Universals and Measurement

[Guyau]

Hi Dan,

Thank you.

Single dimensions are conceptually the most elementary and most simple in the way that the number one is so with respect to higher numbers. But that is no metaphysical priority. Also, being necessary for higher dimensions and being most simple conceptually does not mean one grasps single dimensions earlier in development than one grasps multidimensional objects or episodes. Indeed, the developmental research shows otherwise. Isolation of dimensions succeeds more holistic grasp of objects and episodes. We have object concept and intentionally act in a three-dimensional space long before the advent of language, the single-word stage of speech starting around one year. One can operate and become skillful at operations (reaching, grasping, sitting, crawling, standing, walking) in three-dimensional space without knowing that space is three-dimensional or yet having any notion of dimensions.

“Dimensional” is indefinite as to whether it is only a segment or infinite. Speed of transport of mass-energy is a single dimension (notwithstanding the fact that its values are ratios) whose possibility of values above zero it was natural to assume infinite until indications in electrodynamics led Einstein to think otherwise. Our everyday concepts seem mostly analyzable in terms of multiple dimensions where each is a finite range of possibilities for the conceptualized kind, but with the endpoints fuzzy. Bigness of humans, for example, would have various dimensions, with a lot of mathematical values definitely out of bounds for the concept, though the limits remain fuzzy.

Recognition of possibility begins when thought begins. That is long before language and concepts in development, and linguistic thought requires continued support of our schematic, prelinguistic forms of reflective representation. Concepts, like all thoughts, require engagement with possibility, not only actuality. Metaphysically, existence includes both actuality and possibility; both are part of the identity of existents. Actuality and its nearer possibilities would seem to have some metaphysical priority over actuality and its farther possibilities.

Rand used existence more inclusively than actuality. She did indeed mean to rein in being by switching to existence as her widest concept (and by yoking existence to specific and particular identity), but she did not use the latter so narrowly as commonly had been the case in philosophy and theology.

Stephen

[dlewis]

Thank you Shephen-- that clears up a lot for me.

I guess I'm having a little problem with what Rand often called "implicit concepts"-- concepts that are in percepts but not abstracted or realized yet in conceptual form, and those which may not be implicit. Aren't all concepts to some degree implicit because they depend on percepts? And where does imagination fit into this equation-- don't we also "invent" or construct concepts to some degree? Where do you draw the line between denotative or essential defintions and connotations?

[Guyau]

Dan,

Those issues are pretty involved and would pull me too long away from current lines of work to dig into right now. Rand’s use of implicit in ITOE was ambiguous. At her epistemology seminar a few years after writing ITOE, she showed some greater sensitivity to distinctions within implicit in its applications to cognitive development, and Peikoff also showed some sensitivity to delicacies of implicit in his 1976 lectures on Objectivism. (In a full treatment, Seale’s Chinese Room, and his critics, as well as implicit in its various uses in cognitive psychology need to be assimilated.) In the Index for ITOE, check Rand’s remarks, in the original treatise as well as in the seminar transcripts, under IMPLICIT KNOWLEDGE and under IMPLICIT MEASUREMENT. See also ##24–30* of the “Capturing Concepts” thread.

Using JSTOR at your university library, you will find Robert Campbell’s paper “Goals, Values, and the Implicit – Exporations in Psychological Ontology” in V3N2 of The Journal of Ayn Rand Studies. On my own narrow use of implicit in connection with cognitive development in “Universals and Measurement,” see the endnote 35.* I’ll reprint that below, as the typeset of the paper shrank greatly at this site in one of its upgrades.

Rand thought that all thought was creative, not passive and not amenable to automatization. I expect imagination to figure in Objectivist epistemology in some specific ways, sharing some of the ways it figured in the epistemologies of Aristotle, Avicenna, the schoolmen, and Kant. See “Imagination and Cognition” by Merlin Jetton in Objectivity V1N3.*

On propositions and word- or concept-connotations, see David Kelley’s The Art of Reasoning (pp. 60–61 in the first edition), which would be at your library. I am indebted to Kate Herrick, at an epistemology seminar last fall, for pointer to David’s analysis. Check also CONNOTATION and CONNOTATIVE DEFINITION in the Index of Irving Copi’s Introduction to Logic.

Any reflections you have on any of these matters, however embryonic or researched, I’m sure would be welcome here.

~~~~~~~~~~~~~~~~

35. The sense of implicit here is extracted from the relevant cognitive-development research literature (viz., Gelman and Meck 1983, 344). The child is said to have implicit knowledge of the counting principles if she engages in behavior that is systematically governed by those principles, even though she cannot state them. (See Note 40 for the principles.) Gelman and Meck liken this implicitness of the counting principles at this stage of cognitive development to the way in which we are able to conform to certain rules of syntax when speaking correctly without being able to state those rules. That much seems right, but there is a further distinction I want to make. The child’s implicit counting principles are being learned (and taught) as an integral part of learning to properly count aggregations explicitly, expressly. In contrast, we can (or anyway, my preliterate Choctaw ancestors centuries past could) live out our lives, speaking fine in our mother tongue, following right rules of syntax, yet without being able to state those rules; indeed, without even knowing any of the terminology of syntax. Our learning of tacit rules of syntax is not for the sake of becoming able to follow them explicitly, only tacitly.

In the present developmental discussion, I shall reserve the term implicit to indicate that an operative rule is not only tacit, but has become operative as an integral part of becoming explicitly operative. The tacit logical principles, whose acquisition according to Macnamara is traced in the text, are not implicit in my present sense.

There is, of course, another sense of implicit that I am also happy to use. That is the logicomathematical sense, which was pertinent to our analysis section. It is in that sense that we say a certain theorem is implicit in a set of axioms; Hertz’ wave equation for propagation of electromagnetic radiation is implicit in Maxwell’s field equations; an inverse-cube central force law is implicit in a spiral orbit; dimension reductions are implicit in Kolmogorov superposition-based neural networks; certain measure relations are implicit in any similarity discerned in perception; or certain measure relations are implicit in a concept class.

[dlewis]

Thank you so much Stephen-- I'll be sure to check out some of the sources you've mentioned, and thanks also for posting your endnote-- there seem to be a lot of ways the idea of implicit can be used. Would this be a correct assertation to think of "implicit," in any sense, as the epistemological version of what an "inherent" or more essential trait/property is metaphysically-- If this is the case, I think I understand how implicit can used properly.

You state in in post #176 "Single dimensions are conceptually the most elementary and most simple in the way that the number one is so with respect to higher numbers. But that is no metaphysical priority."

I may disagree with you on the metaphysical priority of "one." The way you described the dimensional/ one-dimensional in post #176 seems very similar to how I explain the axiomatic nature of "self" and the idea of "one" in my book.

I state:

".... Most basically, self is a metaphysical realization of “one.” “One” can be understood as referring to both/either some specific object or part (myself, itself) and/or parts (e.g.“they are one,” i.e. themselves) as a whole. Thus self can work inclusively, referencing any/all boundaries or more broadly “differences,” whether more limited or all-encompassing. For example, most humans seem to identify as one “I,” or some unified body, even though any one of us is a complex composite, a myriad of physical and chemical forces interacting within some larger, environmental “whole.” Thus the difference in the case of “existence” could arise from the fact that it must include anything and everything—no other concept can be more inclusive, and this makes existence unique. If an all-permeating idea like existence is self-bound, containing difference by being the most limitless concept possible, doesn’t this also suggest self must engulf everything?"

You also state in #176: "Also, being necessary for higher dimensions and being most simple conceptually does not mean one grasps single dimensions earlier in development than one grasps multidimensional objects or episodes. Indeed, the developmental research shows otherwise."

I totally agree with you here, but then you go on to say,

"Recognition of possibility begins when thought begins. That is long before language and concepts in development, and linguistic thought requires continued support of our schematic, prelinguistic forms of reflective representation. Concepts, like all thoughts, require engagement with possibility, not only actuality. Metaphysically, existence includes both actuality and possibility; both are part of the identity of existents."

Here is where the implicit ideas of "possibility" and "actuality" get confusing for me. It seems like you have it right when talking about the idea of "one" or the "dimensional" as not being grasped until later in our conceptual development -- that makes empirical sense and is supported by studies, as you say. So... although it may be there implicitly, why are you saying that we recognize "possibility," when thought begins? I don't think we recognize that as a concept until later either-- it is only implicit in percepts, right, but there really isn't much "recognition" of it unitl much later--wouldn't this be accurate?

If so, I think both possibility and actuality could be seen on a similar level with "one", perhaps seen logicomathmatically as some infinity and some more limited measurement, and I think existence and knowledge may be metaphysical reflections of possibility and actuality, just as self may be of one. What do you think?

[dlewis]

Of course I'm using knowledge much differently than most people do--I'd have to go through a lot of explaining-- so please take out that concept for now.

[Selene]

Of course I'm using knowledge much differently than most people do--I'd have to go through a lot of explaining-- so please take out that concept for now.

Sorry, that does not work for me.

I would prefer that you start explaining.

I absolve Desi Arnez from his assertion that, "Lucy, you have a lot of splanin to do!"

[dlewis]

Lol--Okay Selene. This is directly from my book--the first part of the chapter about knowledge. This is the best and easiest way I know how to expalin it.

"Because thoughts, instincts, behaviors, in general all our actions can be considered a natural consequence or embodiment of our knowledge, its axiomatic nature may seem as obvious as the concept of existence. In other words, to be aware of things requires at the very least, acknowledgment of some substance behind that capacity—if we can think of objects, life-forms, the mind, or anything, we must ultimately submit to the idea that something makes that process happen.

However, whether it is through perception or blind faith, a seemingly obvious idea of something alone cannot be used to justify its ultimate certainty unless both its logic and external reality prove inescapable. Popular associations and beliefs have been rationalized and used for centuries to try to prove the existence of God, as well other ephemeral concepts like ethical and aesthetic principles, base substances, and non-empirical worlds.^[1]

Such ideas on the surface may seem no different than a concept like knowledge, but there are some crucial differences. Unlike God or other essences, if existence is an inescapable or axiomatic concept (as was hopefully just demonstrated), then to know this automatically, reciprocally, indicates a concept or “knowledge” was involved. So if we know existence is a self-proven concept, then we know the “self-proven” and some kind of “knowledge” should also exist, whereas with other ideas we cannot make these same direct assumptions.

Though similar, this deduction is not the same as Descartes’s proclamation, “I think, therefore I am.”^[2] Rather, it is first posited that existence exists (not that “I” am or “think”), and in knowing this axiom, both self-proof and the conceptualization must also be inescapable. This does not mean that existence, self-proof and/or knowledge have to be conceptualized to be real. However, because existence is all-pervading, and knowledge is needed to know any existent, knowledge at least carries with it some active self-proof. Just as some notion of existence must predicate all things, some kind of knowledge, at the very least, must be a given for any act of “knowing.”

But for knowledge to fulfill all our qualifications to be an axiomatic concept, it needs some kind of infinite presence, some basic or never-ending link to the external world beyond

any mind, or even any action.^[3] Existence is axiomatic in part because it makes no necessary discernment between the mind and what may lie outside of it. As explored in footnote 18, on a basic level, it doesn’t matter if everything is a mental construct or if the mind exists at all, because everything has the common quality of existence. Knowledge may be mentally or even actively self-proven (if abstracted to envelop all our actions [of awareness or otherwise]), yet if there is no way to really discern the mental from the physical (or an action from its object) though our axiomatic definition of existence anyway, then why should we prejudge knowledge as only “mental” either? We know knowledge must somehow differ from existence, or it would become the same concept, but we have not yet explored what knowledge could include or be, thus we should not preset its limitations. So in some way knowledge is just self-proven to us—in other words, something, whatever it is, allows us to be and/or act. The remainder of this section attempts to understand more specifically how this something should be defined, how knowledge needs to be understood to become an all-encompassing idea.

Common ideas of knowledge usually to tie it with awareness/consciousness, truth, language, or more narrowly, simply brain functions. However, even beyond theories of mind, many scientific discoveries, e.g. in gene sequencing, brain mapping and animal intelligence,^[4] have led us to consider wider definitions for knowledge. For example biologically, knowledge could be any/all that composes life-forms, from DNA to neurons to conceptual structures.

Still, if knowledge is to be considered an axiomatic concept, philosophic problems arise with a definition that applies only to DNA and living things, or even broader scientific ideas. As suggested before, a concept only can be axiomatically purposeful if it defines a universal, inescapable condition of both the mind and outside world. The same philosophic difficulty arises in “life” being a defining qualification for knowledge, as if “universe” were substituted for “any/everything” in the definition of existence. “Life” and “universe” are scientific concepts with composite associations such as “carbon compounds” or “stellar space.” Scientific concepts do not rest on their own self-logic; instead, they depend primarily on external observations and measurements. Ultimately, because scientific method involves studying things by limiting their variables, experimental proof can never be fully inclusive.^[5]

For example, doesn’t a corpse contain knowledge, with its reusable organs, post-sequential reflexes or signature biology? How about the “inanimate” DNA composing our biologies? Couldn’t some “non-biological” extra-terrestrial, new element, invention or anomaly—one that may alter our ideas of life and the universe—possess knowledge? What about the words on this page? If they hold no knowledge, then how is any meaning reaching your brain? Yes, knowledge seems to encompass a wider framework than it is normally granted, and it needs a much wider one to fully perform its axiomatic duties.

Because biologically speaking, many would include the non-living DNA composing life-forms as knowledge, then why not stretch this physical idea to any active quality that makes-up things, like some universal “life-force.” Perhaps knowledge manifests in space-time as wave-cycles not that unlike RNA/DNA helix structures, being able to stretch, bend and/or shift into different patterns of motion, binding together any/all forms and processes. Any motion “recorded” in the fabric of space-time, whether or not it is living, could construct and channel at least all physical events, similar to how DNA programs our bodies and brains.^[6] This idea of knowledge as physical information^[7] is already alive today in fields such as theoretical physics and data systems analysis. Physical information in such contexts may be generally defined as any material record and/or “data capacity” of matter-energy in space-time.

Such an idea abstracted further, could support an axiomatic definition of knowledge as “the way things have been, are, and/or will be”… slightly different than the concept existence in that knowledge would be any or all actualizations of things. So knowledge wouldn’t be any or all possible things at any or all possible times, but only the way things actually express, have expressed, or will express themselves, whatever context that may be. Knowledge as some infinite physical expression, or eternal propagation of information, could frame it as a fundamental active quality within all things, whether inside or outside the mind.^[8]

[1]. This argument is similar to ontological arguments, used by philosophers like Anselm, Leibniz and Kant (to greater and lesser extents). As summarized in Magee’s Story of Philosophy, 57, an ontological argument purports that ‘perfect’ or ‘ultimate’ thoughts or beliefs (like God, Truth, or even our axiomatic concepts) must have external reality, because some most ideal state must exist, because even if our thoughts do not accurately depict this, there would still be something existing outside our conceptions to allow for the best of all possible worlds. However, I think ontological arguments on their own, with no other logic or proof, often reverse cause and effect, where many very abstract, metaphysical ideas can quickly become ‘perfect,’ a priori premises. One example would be the “perfection” often seen in mathematics, or numerology. This can lead to favoring ‘unprovable’ presuppositions versus delving into more cogent logical and/or scientific ideas.

[2]. St. Augustine could have first (informally) uncovered a kind of axiomatic nature in awareness (as consciousness) as is discussed in Rand’s, Introduction to Objectivist Epistemology, 262-263, precluding this famous claim by Descartes.

[3]. It is important not to think a concept axiomatic just because it is inescapable from one’s mind or being. For example, ideas like ‘humanity,’ (stripped of its ethical associations) may be inescapable because we are human, but the idea is far from axiomatic because not all things are human. So an axiomatic concept needs not only internal, logical consistency and certainty, but also some way it can exist outside of ourselves and still permeate things in some infinite way, so that the idea is really inescapable. This is what would give epistemology its metaphysical power.

[4]. Studies on many animals such as elephants, parrots, and primates, have proven not only more computational and language intelligence than previously acknowledged, but also much more self-awareness, creativity, long-term planning, and intra/inter-species empathy (Murchie, The Seven Mysteries of Life, 283-287). Combined with relatively recent biological insights and innovations (e.g. as seen in medical technologies and genetic engineering), these scientific studies have revealed both how limited and non-physical our conceptions of knowledge have been.

[5]. This seems to be due to both mental and physical constraints. Purely physical support for this idea comes from the Heisenberg Uncertainty Principle. It in effect surmises that the exact position and momentum for anything never can be simultaneously pinpointed—the more precise one measurement, the more potential for inaccuracy with the other (Rohmann, World of Ideas, 412-413). Yet also, because there is always some lag time between an occurrence and its observation, there should always be some natural deviation between an object and its perception. The moment we know precisely where and when one thing has occurred, that thing (as well as other things outside one’s empirical field) would have already changed to some degree.

[6]. This wider conception of knowledge may be implicated by our growing understanding of life’s material origins. The physical nuances of atomic substructures and ‘self-regulated’ entities are being increasingly delineated through fine-tuned experiments. Of biological note as documented in Oparin, Genesis and Evolutionary Development of Life, 76-77, amino acids (the building blocks of proteins [which are seen as the building blocks of life]) have been produced from electrically charged elemental gases as early as the 1953 Miller experiment. Gill reports in “‘Artificial life’ breakthrough announced by scientists,” that half a century later in 2003, the first artificial virus was constructed, and in 2010, scientists from the J. Craig Venter Institute planted a completely synthesized DNA sequence (a genome) inside a “blank” cell that then successfully self-replicated.

The quasi-living status of viruses and what separates mere organic substances from intelligent ones still contentious in the fight over what life is. How exactly to define the ‘inanimate’ in contrast to ‘life’ is still unclear, often fuelling a wider debate about ‘self-regulation’—a capacity that could be stretched to apply to all natural, cyclic processes. Considering knowledge as this broader kind of self-regulation could unify all things within one ‘life-like’ continuum of information, helping us better understand and harness all self-regulative processes.

[7]. Generalizing from the Wikipedia article, “Physical Information,” physical information could refer to any or all defining properties contained within a material system. In Barrow’s Constants of Nature, 169-172, he abstracts information into a possible broad-based “memory,” connecting “thinking,” or “information processing” into some wider physical context. These ideas do stretch the limitations of both the physical world and knowledge as we commonly conceive them, but into substantive concepts that are not implausible.

[8]. The reason I do not use ‘information’ in place of knowledge as a more ‘objective’ axiomatic concept is because I think knowledge has better association with an active quality in all things, combining the animated quality of life or awareness with the physical nature of all reality. ‘Action’ also is not a good axiomatic term because it cannot be self-proven deductively. Knowledge more directly associates us with our own minds, all its thoughts and processes, and this is how it functions axiomatically within us. The fact that we attribute knowledge mainly or only to life forms is, I think, unnecessarily limiting. If we rethink the idea of knowledge as an infinite context, it can help us understand more deeply the active processes steering evolution within all things.

[eva matthews]

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

[eva matthews]

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

[BaalChatzaf]

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

Objects possess many properties. How does one say that a particular property is -the- distinguishing property except as an arbitrary designation of that property as essential or distinguishing?

[eva matthews]

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

[tmj]

in #184 Eva said

"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...."

But doesn't Rand's explanation of epistemology also help to identify the 'mechanism' behind 'meaning'? To say a concept is the meaning , says nothing of how the meaning is understood.

[eva matthews]

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

[BaalChatzaf]

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

Very few things are "answered" by simple aggregation of facts. The truth is, just about everything we do are think is -theory laden-. Here is a humble example. I am building a book case and I need shelves 3 feet long an one foot wide. So I take my trust ruler over to a plank and start marking the cut line. But soft!!!! Where is the theory loaded into the simple act of measurement?

It is the assumption that carrying my ruler from hither to yon and not accelerating it greatly in the process will not distort its length. In short I assume my measuring stick is -rigid-. But that is an assumption. I have no way of proving my ruler does not distort when carried. If I try measuring my ruler with another ruler and that ruler has been carried I have raised the same issue with the ruler that measure the ruler. And if I keep attempting to show my first rule is rigid I run into a regress.

So I can't even measure a piece of wood in a manner that is not theory laden.

Ba'al Chatzaf

[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

[Michael Stuart Kelly]

For the record, I think Daniel Kahneman's cool.

He's got some lousy-ass friends, though. I like what I've read by him until he starts talking about some of them. (I only went through Thinking Fast and Slow once so far--that one deserves at least three reads, and I've seen a bunch of lectures and panels by him on YouTube).

He plays footsies with government control-freaks. That's a terrible habit, but it keeps him in goodies, I suppose. He sure looks goofy as a toady. Hell, no accounting for taste.

The name Stadler keeps echoing in my mind... Stadler... Stadler... Stadler...

Michael

[eva matthews]

For the record, I think Daniel Kahneman's cool.

He's got some lousy-ass friends, though. I like what I've read by him until he starts talking about some of them. (I only went through Thinking Fast and Slow once so far--that one deserves at least three reads, and I've seen a bunch of lectures and panels by him on YouTube).

He plays footsies with government control-freaks. That's a terrible habit, but it keeps him in goodies, I suppose. He sure looks goofy as a toady. Hell, no accounting for taste.

The name Stadler keeps echoing in my mind... Stadler... Stadler... Stadler...

Michael

Yeah, he's a real gov-grant parasite. Hopefully, I can follow in his footsteps.

[Michael Stuart Kelly]

Yeah, he's a real gov-grant parasite. Hopefully, I can follow in his footsteps.

Eva,

You have my blessing if that's what your little heart desires.

I don't think they formally teach sucking skills at college, but my suggestion is to bone up on those.

The competition among suck-ups is terrible in the government if you want to go far.

If all you want is a nice comfy job somewhere, living off the fat of the land and letting others pay for it, so to speak, moderate sucking skills are all you need. Once you're dug in, just keep a low profile and kiss the asses of those that need periodic kissing, which is not all that often.

Nice future to spend your life if you can get it.

Michael

[anthony]

Hey Bob, good one! But a carpenter you'll never make. Simple certainty is what's needed, like my mechanic who's advice when measuring a pipe to fit is "Remember, you can cut it off but you can't cut it on again."

[Jules Troy]

Yeah, he's a real gov-grant parasite. Hopefully, I can follow in his footsteps.

Eva,

You have my blessing if that's what your little heart desires.

I don't think they formally teach sucking skills at college, but my suggestion is to bone up on those.

The competition among suck-ups is terrible in the government if you want to go far.

If all you want is a nice comfy job somewhere, living off the fat of the land and letting others pay for it, so to speak, moderate sucking skills are all you need. Once you're dug in, just keep a low profile and kiss the asses of those that need periodic kissing, which is not all that often.

Nice future to spend your life if you can get it.

Michael

[Jules Troy]

Oh man... I for once am at a loss for words so I'm just going to um...

L O L !!

[eva matthews]

Yeah, he's a real gov-grant parasite. Hopefully, I can follow in his footsteps.

Eva,

You have my blessing if that's what your little heart desires.

I don't think they formally teach sucking skills at college, but my suggestion is to bone up on those.

The competition among suck-ups is terrible in the government if you want to go far.

If all you want is a nice comfy job somewhere, living off the fat of the land and letting others pay for it, so to speak, moderate sucking skills are all you need. Once you're dug in, just keep a low profile and kiss the asses of those that need periodic kissing, which is not all that often.

Nice future to spend your life if you can get it.

Michael

Actually, my project hardly involves sucking up top anyone. It's a multi-dimensional analysis of learning and emotions..

My learning model more or less tweaks Kahneman in two dimensions of performance.

The emotive model has n dimensions (Hilbert) because present-day neurosci doesn't support a definitive a,b,c...state response strictly in terms of the measure of brain waves from the thalmic system. Phenomenal states of the sort employed by, say, Branden, are not used.

The grant package --most from private sources!-- awaits upon my graduation with a BS this June. Parts will go to MS and PhD per contract with said donors.

As for this being 'nice & comfy' would depend entirely on one's notion of what really happens on campus. Mine is that grad students compete far more viciously with each other than athletes. At least they do to get momndad's attention, as both are tenured profs here, in psych and math/physics

That's why i prefer to do my own work, then mail in the results for the degree.

Eva

[Michael Stuart Kelly]

Eva,

I've been told I am a smartass at times.

But this is a serious lifestyle decision and the consequences can be brutal, depending on the type of person you are.

I used to have a government job. I played trombone for the São Paulo State Symphony Orchestra and conduct there at times. I tried to filter out all the ask-kissing, sucking up, etc., I saw around me and just concentrate on the music. I was good and Americans were inherently privileged in the orchestra, so I didn't have to participate in it other than remain cordial to lousy people at times.

But I couldn't get it out of my head, especially when the music went poorly and I could trace the problem directly to an incompetent person who was politically connected. Or when we had more people on stage than in the audience at a concert, which happened only a few time, thank goodness. There were other problems not worth detailing. (We also performed some very good concerts for packed houses, so it was not all bad.)

After around 10 years of doing this, I caught myself walking the streets of São Paulo, alone at night, hours at a time, totally miserable, looking at taxi drivers, people working in snack bars, stores, gas stations, and asking myself if these people even knew what a symphony orchestra was. Yet they were paying my salary.

I couldn't stop thinking that. I couldn't make it work in my mind. And God knows I tried.

I kept spiraling down.

This is not the only reason I degenerated into alcoholism, but it was a big one. The guilt was eating me alive. I finally walked out. It was hard after that, and I still had a lot of fucking up to do in life, but walking away from government employment was one of few decisions I feel pride in from those days.

The life of a parasite (even a productive one) includes ask-kissing and sucking up. That's not a sneering putdown. It's reality. It's inherent to the lifestyle. Some people thrive that way.

I couldn't.

I'm not on a holier-than-thou kick in saying that, either. God knows I've done some shit that most civil servants would call despicable--and be right.

But government money is not an illness I will die of.

Confucius say: A wise parasite knows where to suck.

Michael

EDIT: Oops... I don't mean to imply I'm a parasite. I made different bad choices in life, and some good ones. But dayaamm! Gonna have to work on those writing skills if I want to get it right at being a smartass.

[eva matthews]

Michael,

Thanks for the kind post.

Actually, I'm a very practical libertarian who believes that the way to have a much smaller government is to deny it revenue. That means drastically lowering taxes.

Your story does drive home a cogernt point, of which i'm only partially aware. Sucking up works to the extent that the one sucked up to has no other basis for making a decision other than the receipt of flattery.

Classically speaking, we do attribute this to government, But last year's search for privite donors (my decision!) turned up some interesting types who did, indeed, demand not 'just' flattery! Moreover, many of the petitioned insisted that I offer a detailed practical application for 'their' company. in other words, I had a terribly hard time explaning that my work was only 'theoretical'!

Momma, who accompanied me on most of these excursions--and no sucker-upper herself!-- did suggest that i quit pulling a "Cordelia", (Lear's 'good' daughter), and be nicer, less detached, and far less cut n dried.

Well, anyway, it's all there. I'm good for the next ten years, or so. I've been warned, however, that the donors will continue to nag, and inform me that more donations will be based upon their liking of my 'progress'.

You and everyone else says that government granting is far worse, and i believe you. Yetch!

Eva

[deanwins]

Actually, I'm a very practical libertarian who believes that the way to have a much smaller government is to deny it revenue. That means drastically lowering taxes.

For those not following RoR, might I assist you in suggesting that Eva's definition of "Libertarian" is probably not consistent with yours. Furthermore, reading the above, you might get the impression that Eva wants a smaller government. But that is not what Eva is saying... its lawyer/politician speak: stating a fact, but not necessarily desiring that fact, but pandering the implication. Eva will repeat this whenever conversation becomes so antagonistic that you want to stop talking with "her" in order to placate you and give you hope. Ask Eva which parts of government she'd like to see reduced in funding...