebbels, Goering, and all the rest of the SS elite - jumping on the grenade to save them would be, assuming his opposition to these people, a truly wicked act.

Maybe I'm missing something here, but free will is hardly assured or even likely. I'd say it's more likely that it's only an illusion, but philosophically, is there any way - ever - we could know the answer???

An illusion of what?