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Tuesday, February 14, 2006 - 10:36amSanction this postReply
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I would like to share a question from a philosophy professor that I received privately concerning this article. The inquirer asks:

“So, then, some magnitude—or quantity of extension—characterizes every existent, no? So the thought that today is a nice day is quantifiable, given that the thought is an existent?”

 

As I wrote in “Universals and Measurement,” I suppose that every concrete stands in measurable relations to other concretes. I supposed also that

“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.” (JARS 5(2), p. 276)

 

Which type is appropriate is not up to us, but is fundamentally tuned to the kind of magnitude structure being measured. There is an inclusive hierarchy of types and structures. The types of (one-dimensional) measurement are these: absolute, ordinal, hyperordinal, interval, and ratio. In “Universals and Measurement” I discussed the different magnitude structures to which some of these measurement types are appropriate. I discussed also the levels in multidimensional measurement types and their magnitude structures (geometry).

 

Most concept classes are multidimensional. An example would be the class animal (metazoan). To get the dimensions, we begin with the definition. A general-purpose definition of animal would be: a multicellular living being capable of nervous sensation and muscular locomotion. Surely the mathematically determinate form of the concept class animal is multidimensional (cf. Rand in IOE, 16, 24–25, 42).

 

I don’t know a good definition of thought that is well-agreed upon and not quickly circular. Perhaps a reader will help us out with a good definition. I imaging it will need to work upward from some definitions of perception, categorical perception, schematization, conceptualization, and predication.

 

The thought that today is a nice day occurs in a region of space, and for many aspects of that space and many aspects of the neurological processes necessary for the thought, it is the case that the measurement type appropriate to the magnitude is ratio-scale. But for other aspects of that space and those processes, ratio-scale is not appropriate. Scales with lesser structure are appropriate to these still perfectly physical aspects, because that is their magnitude character, not because we don’t know how to measure them with ratio scale. (My authority, I should perhaps say, is the 3-volume work Foundations of Measurement by P. Suppes et al. and the related work in the journals.)

 

The type of measurement appropriate to a thought is unknown to me (and perhaps to anyone so far), but I would bet a coke that it is not ratio-scale (nor an n-dimensional Euclidean space). I stress that, gentle Professor, because of your use of the word extension. That rings of what is called extensive measurement, which is a sub-class of ratio-scale measurement.

 

In addition to that Q&A, I should correct an error in the RoR article. I botched the third line of the illustrations of hierarchies of structure in geometry. The inclusive hierarchical dependencies would be more obvious if I broke apart each of those three lines into their two wings, which are independent anyway. Here, this is better, and it contains all the information of the three lines in the article:

{[(Ordered) Affine] Euclidean}

{[(Ordered) Absolute] Euclidean}

{[(Ordered) Absolute] Hyperbolic}

{[(Projective) Affine] Euclidean}

[(Projective) Elliptic]





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Sunday, December 16, 2007 - 5:55amSanction this postReply
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The first work in this program was my essay “Universals and Measurement.”

It was published in The Journal of Ayn Rand Studies in 2004.
It has now become freely available online, in six segments:

 

Universals and Measurement

              Stephen Boydstun

First

I. Orientation

Second

II. Analysis

     Affordance of Ratio or Interval Measures

Third

II. Analysis (cont.)

     Affordance of Ordinal Measures

     Superordinates and Similarity Classes

     Amended Measure-Definitions of Similarity and Concepts

     Conclusion of Core Task

Fourth

III. Genesis

       Elaboration of Identity

       First Words, First Universals

       Analytic Constraint

Fifth

Notes

Sixth

References




Post 2

Wednesday, July 9, 2008 - 3:53amSanction this postReply
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Nice. Metaphysicis that stays crunchy in milk.



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Wednesday, July 9, 2008 - 5:47amSanction this postReply
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Usually I try not to make replies when I get completely lost reading the post I'm replying to... like a post on advanced physics or math for example.  My eyes glaze over - I realize the amount of work I'd have to do raise my understanding to the level need to continue, I decide it just isn't my area, and I move on.

But this sentence grabbed me: "So the thought that today is a nice day is quantifiable, given that the thought is an existent?”


I knew that I'm was getting lost on the "quantifiable" part - particularly when I saw these forms of notation at the bottom of the post:

{[(Ordered) Affine] Euclidean}

{[(Ordered) Absolute] Euclidean}

{[(Ordered) Absolute] Hyperbolic}

{[(Projective) Affine] Euclidean}

[(Projective) Elliptic]

I should have just moved on till I could find an area that didn't glaze my eyes, But... I started thinking and became interested.

 

Given that the best way to view a "thought" may be as a process, an action, does that change things?

 

I started thinking about it from the view point of grammar (which is about the rules for getting our words to best represent our thoughts).

 

The simplest of complete thoughts, just like the simplest of sentences in grammar, requires a subject and a predicate asserting an action, property or state of being about the subject.  So we have three primary concepts: "Today," "is," and "day." 

 

Then there are some modifiers to the concept of "day."   The first, "a," is identifying that we are talking about a single member of a class of entities (a dog, a day, a concept - one of a possible many and not a concrete that has been identified) and the more important modifier (in the context of this sentence/thought), "nice," is the property type of modifier of the class name.  Because it takes "day" as its antecedent, and because "a" says "day" is a member of a class, then we know that the part of the predicate (separate from the verb) means " a member of the class of 'day' with the property known as 'nice.'   We get to imply that "day" may have other categories, and that 'nice' is but one of the conditions that would work in the chosen category.  But we probably care about those implications, instead we have some purpose.

 

The verb, "is" establishes the relationship between the subject and the rest of the predicate.  With "is" telling us that this is an assertion of a kind of equality - Say for example I had reworded it to make the non-verb portion of the predicate into an appositive ("Today, a nice day, was my first time in Denver).  In that case the "Today" and "a nice day" both function as nouns - the equality is that they are refering to the same existent but with different measurements.  "Today" being the identifier of the particular day of all possible days, and "a nice day" being the condition, needing only the implied context of my time and location of the thought, say, about noon on July 9th, 2008 in my location)

 

The process then, of this thought, is that of identification of the specific category of 'day' that we wish to make for some purpose not clear in that sentence.  There are two levels of purpose in this thought: How we construct it, and the other being what is the purpose of having the throught?  We have chosen the category which contains, among other conditions, the one called "nice."  Again with the use of appositives I'll illustrate what I mean by saying that our purpose (context) is undetermined in the sample sentence, by creating another sentence where the context gives the purpose: "Today, a nice day, a good day for our picnic, energized me as I drove home."

 

I like that every subordinate clause, every modifier, every object, every phrase is identifying properties of the subject or properties about the assertion - an act of identifying and joining - and a rich thought can tell us purpose, time, location, emotional context, etc.  Are we quantifying the process of the joining these elements till they reache completion as a thought?

 

sigh... I look up in my post and see those {[(Ordered) Affine] Euclidean} thingies and figure I may be spewing forth foolishly so I'll stop and maybe someone with an excess of spare time will put me out of my misery by telling what fills the enormous gap between what I've been writing in my grammar-like description and what everyone else is writing about.




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Wednesday, July 9, 2008 - 8:30amSanction this postReply
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 maybe someone with an excess of spare time will put me out of my misery by telling what fills the enormous gap between what I've been writing in my grammar-like description and what everyone else is writing about.


to me, it is clarity - yours' is, theirs' aint....;-)




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Thursday, July 10, 2008 - 7:52amSanction this postReply
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Thanks, Ted.

 

Steve Wolfer, thank you for the thoughtful post.

 

To find a measure-theoretic account of predication right for my Randian measure-theoretic account of concepts (analysis, not genesis) is part of my ongoing research program.

 

My triple-identity view of predication, which is now being cast in appropriate measurement terms, can be found in §10 Existence Is Identity (scroll down to p. 43) of “Induction on Identity” (1991). I no longer draw the distinction between particular and specific identity in entirely the same way as I did in that early essay. (The distinction was my own, but it has been also landed upon by philosopher John Campbell.) The basic simple distinction remains and is as I stated it in Note 34 of “Universals and Measurement.”

 
For the journey from logical quantification in predicate logic to numerically definite quantification (which is still purely logical quantification) to sets to arithmetic (which adds to logic and is the arena of absolute measurement [see Note 13 of U&M], not to be confused with absolute geometry), I recommend Quine’s Methods of Logic. For the journey from logic and set theory to measurement theory, one-dimensional and multidimensional, I recommend Foundations of Measurement by Krantz, Luce, Suppes, and Tversky.
 

On translation of sentences into logical formulas, one good text with exercises is R. L. Simpson’s Essentials of Symbolic Logic. Some advanced contemporary controversies are treated in Logical Form and Language, G. Preyer and G. Peter, editors.

 

I should mention for a general audience that there are no mathematical formulas that cannot be translated into a natural language such as English. That is something that needs frequent mention. Similarly, the epigrammatic strings I improvised above concerning geometry are nothing but abbreviations of English statements. One true rendering of the string {[(Ordered)Affine]Euclidean} would be “Axioms that imply ordered geometry can be joined with certain further axioms to imply affine geometry, and those combined axioms can be joined with certain further axioms to imply Euclidean geometry.” Another true rendering would be “A Euclidean plane (or space) is composed of affine structure and specific additional structure, and the affine structure is composed of order structure and specific additional structure.”

(Edited by Stephen Boydstun on 7/10, 3:04pm)




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Wednesday, October 8, 2008 - 8:19amSanction this postReply
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Under the area Causality and Natural Law, mentioned above in “The ‘With-Measurement’ Program,”

a new help is coming in January.

 

2009

The Law-Governed Universe

John T. Roberts

 

 

Earlier relevant works:

 

2004

Laws in Nature

Stephen Mumford

 

2000

Natural Laws in Scientific Practice

Marc Lang

 

1999

Science without Laws

Ronald N. Giere

 

1999

A Dappled World

Nancy Cartwright

 

1983

How the Laws of Physics Lie

Nancy Cartwright

 

1983

What Is a Law of Nature?

D. M. Armstrong

(Edited by Stephen Boydstun on 10/08, 8:22am)




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Wednesday, October 8, 2008 - 1:14pmSanction this postReply
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re - the laws governing the universe - isnt it essentially the one and the same to say they govern as to say they describe? isnt  it actually using two different ways of saying the cause/effrect relationship?



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Wednesday, October 8, 2008 - 2:14pmSanction this postReply
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Robert is very uncomfortable with the 'G' word :-)





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Wednesday, October 8, 2008 - 3:18pmSanction this postReply
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Steve,

Thanks for reminding us (me, anyhow) that we can go a little further on a subject than we might otherwise credit ourselves, if we are willing to exercise some patience and make the effort.

jt



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Wednesday, October 8, 2008 - 5:55pmSanction this postReply
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Stephen,

On page 44 in the section on Existence is Identity, I found myself wondering about your assertion that the statement, "Spot is brown and white," would, as a true proposition, affirm all three of the relations you mentioned.

First you made the distinction between "a dog" and "Spot" - pointing out that "a dog" is a 'particular' identification, and that "Spot" is a 'specific' identification.

Thus, when one says that "Spot is a dog" one has affirmed the specific identity "Spot" as being "a dog" - a particular identity. It is the fact of this proposition that made me curious. Without that proposition, we don't know what Spot is.

For example, "Spot, my cat, is brown and white."

So, about the proposition that "Spot is brown and white:" We have a proper noun, "Spot," and we predicate the condition of being "brown and white" as a property of being "Spot" - at least at that instance of time. But knowing that "Spot" is a dog, and not a cat, might be outside of that proposition.

One person could say, "The definition of 'Spot' contain his particular nature as a dog, and therefore we don't need to have that proposition, spot is a dog. That is how the particular identity is contained in the brown and white proposition." Someone else could say, "We might need the proposition Spot is a dog to ensure that we communicate the proper concept (particular and specific identity) to our audience and that being true, it is clear that the particular identity may or may not be contained in the proposition, Spot is brown and white."




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Thursday, October 9, 2008 - 12:56amSanction this postReply
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Steve Wolfer,

 

The essay to which you refer, and the theory of predication begun in it, was written in 1991. I did not have the “with-measurement” program until many years later. I have since begun casting that theory in measurement terms, but that is in progress and nothing of it is yet published.

 
You have my usage of particular and specific reversed, but your substantive points make sense all the same. I’ll need to be thinking about them as I develop the theory of predication further. Thanks.



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Thursday, October 9, 2008 - 1:40amSanction this postReply
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Robert Malcom,

 

Yes, the laws are descriptions, and the interest is in capturing the difference between laws and other scientific descriptive statements.

 

One Glance

 

Entries in Obj Index

 

Nozick Intro (pp. 33–34)

 

Stanford Survey




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Thursday, October 9, 2008 - 3:42amSanction this postReply
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I suggest that random, like chaos, is a misnomer - namely that all that is expressed is a present ignorance of cosmotic relating, that complexity as such is a multilayeredness, and more of 'the onion' needs be removed...



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Thursday, October 9, 2008 - 6:01amSanction this postReply
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Robert,

 

Remember that chaotic regimes obtain even in some simple systems, such as a damped pendulum undergoing forced oscillations. These regimes are to be expected by the mathematical equations representing these dynamical systems, and the chaotic regimes are found in physical systems where the mathematics says they should be found.

 

Definitions of randomness are in Objectivity in these essays:

 

“On Probability” (V2N1, pp. 23–26)

 

“Chaos” (V2N1, pp. 35–36)

 

“Volitional Synapses” (V2N4, pp. 187–88)

 

The contrast class for randomness (as used in science and mathematics) is the algorithmic. The contrast class for chaos (in the scientific sense) is the regular, and this division cuts through both classical and quantum regimes.




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Thursday, October 9, 2008 - 8:22amSanction this postReply
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Stephen,
Thanks for the information about John T. Roberts' new book The Law-Governed Universe.  I'm looking forward to it.

As you know, Stephen Mumford, in his book Laws in Nature, reaches the conclusion that there are no laws in nature.  That is, laws don't govern how entities act.  The actions of entities are determined by the dispositions or powers possessed by the entities themselves.  Laws are not something added to passive objects.  I think this is more in line with the Objectivist view of what laws of nature are.

Thanks,
Glenn





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Thursday, October 9, 2008 - 11:23amSanction this postReply
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Glenn,

Right. A physical law, according to Objectivism, is simply a generalization about how things behave under certain conditions. The law of identity, the most universal of all natural laws, says that they behave according to their nature -- that just as a thing has a specific nature, so it will act in specific ways under specific conditions. The view that a "law" exists apart from the things it governs confuses man-made laws with natural laws.

- Bill



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Friday, October 31, 2008 - 7:12amSanction this postReply
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Glenn and Bill,

 

I hope to be able to discuss with you soon the character of scientific laws of nature. Meanwhile, I thought you might like to know of this work, a paper delivered at

History of Philosophy of Science 2008

 

“On Laws of Nature in Aristotle”

  Tiberiu Popa (Butler University)

 

ABSTRACT

Aristotle’s handling of what we would call laws of nature is rarely tackled directly and by contemporary scholars. In this paper I draw on relevant passages in Parts of Animals II, Generation of Animals V and especially Meteorology IV in order to give prominence to the defining aspects of Aristotle’s approach to the laws of nature.

 

The notion of natural law in Aristotle’s works may not be articulated in theoretical terms as neatly as it will be in later authors, but its importance in his “chemistry” and in some sections of his biological corpus is quite remarkable. Conditional accounts often take the following form: if a uniform body consists of certain ingredients (present in it dunamei) in a particular proportion and if the right external conditions obtain (e.g. if sufficient – dry or moist – heat is applied to it), then a certain property will emerge, or (if already existent) it will be manifested. Conversely, Aristotle will also use conditionals to show that, if a body exhibits a certain behavior, under specific conditions (e.g. when affected by heat or cold in such and such a way), then it is bound to have this or that composition.

 

A conditional analysis of properties and processes does not have to be, for Aristotle in any case, an elegant strategy for doing away with dispositions. Conditional analyses can be used in principle to weaken the status of dispositions; in assuming that ‘if factors X1, X2… obtain, then result Y will be produced’, one can bypass the ascription of dispositions to a certain thing. Such a conditional account can be taken simply to (causally) link a set of categorical factors to an actual event. Aristotle, I believe, shuns this temptation.

 

In this context one might wonder how the laws of nature can conceivably hold in the realm of “for the most part.” Granted that phenomena in the sublunary sphere occur with less regularity than in the outer spheres and among the celestial bodies, necessity and “for the most part” are not exactly mutually exclusive concepts: if/when the right conditions are in place, a particular effect will be produced of necessity. It is just that those conditions for the emergence and then for the manifestation of a certain disposition are not present with unfailing regularity and sheer predictability.

 

My study of the place of laws of nature in Aristotle’s applied science aims to contribute to a fuller understanding of his effort to find order, based on causal connections, in what might otherwise look like a variegated slew of phenomena. Aristotle’s treatment of laws of nature is closer to what we might call dispositionalism than to actualism, to use a deliberate anachronism. In other words, Aristotle did not take laws of nature to be just summary descriptions of strictly actual events (an idea that the Megarians would have found perhaps palatable, just as the positivists would have found it so in more recent times); rather, he used law-like formulations to ascribe dispositions to things (especially organic and inorganic uniform materials) in the sublunary sphere.  


(Edited by Stephen Boydstun on 10/31, 8:30am)




Post 18

Friday, October 31, 2008 - 9:05pmSanction this postReply
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I read an essay once which talked about Newton or Newtonian thought or dynamics. I forget by who, or where it was found (but it was online, I remember). Unfortunately, I've forgotten more titles of valuable essays than many folks will ever read. That doesn't make me particularly smart, just well read.

Anyway, the essay explained that you can think of gravity as if it were pulling from the center of mass of one object on the center of mass of the other -- even though every cubic inch of the mass of one object is pulling on every cubic inch of the other. The old and unrefined science of Newton was never meaningfully overturned.

You could think like Newton did about the world of macro-objects, without sacrificing any success in the world. What this says to me is that knowledge of randomness and chaos -- whether realities or not -- aren't needed for success in the world. That's one issue I have; that invoking randomness and chaos may only help with a mathematical outline of reality.

That would make randomness and chaos, like imaginery numbers, helpful in our computation of reality -- but ultimately nonexistent themselves. That would make them useful fictions epistemologically, but absent of any metaphysical or ontological basis.

Ed




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Wednesday, April 1, 2009 - 6:15amSanction this postReply
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New work on causation and laws of nature is here:

Dispositions and Causes
Toby Handfield, editor
Oxford 2009

The publisher writes that causal relations and dispositional properties
“appear to be intimately related to counterfactual conditionals and other modal phenomena such as objective chance, but little work has been done to directly relate them. Dispositions and Causes contains ten essays by scholars working in both metaphysics and in philosophy of science, examining the relation between dispositional and causal concepts.

“Particular issues discussed include the possibility of reducing dispositions to causes, and vice versa; the possibility of a nominalist theory of causal powers; the attempt to reduce all metaphysical necessity to dispositional properties; the relationship between dispositions, causes, and laws of nature; the role of causal capacities in explaining the success of scientific inquiry; the grounding of dispositions and causes in objective chances; and the type of causal power required for free agency.

“The introductory chapter contains a detailed overview of recent work in the area, providing a helpful entry to the literature for non-specialists.”

Rand makes some informal remarks concerning dispositions and causality in exchanges with Professors Walsh, Peikoff, and Gotthelf on pages 282–88 of ITOE.





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