Monday, June 23, 2014

Changed my Subtitle; First Response to Casey

I recently changed my blog subtitle to better reflect the topics and direction of my blog. The basic theme of this blog is that property (and for that matter ethics) is important to the epistemology of economics and finance mainly due to property being what provides economics and finance with analytic structure. In other words, property, as well as the economic concept of subjective value, are ordinal numbers, also called ordinal sets. I believe some of the approaches by philosophers of economics to topics regarding the geometrical patterns/relationships of supply and demand curves and the economic laws (syllogisms) have been misled in dismissing the geometrical patterns being foundational in themselves or the laws lacking scope.  They overlook that ordinals inherently have compositional and mathematical qualities and are what provide truth preserving characteristics of supply and demand curves and economic laws.

This leads to the topic that I've been attempting to write about, that is the problem from Gerard Casey that I've mentioned before.  Casey asked what are the limits of property? [my language: Casey uses the metaphor of drawing a line for limits.]. 'Limits' is an ordinal concept, which I can say uncontroversially since Bertrand Russell said it too. Casey points out that property has limits that are vague and have continuum problems. However, Casey's problem is solved through the use of infinitesimals. We do not just understand property as a ordinal set, but as a cardinal set also.  Cardinality is evident whenever we mark off the boundaries of a property.  We use measurement, natural and unnatural barriers, GPS, legal codes, contracts, standardized lots, etc... In other words, there are cardinal relationships involved in property when it is situated within a society. The relationship of cardinals and ordinals is controversial in the philosophy of mathematics. Axiomatic set theory builds cardinals on top of ordinals, but Michael Potter, in Set Theory and Its Philosophy: A Critical Introduction (best current work on the subject that I'm aware), used an overlapping theory. Intuitively, cardinals seem to be build onto ordinals because ordinals lack qualities of cardinals (same-size), yet cardinals have qualities of ordinals, i.e. order.

Casey's continuum problems seems to trace back to Walter Block. I happen to be an UWBF (Ultimate Walter Block Fan), but I have found that Block is misled on his attack on cardinals and supply & demand functions. Supply & demand functions are only used for pedagogical reasons within economics. They are only used, along with geometrical patterns of supply and demand curves, in economic courses. Even if it skips the foundational issues of economics, it serves a purpose in understanding the relationship.

Casey's question really opened up a Pandora's box, since it leads me to other topics of interest. This is one of the joys of philosophy (or I would say the philosophical approach) though. Hopefully, as time permits I will investigate those topics. Expect to see something on terminology.

 Fuzzy Sets: A Primer

Laxmidhar Behera explains fuzziness on 3:10 to about 30:00. [Ex. on 14:40 he describes the ambiguity of height in a similar way as Casey.] Behera defines fuzziness as that which is not precise. I would rather explain fuzziness or vagueness as something that lacks cardinality (although not completely), but has ordinal relationships. I suggest that a theory of rights, laws, etc... should take into account a transition from a Wittensteinian family resemblance of shared but ambiguous norms into increasing levels of cardinal relationships with standardization, laws, barriers etc. Most ethical and moral systems seem to have the tendency to find concrete laws as the ultimate source, whereas I argue that origins are Humean and Nietzchean with a few presuppositions based on the physical world and the exercise of actions. A theory such as this would taken into account of the diverse influences, in terms of cultural, religious, political, etc..., as well as the ambiguous nature that serves as the foundation.

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