Music Video: Saved Another by Mike Borgia & The Problems

Helped with the camera work on this one, Check It Out Here (note: I can't seem to embed the vimeo link, so once I get it on youtube I'll come back and edit this posting.

Wakarusa Artist Spotlights

I recently completed a series of promotional videos for Pipeline Productions in Lawrence, KS.  I interview four different bands from all different parts of the country, and one sent in their own footage.  I haven't done too much stuff like this, but it was an enlightening experience and the diversity of it is great for portfolio.

Spotlight #1: Wick-It the Instigator

Spotlight #2: Railroad Earth

Spotlight #3: Dumptruck Butterlips

Spotlight #4: The Lumineer's

Spotlight #5: Orgone

Thanks to Sheree for organizing everything, Travis, Grant and the other guy at Wick-It for all their help; Ziggy, Surka, Megan and Mustard for being themselves; Nicki, Stuart and all the other guys in Orgone for being so damn cool, and to Wick-It, Railroad Earth and the Lumineers for letting me work with them.

St.Patrick's Day Protest

This March 17 is a holiday known as St. Patricks Day. This is the drunken celebration of the genocide of the true Irish (or Celtic) peoples and their culture by Maewyn Succat, who came from Roman England. He came to be Romanized as Patricius, which eventually became Saint Patrick as we know him today.

As a youth, Succat was captured by pirates and held in slavery, until six years later when he escaped. Succat then went to England and eventually France where he studied under St. Germain, the Bishop of Auxerre, for approximately twelve years. At the end of this period, he took Holy Orders and became a Bishop in the ROMAN Catholic Church. He was given the name Patricius.

After taking his Holy Orders, Patricius claimed that he had received a message from God. This message he claimed told him that he was to convert all of Ireland to Catholicism by any means necessary. With the Pope's blessing, Patricius was on a ship to Ireland to carry out this mission.

When Patricius first arrived, he was imprisoned for speaking out against numerous Druidic leaders and the religion these people had for generations. After his release, for the next twenty years Patricius traveled Ireland, a crucial leader in the church's movement to convert Ireland to a ROMAN Catholic State. Once the Catholic population was clearly in the majority in Ireland, the Pope gave Patricius orders to crusade against the peaceful and pagan Druidic people who remained in Ireland, a people who were native to this island, and to kill all of those who stood in his way.  And he did, and gave the nation of Ireland a distorted view of their own history that is celebrated today in St. Patrick's Day.

In short, Maewyn Succat, an either English or Scotish born slave to pirates, became a ROMAN Catholic Bishop, changed his name to Patricius, eventually became a Bishop. He said God talked to him and told him to go to Ireland and convert the entire country, got the Popes blessing and went to Ireland, a country he had no connection with, and took it upon himself to kill their native religion, as well as those who practiced because he and his religion deemed to be "of Satan"

My plea to my fellow Irishmen is this:
Do not accept this faux holiday this year as a celebration of our people!!! If you drink the green beer, drink it in PROTEST of this holiday and in honor of the true history and culture of our people! As this is truly a celebration of, to use the words of Bill ‘The Butcher’ Cutting in the excellent Martin Scorsese film Gangs of New York, Roman Popery and NOT THE TRUE HISTORY OF PAGAN IRELAND!

Instead of accepting these myths surrounding this holiday, inform yourself and if you see fit, protest it. This is truly the holiday dedicated to a non-Irish Bishop Maewyn ‘Patricius ‘ Succat and the Roman Catholic Church's attempt to commit genocide upon the innocent people of an island!

The Influence of Wittgenstein’s ‘Middle-Period’ Philosophy of Mathematics on his Later Account of Possibility.

Michael Nielson

Ludwig Wittgenstein held various beliefs through the publication of the Tractatus Logico-Philosophicus that he would later come to repudiate in the Philosophical Investigations.  One of these was the atomistic notion that sentences which could be understood could also be analyzed into elementary propositions, termed by Diane Gottlieb in “The Tractatus View of Rules” as ‘the truth-functional thesis’.  One of the primary reasons for this rejection of the truth-functional thesis in the Tractatus Logico-Philosophicus is its conception of rules being motivated by an idealized picture of language’s use.    In the next phase of his career, he would become preoccupied with the philosophy of mathematics and forge an attack on the idea of infinite mathematical sets as anything more than possibilities due to their reliance on finite mathematical calculi.  While in the TLP rules were given a much more strict application and “alone determined meaning”, in the PI meaning and truth could only “be accounted for only in the context of practice”[1]. During this later period, he would return his focus to language, and though it would deviate from the middle period, his discoveries about the nature of mathematics would come to transform many of Wittgenstein’s ideas through the development of language-games, allowing him to account for the variation and possibility in our languages. 

            In order to illustrate the effect his philosophy of mathematics had on the evolution of his conception of rules, I will first outline the view of rules in Wittgenstein’s Tractatus, and examine both syntactical and translation rules.  Next I will detail how his preoccupation with mathematics led him to classify various mathematical propositions, such as set theory and infinite numbers, not as mathematical calculi in and of themselves, but instead as a mere infinite possibilities.  Finally, I will explain how, despite the differences between the two, this questioning of mathematical propositions would play a factor in the Philosophical Investigations repudiation of the truth-functional thesis within logical atomism, as well as the rejection of a rule functioning inside any sort of mental mechanism.

The Early Wittgenstein  

In the only work published during his lifetime, the Tractatus Logico –Philosophicus(TLP), Ludwig Wittgenstein expounded a picture-theory of meaning.  At the foundation of this picture-theory was logical atomism.  According to this doctrine, both meaning and language were examined “in terms of logical form and definiteness of sense”[2].   This theory held the essential metaphysical form of the world and the logical form of language were isomorphic with one another due to their similar structure[3].   Consequently, the objects that the names stood for had to be indestructible,[4] and therefore definite.

Central to Wittgenstein’s atomism was ‘the truth-functional thesis’, which “held that on any occasion when a sentence of ordinary language was meant and understood, the sentence was analyzable into elementary propositions of which it was a logical product”[5].  Implicit within the truth-functional thesis, according to Diane Gottlieb, are rules[6].  These rules are defined in two distinct ways within the TLP, as rules of translation and rules of syntax.

3.334 – The rules of logical syntax must go without saying, once we know how each individual sign signifies

3.343 – Definitions are rules for translating from one language into another.  Any correct sign-language must be translatable into any other in accordance with such rules: it is this that they all have in common.[7]

The rules of definition “play a role in the processes of meaning and understanding”[8].  The rules of logical syntax on the other hand were much more definite, and though it is unclear how Wittgenstein saw them, Hans-Johann Glock theorizes he felt that they mirrored “the essence of reality”[9].  A single logical syntax was “the logico-metaphysical structure which all meaningful languages…must have in common”[10].  However, during his post-TLP sabbatical from philosophy, the Vienna Circle would develop their own unique interpretation of the rules of syntax as “arbitrary conventions governing the use of signs”[11].  Despite these differences both interpretations share the commonality that the only contexts they were able to be discussed was with regard to their use.

            As opposed to these implicit rules, it was explicit within the truth-functional thesis that “all sentences with sense…are in perfect logical order” and possess “a determinate or definite sense” with little account taken for possibility[12].  It was in reference to this that the rules of the TLP lacked any sense of possibility.  This is one of the multiple reasons I theorize why Wittgenstein would came to question the TLP and view logical atomism as dogmatic in character[13].  These factors caused him to see at the root of logical atomism was “a false and idealized picture of the use of language” that would cause him to first leave philosophy entirely before ultimately reassessing his philosophical system upon his return[14].

The Middle Wittgenstein & The Philosophy of Mathematics

Though his philosophical system would progress and evolve after the completion of the TLP, a formalistic conception of mathematics was always foundational to his system[15].  Formalism in mathematics is identified as “the philosophical theory that formal (logical or mathematical) statements have no meaning but that its symbols (regarded as physical entities) exhibit a form that has useful applications”[16].  These mathematical views would take center stage in the middle period of his career after Wittgenstein attended Vienna lecture entitled ‘Science, Mathematics and Language’ by L.E.J Brouwer on March 10, 1928 and became more aware of the interpretations of the TLP[17].  This period is often seen as a black hole in Wittgenstein’s philosophy and is termed by Steve Gerrard in “Wittgenstein’s Philosophies of Mathematics” as ‘the calculus conception of mathematics’.

During this period Wittgenstein would carry from the TLP “his strong brand of formalism, according to which…we invent mathematics, bit-by-little-bit”[18].  Due to being our own creation mathematical propositions only have “intra-systemic meaning, which is wholly determined by its syntactical relations to other propositions of the calculus”[19].  Mathematics was “a closed, self-contained system” where rules were given a much larger role and “alone determined meaning, and thus became the final and only court of appeal”[20].  This reformulation of mathematical rules was only the first of the changes that will be discussed as ultimately crossing over into his later periods philosophy of language and his conception of rules.

Despite these loyalties to a formalistic idea of mathematics, in this period much of his focus would shift to rejecting “quantification over an infinite mathematical domain”[21].  The idea of an infinite class does not have the same syntax as a finite class, because “an infinite mathematical extension is a contradiction in terms”[22].  To further illuminate this, Wittgenstein is quoted in the Philosophical Grammer(PG) as saying “the infinite is understood rightly when it is understood, not as a quantity, but as an ‘infinite possibility’”[23].  We are only able to know it as a possibility through acquaintance with the “criteria for the truth of similar propositions”[24].  In other words, infinite mathematical sets can only be understood in reference to finite propositions because “there are no criteria for mathematical correctness outside the rules of individual calculi”[25].  We are unequipped to even consider grasping anything more than this mere possibility.

Regardless of this rejection of infinite number sets, Wittgenstein did not completely object to the idea of an underlying mathematical reality[26].  What he rejected was “a conception of mathematical reality that is independent of our practice and language” and “is capable of overruling how we actually do mathematics”[27].  This ‘faulty conception of mathematical reality’ can be seen as leading him to critique various mathematical theories surrounding the concept of an infinite set.  Two examples of these theories examined by Victor Rodych in the Stanford Encyclopedia of Philosophy include ‘Fetmat’s Last Theorem’ and ‘Goldbach’s Conjecture’.  The formal statements for both appear as follows:

                            -----------------------------------------------------------------

[28]

----------------------------------------------------------------

[29]

-----------------------------------------------------------------

            Goldbach’s conjecture, which to this day has yet to be proven, was first discovered in 1742 in a letter written to Euler by Goldbach, in which he states “at least it seems that every number that is greater than 2 is the sum of three primes”[30].  The other example, Fermat’s last theorem, was first discovered posthumously in the margin of his copy of Arithmetica by Diophantus, appeared as follows:

"It is impossible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers. I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain”[31].

What both of these theories had in common is that the use of the variable ‘n’ designates the n^th number, and leads to a set of ‘any number’ or ‘every number’ that is greater than ‘x’.  Because these theories are based around this conception of a set including any or every number greater than ‘x’, “contrary to our proof it could be false that there is not a largest number”[32].  We can never fully prove these equations because when we examine an infinite set, it “resides only in recursive rules”.  Further exploration into Wittgenstein’s reasoning behind rejecting anything more than this possibility when dealing with infinite number sets will further illuminate the evolution of the concept of rules and why at the base of this was a “faulty conception…of a mathematical reality that is capable of overruling how we actually do mathematics”[33]. 

The Later Wittgenstein and his Return to Language

Around 1944 this faulty conception of mathematics would cause Wittgenstein to once again return his focus to language, in a period viewed by Gerrard as ‘the language-game conception of mathematics’[34].  This both deviates from and carries over many of the concepts within the calculus conception[35].  Although he continues his “formalistic conception of mathematical propositions and terms” he would reject the calculus conception based on mistakes that “come from reaching too far and from unnecessarily restricting the scope of language”[36].  These mistakes involving the restricted scope of language run parallel to many of the same errors that were fundamental to the critique of the truth-functional thesis and rules of syntax, in that both failed to take full account for possibility.

This new conception of both language and mathematics would strip itself of his previous mistakes regarding definiteness by taking “account for the change and growth of mathematics”[37] and both meaning and truth were “accounted for only in the context of a practice”[38].  This would move the idea of a criterion for mathematical correctness from the rules of the calculi to the mathematical practice itself[39].  The reasoning behind this shift from the calculus conception can be seen in its inability to account for change, growth and possibility in mathematics and language[40].  This section of the paper will introduce just a few aspects of the PI and detail how they both deviated from and built upon his earlier career, leading him to take account for this possibility in language by viewing it within “the context of a practice”[41].

One of these aspects was another dualism within Wittgenstein’s philosophy identified by Gottlieb, only this time instead of identification with rules, it concerned connections.  The first of these connections are set up by a calculus, here the result “is not dependent upon, nor vulnerable to, the accidents of fortune”[42].  The other is set up in a mechanism where “the effect can unexpectedly be determined by some unforeseen occurrence such as the malfunctioning of the mechanism for various reasons”[43].  Through the acknowledgement of this mechanistic aspect of connections two key notions in the PI are addressed.  The first is that the “rules of language ought not be presumed to have strict application” and the second is the logical inconsistency in thinking of a rule of language “as something functioning in a mental medium”[44].

Sections 193 and 194 of the PI concern themselves with this distinction between both types of connections by using an example of machines to both expound his new view and further the critique of syntactical and translational rules[45].  The distinction he has made between the ideal machine, or machine-as-symbol, and the actual machine builds upon the notion of the rules themselves functioning outside of the mental mechanism.  The ideal machine can be seen as merely a blueprint or design of the machine, it does not account for any sort of possibility that may occur and acts “as if the parts of the machine ‘could do no other’”[46].  This classification of an ideal machine can be seen as acknowledging many of the same problems he had found within the conception of anything more than a possibility of an infinite set. 

In PI 193 Wittgenstein draws a parallel between the assumption that someone “will derive the movement of the parts from” this ideal machine and telling someone “it is the twenty-fifth number in the series 1, 4, 9, 16, …”[47].  This comparison serves as an example that similar to middle period’s criticisms of Goldbach’s Conjecture and Fermat’s Last Theorem, merely telling someone the twenty-fifth number in a sequence is unable to prove anything more than a possibility.  The most we can comprehend is a possibility, “the movement of the machine-as-symbol is predetermined in a different sense from that in which the movement of any given, actual machine is predetermined”[48].

On the other hand, the actual machine does take account for actual movements, and the possibility of the machine bending, breaking or evolving[49], placing him at odds with the view presented in the TLP[50].  These possibilities of movement are identified by Wittgenstein through a vague example as “the shadow of the movement”[51]  However, Wittgenstein takes this notion of possibility to be much more foundational, and critiquing the picture theory, he states that a possibility of movement “stands in a unique relation to the movement; closer than that of a picture to its subject”[52].  Because of this possibility “we are at liberty to construct novel calculi, constrained only by the demand for consistence and considerations like ease of explanation and avoidance of puzzlement”[53].  This possibility within language depicted by the machine analogy can be seen as building upon many notions of his philosophy of mathematics.  The analogy serves as an example of the influence Wittgenstein’s belief that we were only able know an infinite set as a possibility, as opposed to being the genuine result of a mathematical calculi, had on both his philosophy of language during the final stages of his career and criticisms of both his conception of rules and the truth-functional thesis within the TLP.

Conclusion

            Wittgenstein was able to take account for the possibility within both language and mathematics through the more fluid and constructivist approach developed in the PI.  This stands in a sharp contrast to the more definite view found in the TLP.  Many of these contrasts between the early and late system were greatly influenced by the function rules were given to perform.  Wittgenstein’s mathematical formalism and criticisms of theories regarding infinite sets shed light motives behind this shift in thought, of which the most notable consequences were the more fluid account of language.

Notes

---

[1] Gerrard, Steve. “Wittgenstein’s Philosophies of Mathematics.” Synthese 87.1 (1991): 126

[2] Gerrard, 131

[3] Glock, Hans-Johann. “The Development of Wittgenstein’s Philosophy.” Wittgenstein: A Critical Reader. Ed. Hans-Johann Glock. Massachusetts and Oxford: Blackwell Publishing, 2001:7.

[4] Glock. “The Development of Wittgenstein”, 8.

[5] Gottlieb, Diane F. “Wittgenstein’s Critique of the ‘Tractatus’ View of Rules.” Synthese 56.2 (1983):  239.

[6] Gottlieb, 241.

[7] Wittgenstein, Ludwig. Tractatus Logico-Philosophicus. Trans. D.F. Pears and B.F. McGuinness. London and New York: Routledge Classics, 2008: 20-21.

[8] Gottlieb, 241.

[9] Glock. “The Development of Wittgenstein”, 11.

[10]Glock, Hans-Johann. “The Development of Analytic Philosophy: Wittgenstein and After.”  The Routledge Companion to Twentieth Century Philosophy. Ed. Dermot Moran. London and New York: Routledge, 2008: 82.

[11] Glock. “The Development of Wittgenstein”, 11.

[12] Gottlieb, 240-241.

[13]Biletzki, Anat. “Ludwig Wittgenstein.” Stanford Encyclopedia of Philosophy. 23 Feb. 2007. http://plato.stanford.edu/entries/wittgenstein, 29 Nov. 2009. 3.1.

[14] Gottlieb, 242.

[15] Rodych, Victor. “Wittgenstein’s Philosophy of Mathematics.” Stanford Encyclopedia of Philosophy. 23 Feb. 2007. http://plato.stanford.edu/entries/wittgenstein-mathematics, 16 Dec. 2009. 1.0.

[16] “Formalism.” Princeton WordNet. Princeton University, http://wordnetweb.princeton.edu/perl/webwn?s=formalism. 8 May. 2010.

[17] Rodych, 2.0.

[18] Rodych, 2.1.

[19] Rodych, 2.1.

[20] Gerrard, 126.

[21] Rodych, 2.2.

[22] Rodych, 2.2.

[23] Rodych, 2.2.

[24] Rodych, 2.4.

[25] Gerrard, 131.

[26] Gerrard, 128.

[27] Gerrard, 128.

[28] “Fermat’s Last Theorem.” Wolfram Alpha. http://www.wolframalpha.com/input/?i=fermat%27s+last+theorum. 8 May 2010.

[29] “Goldbach Conjecture.” Wolfram Alpha. http://www.wolframalpha.com/input/?i=goldbach+conjecture. 8 May 2010.

[30] Weisstein, Eric W. "Goldbach Conjecture." Wolfram MathWorld. http://mathworld.wolfram.com/GoldbachConjecture.html. 8 May 2010.

[31] Weisstein, Eric W. "Fermat's Last Theorem." Wolfram MathWorld. http://mathworld.wolfram.com/FermatsLastTheorem.html. 8 May 2010.

[32] Gerrard, 130.

[33] Gerrard, 128.

[34] Gerrard, 126.

[35] Gerrard, 126.

[36] Gerrard, 132.

[37] Gerrard, 132.

[38] Gerrard, 126.

[39] Gerrard, 131.

[40] Gerrard, 132.

[41] Gerrard, 126.

[42] Gottlieb, 243.

[43] Gottlieb, 243.

[44] Gottlieb, 243.

[45]Wittgenstein, Ludwig. Philosophical Investigations. Trans. G.E.M. Anscombe. Massachusetts and Oxford: Blackwell Publishing, 1999. 77-79.

[46] Gottlieb, 247.

[47] Wittgenstein. Philosophical Investigations, 79.

[48] Wittgenstein. Philosophical Investigations, 77-78.

[49] Wittgenstein. Philosophical Investigations, 79

[50] Glock. “The Development of Analytic”, 82.

[51] Wittgenstein. Philosophical Investigations, 79.

[52] Wittgenstein. Philosophical Investigations, 79.

[53] Glock. “The Development of Analytic”, 82.