eva matthews

With all due respect, no, most everything is answered by a simple aggregation of facts. That's because we take the world we live in as a given assortmant of facts to begin with. 'Aggregation', in this case, means clumping facts into a class of objects that's also pre-given because our particular culture, via language, has informed us of that.

An excellent case in point is the ruler-- a culturally-defined artifact is there ever was one. Because we assume a given standard of inch and meter, we likewise assume that the markings accord from ruler to ruler. If use of common objects were not of assumed qualities, we'd all go crazy.

Now if this sounds like Hume, well, it is. Before we can seriously discuss creative thought, we have to come to terms with how we spend 99% of our thinking time putting thought-objects into pre-conceived pidgeon holes.

This also corresponds to the psychology of Kahneman, whose work will eventually constitute half of my 10-year plan...BS, MS,PHD, PostDoc...whatever...as mom's in the field, regardless of the paperchase, I've got a good idea as to what i need to learn...

Anyway, Kahneman described type1 thought , or the heuristic, as what we normally do to get by. Type 2 analytical thought takes us (briefly) out of the box. This is when we challenge both what facts are, and the groupings into which they belong.

Despite her neological misuse of 'concept', Rand offers us an adequate explanation as to how Kahneman's Type2 might be seen as a process of re-aggregating facts into an alternative frame of refrence, ostensibly different than the one we're born into.

My caveat, again, is that her description, as detailed in accuracy as it is, still represents only a small exception to thought in general.

Eva

The response Socrates would have given Rand was, 'Then female dogs have it better than human females. Female dogs give birth, nurse, then go about their doggish business". In other words, in this particular, Rand was silly-wrong, and does not deserve a serious response.

BTW, the bioblical command that Paul gave women was 'upotassestheai'.. If women speak up in congregation, let them be tied down as a ox on a harness.

Eva

Questioner under fire for asking Bachmann what it means to be a ‘submissive’ wife

"The Lord says: Be submissive, wives. You are to be submissive to your husbands," [Michele] Bachmann said at the time[2006], according to the [Washington] Post. Her campaign hasn't disputed the remarks.

On Thursday, the Washington Examiner's Byron York, a conservative columnist who was one of the moderators of the 2012 debate, asked Bachmann directly about that quote.

"As president, would you be submissive to your husband?" he asked, a question that prompted the crowd to erupt in loud boos.

After a slight pause, Bachmann smiled and thanked York for his question.

"Marcus and I will be married for 33 years this September 10th," she said. "What submission means to us it means respect. I respect my husband. He's a wonderful, godly man and a great father, and he respects me as his wife. That's how we operate our marriage."

Obviously, Bachmann was lying about what the word “submission” means. No doubt it means something very different to her as opposed to what it meant to Ayn Rand, but it doesn’t simply mean ‘respect.’ I think the issue raises same fascinating questions—whether or not you agree that femininity means “hero-worship” as it did for Rand. There is a definite sense in which a female is “submissive” to the male sexually. Quite aside from all that religious crap, there is something going on here psychologically that could potentially present a problem for a woman president. I think the fact that this issue came up means that it does have significance, even if the public discussions do not begin to address what that significance really is.

Excerpts from Rand’s 1968 article:

I do not think that a rational woman can want to be president. Observe that I did not say she would be unable to do the job; I said that she could not want it. It is not a matter of her ability, but of her values.

...when it comes to the post of president, ...do not ask: "Could she do the job and would it be good for the country?" Conceivably, she could and it would - but what would it do to her?

The issue is primarily psychological. . .

...the higher [a woman's] view of masculinity, the more severely demanding her standards. It means that she never loses the awareness of her own sexual identity and theirs. It means that a properly feminine woman does not treat men as if she were their pal, sister, mother - or leader.

Now consider the meaning of the presidency: in all his professional relationships, within the entire sphere of his work, the president is the highest authority; he is the "chief executive," the "commander-in-chief." ...In the performance of his duties, a president does not deal with equals, but only with inferiors (not inferiors as persons, but in respect to the hierarchy of their positions, their work, and their responsibilities).

This, for a rational woman, would be an unbearable situation. ... To act as the superior, the leader, virtually the ruler of all the men she deals with, would be an excruciating psychological torture. It would require a total depersonalization, an utter selflessness, and an incommunicable loneliness; she would have to suppress (or repress) every personal aspect of her own character and attitude; she could not be herself, i.e., a woman; she would have to function only as a mind, not as a person, i.e., as a thinker devoid of personal values - a dangerously artificial dichotomy which no one could sustain for long. By the nature of her duties and daily activities, she would beome the most unfeminine, sexless, metaphysically inappropriate, and rationally revolting figure of all: a matriarch.

For a woman to seek or desire the presidency is, in fact, so terrible a prospect of spiritual self-immolation that the woman who would seek it is psychologically unworthy of the job.

From “An Answer to Readers (About a Woman President),”

The Objectivist, Dec. 1968

The response Socrates would have given Rand was, 'Then female dogs have it better than human females. Female dogs give birth, nurse, then go about their doggish business". In other words, in this particular, Rand was silly-wrong, and does not deserve a serious response.

BTW, the bioblical command that Paul gave women was 'upotassestheai'.. If women speak up in congregation, let them be tied down as a ox on a harness.

January 2 Self-Esteem Every Day

The "I," the ego, the deepest self, is the faculty of awareness, the ability to think. Across a lifetime, knowledge grows, convictions may change, emotions come and go; but that which knows, judges, and feelsthat is the changeless constant within us.

There is no evidence that self-awareness, or I-ness, exists at a deeper level than any other thought, say, whether to hit on that cute guy from Neurobio, do I have time to read sissy's latest and greatest immitation of TS Eliot, how do I explain my adherence to Libertarianism to fellow students?

In any case, the ability to think does not depend upon any sort of awareness that one is, indeed, thinking. I thought Descartes solved that one some 300+ years ago.

Branden's Six Pillars is interesting; i'll append my comments at a later time. For now, it seems as if he caught the Freudian flu.

Eva

Yes, but please keep in mind that it was a mutative qwirk in mutations that gave h.sapiens a much larger brain than the other great apes. Reason is what we do with said brain.

Existence and consciousness are not irreductables for branches pf philosophy that study there in's and out's. To study what's most important in existence (and parts that are not) is called 'Ontology'. Lots of existence questions connect to the free- will debate.

To study consciousness and how it might be defined in ways not biomedical is called ...'consciousness'. For example, can it be explained by a computer model? Can it really be explained by neuronal processes, or do we need a second property altogether, or "property dualism"?

I'm really not sure how adding 'axiom' into the stew enhances understanding. From the Greek meaning 'worthy', the word worked its waty into Euclidian geometry behind the master's back,

Today, it's a fun metaphor to get high-schoolers to nail down abstract geometric forms. Likewise, it describes tactics of warfare of some Chinese guy that supposed to be good for businessmen to memorize. Then, of course, there's football: challenge the speed of the MLB when they go into Cover 2! Eventually, you will get enough concussions to cause permanent brain damage!

Worthy statements, all.

Eva

One of the major questions asked by those who first believed in an expansionary universe was precisely yours: If big bang caused expansion outwards, when and if will gravity take effect and pull the universe again into a tiny ball. Moreover, what's the proof that this isn't happening?

The answer is that objects coming towards us will bend light towards the blue of the spectra.

EM

'Time dilation" is nothing but the Lorentz modifier to Maxwell's wave equations being taken over to Newtonian Mechanics.

Hence, "All Newtonian mechanics are altered to now possess a third coefficient, the Lorentz"--Einstein. Therefore, F=MA(G), or special relativity.

Moreover, the discovery of the quanta by Planck as 'energy' gave the left side of the equation a real synthetic value, as opposed to an analytic outcome: (q)h =E= MAG. Padoddle this a bit with algebra and the simple expansion of h and you get E=MC^2.

Well, actually, E^2=M^2(C^4)...another story.

As for the how's, in a strictly foundational sense, yes, it's absent. That it works and predicts makes it 'coherentist'.

Eva

tmj,

No, I don't believe so, although I'm open for correction by those far more familiar with Rand.

if Epistemology is taken to mean 'how one justifies beliefs', we cam all agree that using reason is the only real way.

That said, there are many different avenues that reason might take that describe epistemology as such. These avenues, i might emphasize, offer contradictory results--although all are ostensibly 'reasonable'.

for example, a classical divison of epistemology is "justificationism" vs "coherentism" In other words, we can argue for the foundational basis of an idea, or argue that we're simply better with than without because, after all, foundations form an infinite regress.

Such, by the way, is the argument against any reductive scheme that suggests 'everything' is ultimately a matter of Quantum eigenstates. so coherentism is far more honored in use than in the abstract....

As for meaning, it's source seems to be a personal irritation with precisely those things which we haven't been able to reason out. In other words, we conceptuialize when we hit a road block in our process otf thinking through, and thereby become irritated.

Things which are not thought out-- yet do not seem worthy of irritation-- are simply forgotten...

Eva

Michael and Dide,

* My point was not that metaphors are bad; we obviously use them all of the time to make complex stuff simple.

Rather, there are good and bad metaphors. Use the wrong one and the listener will get the wrong idea.

To this end, heuristic, system #1 is best metaphorized by Kahneman himself: "Uhhh, you were thinking too fast. Slow down a little, amigo, so you can think things out!"

**No one seems happy over at RoR except a small coterie of fissiles. I've gotten several letters from others who have been driven off.

*** No, I'm just an average gurly-gurl who's lucky enuf to have taken a self-defense course, and to have been able to use it at the right time. The mace-spray helped, too.

**** Lastly, on learning as such: yes boredom is an inhibitor. But the listener must also make an effort. Or as i expressed myself in my high-school teaching stint of last year (math, physics, and philo), don't be a Goldilocks! Not eberything is going to be just the way you want it!

Eva

Ba'al,

For the scientist, the answer is relatively simple: Concepts- as- meaning involve causal properties. of course, it get a lot more complicated from there, involving method, measurement, and even how 'cause' might be better defined.

In terms of philosophy,however, the great mystery has always been the origin of meaningful questions. I suppose it involves, in all cases, some sort of irritation, or a desire to set things right that seem to be glaringly out of place.

For the scholastics, it was the justification of god in a discursive world that seemed to favor nominalism. For Rand, obviously her ire at a bolshevik revolution that seemed to be able to spread to America. For others....perhaps a desire to answer big questions that are not answered by a simple aggregation of facts...

Eva

No, 'exponent', previously misspelled.

Math designates aside, the photon is a quadrillion times smaller than an electron.

As the brain 'runs' on elecrrons, how could photon emissions survive?

Actually, I see philosophy as being about the challenging of premises. In other words, we all go about making decisions based upon assumptions that haven't been examined.

One of the tropes that explains how we examine our assumptions (premises) is, "Am I using reason, emotion, blind faith, or simply repeating to conform? And if reason is used, per Kahneman, am I taking time to analyze, or merely using a heuristic?

Otherwise, no, what we encounter a zillion times a day are 'facts' that we have neither the time nor the wherewithall to properly examine. For its part, academia tries to offer proof and reason as part of factual revealing, and tries to get students into the habit of doing the same...obviously with spotty results as the problem is to big to really resolve.

But calling all of these 'non-facts' because i haven't properly examined them is a solipsism. In other words, verbally admitting that we live mostly in a world of premises, assumptions and unexamined facts is to do nothing but bring thought into line with lived reality.

So the examination of premises/assumptions is a matter of choosing one's battles. This involves the examination of said assumptions and premisies thought to be meaningful, or important enough. The Scholastic word for meaning-as-importance was 'concept'. philosophy, therefore, can be understood as a study of conepts.

Eva

To the extent that all epistemologies employ the human faculty of reason, or 'thought', it would indeed seem that 'primacy' is putting ontological lipstick on an epistemological pig. NB: 'Primacy' means 'state of being primary'

First, since 'primacy' easily translates from the fancy word 'ontology' (ontos='prime, strange to tell!), to unwind 'primacy of reason' would snatch 'reason' out of the human faculty department and place it as an essence. of being. ,

So now we have , "The being-essence of humanity, being the ability to reason, is the most important aspect of epistemology."

Next, by consequence, you're really saying, "Our true essence is our ability to do epistemology."

Or, of course, ontology=epistemology!(?)

In all seriousness, epistenmology means 'justifying what we believe'. Among reasonable people, this indeed means using thought.

But since there are many thought-bearing epistemologies that disagree.with each other, the claim that the one espoused by your opponent is 'unreasonable' is merely a well-poisioning rhetorical device. It has nothing to do with philosophy.

Eva

Rand wrote as you cited: >>>Concepts are mental integrations of "two or more units possessing the same distinguishing characteristic>>>

This is hopelessly redundant. Knowing that said 'units' possess 'sameness' of distinguishing characteristic would by definition be an 'integration'. the trick is knowing what sameness to distinguish..

This problem was solved by the two scholastics who created the tern 'concept' to begin with: Abelard and Ochkam. Both, in their own way, saw concept as 'meaning'. Therefore, to conceptualize is not just 'any' integration, but rather the most meaningful....

Eva

II. Analysis

Rand gave three definitions of concept. I shall tie them all together in the next section, but for the present section, we need this one alone: Concepts are mental integrations of "two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted" (Rand 1966, 13)[6].

The units spoken of in this definition are items appropriately construed as units by the conceiving mind. They are items construed as units in two senses, as substitution units and as measure values (Rand 1969, 184, 18688). As substitution units, the items in the concept class are regarded as indifferently interchangeable, all of them standing as members of the class and as instances of the concept. 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.

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.

Before entering argumentation for the minimal mathematical structure implied for the metaphysical structure of the world, let us check that we have our proper bearings on objective structure and intrinsic structure. I have ten fingers, eight spaces between those fingers, and two of my fingers are thumbs. That's how many I have of those items. Period. Those numerosities are out there in the world, ready to be counted, and they are what they are whether I count them or not. In our positional notation for expressing and calculating numbers, we choose the number base, but the different base systems designate the same things, the numbers. In base ten, my (fingers, spaces, thumbs) are (10, 8, 2); in base eight (12, 10, 2); and in base two (1010, 1000, 10). The three numbers referred to in all these bases are the same three numbers. In Rand's terminology, the various bases are objective schemes; they are appropriate tools for getting to the intrinsic structure of numbers. But the numbers have intrinsic charactereven or odd, whole or fraction, rational or irrational, analytic or transcendentalquite independently of our choices, such as choice of number base.

In asking for the minimal magnitude structure that all concretes must possess if all concretes can be subsumed under concepts for which Rand's measurement-omission analysis holds, we are seeking intrinsic structure, obtaining under every adequate objective expression of that structure. Now we are ready.

Affordance of Ratio or Interval Measures

I have said that the units suspended in the formula "two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted" are units in a double sense: substitution units and measure values. We focus now on units in the latter sense. Rand spoke of measurement as "identification of a relationship in numerical terms" (1966, 39) and as "identification of a relationshipa quantitative relationship established by means of a standard that serves as a unit" (1966, 7; also 33; see further 1969, 188, 199200). The measure-value sense of unit is the one at work here.

By the expression "a standard that serves as a unit" and by some of her examples of concepts and their measurement bases, one might suppose that Rand's theory of concepts entails that all concretes stand under magnitude relations affording some sort of concatenation measurement. That supposition would be incorrect.

Rand illustrates her theory with the concept length. The pertinent magnitudes of items possessing length are magnitudes of spatial extent in one dimension. Another illustration of Rand's is the concept shape (1966, 1114; 1969, 18487). The pertinent magnitudes of items possessing shape, in 3D space, are pairs of linear, spatial magnitudes such as curvature and torsion for shapes of curves or the two principal curvatures for shapes of surfaces[8].

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

The magnitude structure of the concretes falling under the concept length affords concatenations. Take as unit of length a sixteenth of an inch. Copies of this unit can be placed end-to-end, in principle, to form any greater length, such as foot, mile, or light-year. This standard concatenation of lengths is properly represented mathematically by simple addition. That is a numerical rule of combination appropriate to concatenations of the concrete magnitude structure in the case of length.

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.

Mass is another concept whose concept-class magnitude structure affords simple-addition concatenations and affords ratios of its values that are independent of choice of elementary unit. Because of the latter feature, conversion of pounds to kilograms requires only multiplication by a constant. Such measurement scales are called ratio scales[10]. The mathematical combinations reflecting the concatenations need not be simple addition. This category of scales is somewhat more inclusive than that. It would include the scale for the concept grade (grades of roads, say). Grades can be concatenated, although the proper mathematical reflection of this concatenation is not simple addition[11].

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].

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.

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 ratio scale. But Rand's theory does not entail that all concretes afford ratio-scale measures. For Rand's theory does not necessitate that the scale type from which measurements be omitted be ratio scale. Her analysis also works perfectly well for scales having less structure. The magnitude structure entailed for all concretes by Rand's theory is less than the considerable structure that ratio scales reflect.

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 both affine structure and absolute structure, as Euclidean geometry has[14]. That is, Rand's theory does not entail that multidimensional magnitude structures of concept classes afford a metric (a measure of the interval between two value-points) definable from a scalar product (a measure of perpendicularity of value-lines)[15].

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].

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].

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.

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]. But Rand's theory does not entail that all concretes afford interval-scale measures. For Rand's theory does not necessitate that the scale type from which measurements be omitted be interval scale. Her analysis also works perfectly well for a kind of scale having less structure. The magnitude structure entailed for all concretes by Rand's theory is still less than the considerable structure that interval scales reflect.

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].

(II. Analysis continued below)

Concepts are mental integrations of "two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted" (Rand 1966, 13)[6].

II. Analysis

Rand gave three definitions of concept. I shall tie them all together in the next section, but for the present section, we need this one alone: Concepts are mental integrations of "two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted" (Rand 1966, 13)[6].

The units spoken of in this definition are items appropriately construed as units by the conceiving mind. They are items construed as units in two senses, as substitution units and as measure values (Rand 1969, 184, 18688). As substitution units, the items in the concept class are regarded as indifferently interchangeable, all of them standing as members of the class and as instances of the concept. 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.

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.

Before entering argumentation for the minimal mathematical structure implied for the metaphysical structure of the world, let us check that we have our proper bearings on objective structure and intrinsic structure. I have ten fingers, eight spaces between those fingers, and two of my fingers are thumbs. That's how many I have of those items. Period. Those numerosities are out there in the world, ready to be counted, and they are what they are whether I count them or not. In our positional notation for expressing and calculating numbers, we choose the number base, but the different base systems designate the same things, the numbers. In base ten, my (fingers, spaces, thumbs) are (10, 8, 2); in base eight (12, 10, 2); and in base two (1010, 1000, 10). The three numbers referred to in all these bases are the same three numbers. In Rand's terminology, the various bases are objective schemes; they are appropriate tools for getting to the intrinsic structure of numbers. But the numbers have intrinsic charactereven or odd, whole or fraction, rational or irrational, analytic or transcendentalquite independently of our choices, such as choice of number base.

In asking for the minimal magnitude structure that all concretes must possess if all concretes can be subsumed under concepts for which Rand's measurement-omission analysis holds, we are seeking intrinsic structure, obtaining under every adequate objective expression of that structure. Now we are ready.

Affordance of Ratio or Interval Measures

I have said that the units suspended in the formula "two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted" are units in a double sense: substitution units and measure values. We focus now on units in the latter sense. Rand spoke of measurement as "identification of a relationship in numerical terms" (1966, 39) and as "identification of a relationshipa quantitative relationship established by means of a standard that serves as a unit" (1966, 7; also 33; see further 1969, 188, 199200). The measure-value sense of unit is the one at work here.

By the expression "a standard that serves as a unit" and by some of her examples of concepts and their measurement bases, one might suppose that Rand's theory of concepts entails that all concretes stand under magnitude relations affording some sort of concatenation measurement. That supposition would be incorrect.

Rand illustrates her theory with the concept length. The pertinent magnitudes of items possessing length are magnitudes of spatial extent in one dimension. Another illustration of Rand's is the concept shape (1966, 1114; 1969, 18487). The pertinent magnitudes of items possessing shape, in 3D space, are pairs of linear, spatial magnitudes such as curvature and torsion for shapes of curves or the two principal curvatures for shapes of surfaces[8].

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

The magnitude structure of the concretes falling under the concept length affords concatenations. Take as unit of length a sixteenth of an inch. Copies of this unit can be placed end-to-end, in principle, to form any greater length, such as foot, mile, or light-year. This standard concatenation of lengths is properly represented mathematically by simple addition. That is a numerical rule of combination appropriate to concatenations of the concrete magnitude structure in the case of length.

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.

Mass is another concept whose concept-class magnitude structure affords simple-addition concatenations and affords ratios of its values that are independent of choice of elementary unit. Because of the latter feature, conversion of pounds to kilograms requires only multiplication by a constant. Such measurement scales are called ratio scales[10]. The mathematical combinations reflecting the concatenations need not be simple addition. This category of scales is somewhat more inclusive than that. It would include the scale for the concept grade (grades of roads, say). Grades can be concatenated, although the proper mathematical reflection of this concatenation is not simple addition[11].

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].

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.

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 ratio scale. But Rand's theory does not entail that all concretes afford ratio-scale measures. For Rand's theory does not necessitate that the scale type from which measurements be omitted be ratio scale. Her analysis also works perfectly well for scales having less structure. The magnitude structure entailed for all concretes by Rand's theory is less than the considerable structure that ratio scales reflect.

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 both affine structure and absolute structure, as Euclidean geometry has[14]. That is, Rand's theory does not entail that multidimensional magnitude structures of concept classes afford a metric (a measure of the interval between two value-points) definable from a scalar product (a measure of perpendicularity of value-lines)[15].

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].

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].

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.

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]. But Rand's theory does not entail that all concretes afford interval-scale measures. For Rand's theory does not necessitate that the scale type from which measurements be omitted be interval scale. Her analysis also works perfectly well for a kind of scale having less structure. The magnitude structure entailed for all concretes by Rand's theory is still less than the considerable structure that interval scales reflect.

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].

(II. Analysis continued below)

Rand wrote as you cited: >>>Concepts are mental integrations of "two or more units possessing the same distinguishing characteristic>>>

This is hopelessly redundant. Knowing that said 'units' possess 'sameness' of distinguishing characteristic would by definition be an 'integration'. the trick is knowing what sameness to distinguish..

This problem was solved by the two scholastics who created the tern 'concept' to begin with: Abelard and Ochkam. Both, in their own way, saw concept as 'meaning'. Therefore, to conceptualize is not just 'any' integration, but rather the most meaningful....

Eva

No, bouncing photons off electrons doesn't work, except in the most exceptional of circumstances.

Basically, to give you some idea, the expionent normally associated with the photon is the planck, at exp --32, while the elecrtron range is about --18 give or take at rest state.

That's fifteen zeros of difference...or a 'quadrillion' times!

Theoretically, by means of the Heisenberg (as understood by Gamow's 'quantum tunneling') the velocity of a particular photon can become nearly infinite. But that's only one photon per the gazillion that are emitted when electrons nearly collide.

The Josephson junction permits a singular stream of photons through an electron screen, but these have to be carried by electrons that couple at extremely high velocities. of course this stream has had enormous medical applications....

By the same token, per Schrodinger's 'i', some photons can even travel backwards in time --another stiory.

In any case, the notion that the brain can emit photons is nearly impossible, and not completely so because of Penrose's 'theory'. The reason, again is the reality of electron flow in the brain would easily stop any photon.

EM

Michael,

Thanks for your replies. You're the consumate host who's able to keep lively discussion going.; I therefore invite you over to RoR to set things right.

My responses:

* I have no death wish. I believe that the guy to tried to rape me called my 'dollhead', too. I understand that his frat brothers still leave flowers at his gravesite, some three years later.

This is why I object to the constant flow of 'rape' over at RoR. Cutie-pie names are fine, however. I'm slender, 5-6 with light brown hair, huge blue eyes, smile and cheekbones to match. 'Not at all dikey. 'Just had a breakup (sob!). Attend college in Atlanta....

** Yes, I agree that the Redskin issue may be an excuse to get things riled up. So thanks for the Kahneman analogy. The acid test is whether or not real native americans give a shit. So for once we have every reason to believe Limbaught that they don't.

The hopeless sanctimony of liberalism is their efforts to create outrage independent of the non-outraged subject. This is racism at its worst--telling other people how to feel. The fact that they do it all the time (and as a raised- on- campus brat I do see it that often!) may indicate some sort of ill-conceived sincerity on their part.

*** 'Sub-conscious' is simply a bad metaphor on the layman's level because it assumes a layered effect to cognition which belabors the point. We zap people all of the time and fail to find said 'layers'. Zones in the cortex and a Thalmic systemiof many parts. yes....but what needs to be emphasized is that all thought occurs within the thin depth of four stacked cloth table napkins.

A similar misguided metaphor is that awful nuclear symbol with electrons orbiting a nucleus. The proplem is that having these notions to contend with inhibits learning how things work...

Eva

Michael,

No, in my own field of Psychology (my 'major', really!) people not only don't understand cause, but also argue over effects.

A classical example of this is 'self-esteem': always good, or a happy medium?

The interesting point of QM is that the results are undisputed, yet no real understanding of the how's. So sure, one is 'allowed' to say that they 'understand' QM. So explain away! Scienceworld awaits with bated breath!

Do fields cause particles? Uhhh....the question is 'way over my head.

Eva

Ba'al,,

Also, please don't forget that the symmetries of physics are made possible by her working of Group Theory (Gallois>Abel>Lie) into Thermodynamics....

Michael,

No, the field is real because it can be 'observed' as an 'effect'. We then iterate back and infer what are the specifics (mass, spin,speed) of a particle that might cause the energy that creates the 'wave' that can be expressed as a field.

What's important to note is that the particle isn't 'real' to the extent that it cannot be observed.

Forty years ago, both this non-observation of said particle and the expression of probability that the particle could be anywhere within the field caused philosophical concern: 'fiction', illusion', etc..... Well, that was long before my time--as I'm 20!

Even though , as Feynman said, "If you say that you understand QM, then you're lying", the bigger picture is that we obtain fantastic measurement. So go withthe flow!

Eva

Kahneman, with Tversky, began to develop the 'system one' as 'heuristic' in the 70's.

What it came to mean was that 'fast thinking' failed to measure up to 'Rational expectations'-- much to the later's demerit as the reigning general economic theory of Chicago School. Hence his Nobel in Economics.

Re Redskins, I fail to see how/wher there might be a 'substitution effect'. For what,exactly, might you kindly explain?

Lastly, as a research psychologist (also my chosen field as a hyper-involved senior), Kahneman would most likely caution against any reference to the 'subconscious'. Although Freudians can play fast and loose with metaphor, for an empiricist, sub-conscious must refer to an identifiable site.within the brain.

However that might be, Kahneman does offer a good evolutionaly-adaptive explanation for the use of heuristic judgment to assure survival: You're far better off throwing the spear under the assumption that it's a tiger in the bush...than not. So if it happens to be your neighbor's child instead, it was still a risk worth taking under circumstances that do not permit system 2.

Eva

Ba'al,

I'll watch the presentation to see the context of his symmetry remark. But for now:

No, mankind didn't want symmetry, Emmy Noether did.

Michael,

''Field" simply describes the mathematical nature of the equations.used. This is necessary because 'particles' are said to exist anywhere within the field.

Eva