Bertrand Russell's Critique of Fregean Logico-Mathematical Objects

 

Bertrand Russell's Critique of Fregean Logico-Mathematical Objects

“…the arithmetic of cookies and pebbles.”—Gottlob Frege

 

Introduction

Last July 1, 2020 I began a reading regime of Ernst Cassirer’s three-volume work on his philosophy of symbolic form and thirteen books by other authors. These volumes were written between 1923 and 1929 with the titles of The Philosophy of Symbolic Forms: Vol. 1, Language (pdf.): Vol. 2, Mythic Thought (pdf.), and, Vol. 3, Phenomenology of Knowledge (pdf.). I included in my reading routine other works by Cassirer such as, An Essay on Man,”(1944)(pdf.) and Language and Myth (1925).

 I knew there would be a big pay-off reading Ernst Cassirer’s three volumes on the philosophy of symbolic forms, and in particular the third book on the phenomenology of knowledge in Chapter 4, “The Object of Mathematics.”  Numbers, sets, and classes are examples of mathematical objects. This fourth chapter is complex, and examines a famous contradiction discovered in May 1901 by Bertrand Russell within Gottlob Frege’s set theory logic that attempted to establish mathematics on logic as its foundation. This discovered antinomy is referred to in the history of philosophy as “Russell’s Paradox,” and is relevant to many of the issues I have written about in this collection of essays concerning classic philosophical problems that are still relevant today.

My thinking was already moving toward this direction of Russell’s paradox in the essay, “The Struggle Against Solipsism,” but stopped short of exploring the structure of mathematical objects. I will further develop the critique of solipsism by further examining Russell’s paradox that resulted from Frege’s conception of number. Russell sums up the solipsistic worldview in the saying, “I alone exist.”

The timeline of persons, publications, and events are important for understanding the philosophical differences between Bertrand Russell and Wittgenstein’s later radically changed view of language. Gottlob Frege published “The Foundations of Arithmetic, in 1884 (pdf.). Russell also published “The Principles of Mathematics, 1903 (pdf.).”  Russell authored “Introduction to Mathematical Philosophy,"(1919)(pdf.), while imprisoned six months for his history of opposing the First World War.

Wittgenstein did not meet Russell in person until 1911. Wittgenstein completed the Tractatus (pdf.) in August 1918 shortly before the Italians held him as an enemy war prisoner for nine months in 1919. In both cases, the two philosophers were not treated as ordinary prisoners. By 1929 Wittgenstein’s view of logic had so evolved away from the Tractatus that he returned to Cambridge and become a lecturer of Trinity College after submitting the Tractatus, finally published in 1922, as his doctoral thesis. It was actually Russell that did all the necessary footwork to get the Tractatus published, then Wittgenstein did not like Russell’s introductory preface to the book.

Many authors have written about Russell’s discovered contradiction in Frege’s logical system, but often fail to explain what this contradiction actually means. How important could an abstract logical contradiction possibly be?  Russell’s paradox also sheds light on Wittgenstein’s motivations for studying philosophy; why he changed his views about language later in his life; and his many cryptic aphorisms about language, logic, and philosophy. 

Russell’s discovered antinomy cannot be fully understood without first briefly describing the relevant schools of mathematics; views on the nature of logical systems; and theories of truth that were common among philosophers in the early 1900s. I will then attempt to generally classify key contributing scholars including Gottlob Frege (1848-1925), G.E. Moore (1873-1958 ), Bertrand Russell (1872-1970), Ludwig Wittgenstein (1889-1951), mathematicians David Hilbert (1862-1943), Heinrich Rickert (1863-1936), and L.E.J. Brouwer (1881-1966). These academicians will sometimes change schools of thought, or hold incompatible doctrines causing multiple variations so that classification of each thinker can be ambiguously on the edge of another group. Yet, this kind of school classification is in the academic literature, and is useful for getting a wide view of the historical philosophical landscape during this era of changing mathematical thinking.

To better understand Frege’s contradiction, Russell’s paradox will be expressed both in terms of ordinary language that does not presuppose knowledge of logical symbolism, and in symbolic notation for the interested reader. The logical sign, Cassirer observed, compels “thought to come forth from its inner workshop and manifest itself in its involvements and complexities.” Lastly, I want to comment on Ernst Cassirer (1874-1945) and Wittgenstein’s insightful critiques of logic resulting from the antinomy and what the implications mean for philosophy and the physical sciences.

While researching this essay I got perverse pleasure reading that until Wittgenstein was 20 years old, he was a bad speller.

Part I

Paradigms of Truth And Logic

"If I designate phenomenal insight as knowledge, then theoretical insight rests on faith--faith in the reality of one's own ego and that of others, or in the reality of the outside world or of God"—Mathematician, Hermann Weyl (1885 – 1955)

1.)    The Pragmatic Theory of Truth is often associated with the American philosopher William James (1842-1910). The Greek term “πρᾶγμα” (prag-ma) is translated as “deed,” “fact,” or “business” and in this context truth means the utility of achieving a goal or end. A statement is true based on its usefulness as a belief: “X is useful; therefore, X is true.” Pragmatism does not seem to be an appropriate theory of truth in mathematics; however, some mathematicians note that pragmatism is important in the creation and use of signs in symbolic logic notation and math. Pragmatism in science is the successful manipulation of objects for a desired purpose. However, ordinary language philosophers have the recurrent theme of pragmatism throughout their understanding of how language actually works and how systematic thinking emerges. 

 2.)    The Coherence Theory of Truth is a more common concept of truth embraced by modern mathematicians by defining logical truth in relation to consistency and not by some content in the world; but instead, by the relation of content to other content, or by belief in relation to another belief. In symbolic logic, a valid argument is merely non-contradictory propositions in relation with another proposition; for example, “A is not non-A” is a consistent proposition, or coherent, and merely tautologically true (A is A). 

3.)    The Correspondence Theory of Truth holds that truth is the correspondence of some propositional content within the world since mere consistency alone is an inadequate criterion for truth. Propositional content is understood in this theory as descriptive statements such as “A is B.” The argument “All men are cows, and John is a man; therefore, John is a cow,” is a perfectly valid (consistent) argument. We can rewrite the same propositions as “All M are C, and J is M; therefore J is C” which is a valid argument form known as a hypothetical syllogism. In addition to a valid (consistent) inference, a propositional argument must also have true premises before it can be called a “sound argument.” Sound arguments are what philosophers seek to present into the market place of ideas since, in a deductive argument, if the premise are true, and the inferences are valid; then, the conclusion must be true. 

A true proposition in this theory is one that corresponds to the state of something in the world, or a fact. A belief is true if it corresponds to an existing factual object. There are differences among logicians and philosopher on whether truth is an attribute of an object, or a proposition, or belief.

Wittgenstein influenced Russell into accepting the correspondence theory of truth although their ontologies are different (Dr. K. Banick video lecture on Russell and Wittgenstein’s dissimilar metaphysics). Interestingly, around 1904, Russell and Moore held the identity theory of truth in which a true proposition is the object of belief: “When a proposition is true, it is identical to a fact, and a belief in that proposition is correct.” In other words, truth was a property of a proposition itself and not something else external to it. The nature of correspondence and truth bearing propositions forced Russell and Moore to abandon the identity theory after they were unable to define the difference between true and false propositions within this particular theory of truth.

Theories of Logic and Mathematics

 

1.)    Logical Conventionalism is the view that logical systems are invented cultural norms, signs, and linguistic conventions. The denial of logical necessity is key to conventionalism. All logical analytic a priori necessity (A in not non-A) is a disguise of collective non-arbitrary agreement on procedural and definitional rules that work when applied to the world. There are no real necessary independent truths of meaning, logic, or mathematics, but instead only a set of axiomatic rules for the manipulation of intuitive empirical signs. This school is also called “mathematical terminism” and views signs as mere “intuitive figures without any real independent meaning (Cassirer, Vol. 3, p. 381).”  Mathematician David Hilbert wrote, "In the beginning was the sign (Ibid., p. 380).” Conventionalism is associated with pragmatism in its way of analyzing how ordinary language is actually used.

Henri Poincaré (1855-1912) held to the coherence theory of truth and was among the first conventionalist mathematicians who viewed all mathematical objects as independent human constructions that have no reality in existence. He believed that natural numbers were innate to human understanding and could not be reduced to symbolic logic set theory objects. The logical positivists also held a conventionalist viewpoint of logic and mathematics as pure form, and completely independent of the world.

The late Wittgenstein is an extreme conventionalist by understanding language as a public tool consisting of norms of linguistic usage created from a certain way of life, and not possessing a hidden necessary essence of some ideal language. Wittgenstein’s late lecture notes were published posthumously in 1953 as, Philosophical Investigations that treats language and logic like the intuitionists who believe that mathematics emerge from a “primordial intuition” of space and time, which we impose on language and the world. Many of his ideas about language toward the end of his life were antithetical to the early Tractatus that instead attempted to discover a hidden calculus concealed within ordinary language. Wittgenstein’s philosophical “investigation” was about why the formalist Tractatus conception of language is wrong.

Wittgenstein respected ordinary language; and even though it can be entangled in misunderstandings from misuse, “philosophy may in no way interfere with the actual use of language; it can in the end only describe it…it cannot give it any foundation either, It leaves everything as it is….(Philosophical Investigations, paragraph 124).”

We can also place early Wittgenstein (Tractatus) in the conventionalist group since he has described logical propositions (A is not non-A) as senseless (Sinnolos) tautologies. Furthermore, Wittgenstein posited the existence of “simple objects” (Tractatus; 2.02) that are the smallest possible entities that names denote so that there is a connection between existence and logic through language. He was unable to give a actual example of the posited a priori simple object. And yet Wittgenstein writes of the simple object as both physical and as a non-physical object so that he is straddling two different schools of thought (conventionalism and intuitionism) if we try to force him into a category. Wittgenstein is again being deliberately ambiguous. 

2.)    Logical Formalism is a modern form of Platonism that included such thinkers as Frege, Russell, Hilbert, and the early Wittgenstein. This simplest version of Platonism believes in a totality of natural numbers (counting numbers) that exist independently of mind and can be symbolically defined as quantifying propositions (All X is Y) bearing decidable truth-values. Formalism typically holds to the consistency, or coherence theory of truth, and to sign conventionalism. As the leading figure of formalism, Hilbert viewed mathematics as the “manipulation of symbols” according to an axiomatic decision procedure for proof of consistency in a logical system. 

However, Hilbert also held some theoretical positions that were consistent with logical intuitionalism so that he is called by some as a “passive logical intuitionist” rejecting Russell and Frege’s version of Platonic objective realism while at the same time he sought to establish mathematics on a Platonist mathematical foundation in opposition to intuitionalism. 

Hilbert thought he could achieve his goal by the notion of a pure theory of mathematical “signs.” His project is to require verification of consistency with his theory of proof so “the process of verification is shifted from the sphere of content to that of symbolic thinking. As precondition for the use of logical inferences… certain sensuous and intuitive characters must always be given to us (Cassirer, Vol. 8, p. 379)."  There is seemingly an inherent conflict between these two doctrines: intuitionalism understands the symbol, or sign as an essential expression of thinking, but the formalist sees the symbol as merely marks on paper (Ibid., p. 381 ff). With empirical signs, mathematical-logical proofs seeking to identify contradictory signs could be completed by machine. Hilbert held to the doctrine that “mathematical symbols themselves, and not any meaning that might be ascribed to them, that are the basic objects of mathematical thought (see, Formalism: Britannica).” Cassirer’s comment on Hilbert’s project is “… that mathematics can retrieve its threatened autonomy only by becoming a pure theory of signs. Among present day mathematicians it is Hilbert who has drawn this conclusion most decisively. In direct opposition to intuitionism he strives to rehabilitate the classical form of analysis and theory of sets (Ibid., p. 379)." 

However, terminism transforms mathematics into a “monstrous tautology.” Authors Russell and Alfred North Whitehead believed they were able to develop a coherent and complete minimalist set of logical symbols as presented in their famous three volume work,“Principia Mathematica,”(1910,1912, and 1913). 

Logicism is consistent with formalism and is the effort by mathematicians to show mathematics has its foundation in logic, or that some mathematics can be reduced to logic. Frege, the early Wittgenstein, and Russell as the leading member of this school, attempted to prove this relationship using the theory of sets, and the concept of classes. Wittgenstein’s Tractatus is a classic example of logicism. The assumption of the Tractatus, shared by young Wittgenstein and all the Logical Positivists, is that natural language has a concealed calculus that can be symbolized and expressed as logical rules. 

3.)  Intuitionism is a rejection of mathematical Platonism. L.E.J. Brouwer (1881-1966) represents the position that mathematical objects (numbers) are mentally constructed and that mathematics is inherent in human experience. Brouwer believes that mathematics is "far more an action than a theory (Ibid., p. 371)." This inherent ability of reasoning is enabled by the intuitions of space and time conceptual totalities. Whereas mathematical objects such as numbers are autonomous entities in Platonism, they are instead reified “constructed” symbolic objects for the intuitionist. Brouwer’s intuitionism required a defining procedure for constructing a mathematical object before asserting its existence (see, Russell’s Paradox: Stanford Encyclopedia of Philosophy). Brouwer is anti-formalistic and was opposed to set-theory ideas even before the discovery of Russell’s paradox (Encyclopedia of Philosophy,1967, Macmillan, Vol. 5, p 204). Wittgenstein started out as a formal logicist, but ended up a Brouwerian intuitionalist concluding that language--like a game--has no essence, but is a pragmatic constructivist activity. Philosopher William Barrett summed up the insight of intuitionism as: “Technique has no meaning apart from some informing vision (The Illusion of Technique, Barrett, William, Anchor/Doubleday, 1979, p. 88).”

Part II

 

The Contradiction

 

“Alas, arithmetic totters.”--Gottlieb Frege

 

A tautology is a proposition that is necessarily true such as with the proposition, “Either it is going to Rain, or not Rain.” Every possible combination of the truth-value of ‘R’ in a disjunctive proposition is true, “R v ~R”.

On the other hand, the denial of a tautology is necessarily false, “It is false that either it is going to rain, or not rain,” ~(R v ~R). 

Every possible combination of truth-values that compose a contradiction result in a proposition that is false necessarily as in the first truth-table column.

Typically, we think of a noun as a name denoting some ‘thing’ in the world—some corresponding referent that is the sense of a name. However, we also use names to describe something that has no referent because it does not exist, but still has sense like the name “unicorn” in a folk tale. On the other hand, self-referential propositions refer to themselves as propositions--“Everything I say is false”--creating endless paradoxes (see, Graham Priest on Paradoxes). 

A contradiction can have many disguises, and some might appear as the simple equivocation of words. I have discussed contradiction is the essay, “The Machine Paradigm of Nature And Disenchantment” and there are other well-known examples of stated contradictions such as the self-referential contradiction, or the “Liar’s Paradox” in which a liar states that everything they say is a lie which leads to the contradiction that if it is the case the liar is lying, then the liar is telling the truth, but then it also means he, the liar, just lied. These contradictions run in a vicious circle. 

Another well-known contradiction is the “Barber’s Paradox” that even puzzled Russell. This example is a story telling of a barber on an island who shaves all those, and only those, who do not shave themselves. The question posed is “Does the barber shave himself?” If the barber shaves himself then he is a man on the island who shaves himself; hence he, the barber, does not shave himself. However, if the barber does not shave himself then he is a man on the island who does not shave himself; hence he, cannot be the barber. In other words:

·       If he does, he cannot be a barber, since a barber does not shave himself.

·       If he doesn't, he falls in the category of those who do not shave themselves, and so, cannot be a barber. 

We can express this paradox in symbolic notation as the following:

{(∃x)[Bx * (∀y)(Py ⊃ Sxy)] ≡ ~Syy}

“A Barber on an island (x) Shaves all those island Persons (y), and only those (≡) who do Not shave himself."

When we replace variable “x” with any person “y” we get the contradiction:

Syy ≡ ~Syy

In my thinking the Barber’s Paradox might be more of an analogy to Anthony Flew’s “No true Scotsman,” informal fallacy. A factual statement such as “The circle is green,” is a “synthetic” statement that may be true or false. The statement “Circles are round” is true by definition, or “analytically,” and cannot be false for it is a tautology.  This fallacy is committed, for example, if a person declares as a fact, “No true Scotsman puts sugar in their beer.” However, when the speaker is faced with a counter-example of a Scotsman putting sugar in their beer, they immediately equivocate from the initial factual (synthetic) proposition by declaring by definition (analytically), “He is not a true Scotsman!” So the Barber’s Paradox, depending on how it is stated, could be interpreted as another informal fallacy with “barber” defined analytically and then equivocates to a synthetic description of the barber in an endless circle. 

The essential feature of the No True Scotsman fallacy can be described in this way: the faulty argument takes an empirical proposition and covertly shifts it into a postulate making it a methodological proposition which becomes a norm of description. The No True Scotsman fallacy is not addressed by Wittgenstein, but this interpretation of how the fallacy works is inspired by his last essay, “On Certainty,” (1950)(pdf.), lines: 318, and 321.

A Formal Symbolic Expression of Russell’s Paradox

Our immediate interest is in Russell’s paradox and so we are going to turn away from lairs, barbers, and Scotsmen to class attributes which are “predicable,” and “impredicable.” I am going to present a slightly expanded argument form of Russell’s paradox by borrowing some logical symbols provided by logician I.M. Copi in his textbook, “Symbolic Logic: Fifth edition,” p. 153 (pdf.). We must have some symbols to represent a formal expression of the contradiction in order to symbolize quantitative propositions like, “Socrates has some attribute.” 

Definitions: 

‘s’ = Socrates

~ = negation

≡ Equivalent truth-value of proposition.

F = Predicate variable for the concept of an “attribute”.

(∃F) = This is a special symbol to mean “At least one attribute.”

 (∃F)Fs means “some attribute” as in writing, “Socrates has some attribute.”

(x)(F) means “all attributes.” 

These symbols now enable us to symbolize the following statements such as: 

(x)(F)Fx

“Everything has an attribute.”

(x)( ∃F)Fx

“Everything has some attribute or other.”

(F)(∃x)Fx

“Every attribute belongs to some thing or other.” 

Now we need a symbol to represent “impredicable attributes” of classes. For example, the class of pebbles is not itself a pebble. The class of pebbles does not share any attribute of any of its members (pebbles) so the class is defined as “impredicable” represented by the symbol “I”. Impredicable class attributes are ordinary classes. 

On the other hand, there are some unordinary classes that share predicable attributes the same as its members such as the class of all abstract ideas which is itself abstract. Predicable class attributes are defined as “FF”. Predicable class attributes are attributes of attributes. 

 

1.) IF ≡ df ~FF

Impredicable class attributes are now defined (≡ df) as non-predicable class attributes:

 

2.) (F)(IF ≡ ~FF)

All impredicable class attributes (ordinary classes) are defined as non-predicable class attributes.

 

3.) Therefore: II ≡ ~II

Universal Instantiation, applied to premise 2.

“Impredicable class attributes are not impredicable class attributes,” by replacing “F” with “I” in premise 2 resulting in a contradiction. 

The rule of universal instantiation applied to premise 2 is analogous to the argument:

Definition: Zeus is not mortal.

1.) All Greeks are mortal.

2.) Zeus is Greek. 

3.) Therefore, Zeus is mortal.

But Zeus is by definition not mortal! 

Likewise, there are no predicable class attributes either: “FF” and “~FF” turn out to be meaningless symbols—pseudo-universals.

 

Part III

 

The Depth of Reason

 

 

"There is a crack in everything. That's how the light gets in."--Leonard Cohen 

 

The closed system of schematized formalistic logicism had a flaw. Much has been written about the contradiction found in Fregean set-theoretic logic of classes and in the process of review turned attention toward a new realm of logic that moves way from mathematical objects to the “extra-logical discrete objects” of mathematical “signs” themselves (Cassirer, p. 378 ff). Hilbert points out mathematical problems have a completely different meaning in relation to signs as “concrete forms.” Signs are an independent power in themselves by ignoring content and ideas; yet, contradiction is still effectively detected by “the appearance of certain constellations of signs (Ibid., p. 381).” 

Wittgenstein defined three intentionally ambiguous logical categories: “sense,” “senseless,” and “nonsense.” He writes, “Tautology, and contradiction are without sense (Tractatus, 4.461).  However, they are not metaphysical nonsense, “Unsinning.” He further clarifies what he means: “Tautology and contradiction are, however, not senseless; they are part of the symbolism, in the same way that “0” is part of the symbolism of Arithmetic (Tractatus, 4.4611).” The original English editions of the Tractatus mistranslated both “Unsinning,” and “Sinnolos” as “senseless.” (see, Wittgenstein’s Conception of Philosophy, K.T. Fann, Univer. of Cal. Press, 1969, p. 25). 

 

Cassirer reminds us that Leibnitz called formulas the “logic of discovery,” the “logica inventionis (Cassirer, p. 440).” The sign represents not a real order, but a possible order according to some fixed principle: “atomic weight” as a unit of the periodic table is one example of a principled ordered system based on fixed principles. From similarly ordered totalities, mathematicians are able to create Imaginary numbers: negative numbers, irrational numbers, squares, and square root of a negative number. Now, the “heuristic maxim” of mathematicians is the unlimited use of form (Cassirer, p. 442). However, a contradiction is the sign of an impossible object. 

Fregean logicism is based on the concepts of sets, classes, and member objects; also known generally as the theory of groups. Russell writes, “But all finite collections of individuals form classes, so that what results is after all the number of a class (Principles of Mathematics, POM, p. 113).” The idea of numbers as properties of classes arose from the mathematics of Giuseppe Peano arguing that arithmetic and algebra could be derived from idea of class (A History of Philosophy: Modern Philosophy, Fichte to Hegel, Vol. 8, Part II, Frederick Copleston, Doubleday, 1967, p. 198).” As a Platonist Russell adopts this idea of number in 1900. Both Russell, and early Wittgenstein, viewed language as ultimately an “object-language.” Gradually, Russell became uncertain of the term “class” comparing it to a parenthesis, “The parenthesis is clear only if what falls inside the two parentheses is clear and definite (Barrett, p. 97). However, unconscious Platonism allowed logicism to reify the concept of class giving priority to the object by hypostatizing the object. 

Χωρισμός is the Greek term for “separation,” “abstraction,” and is used to describe the “secretion of sap.” Set theory applies to first level abstractions, but not abstractions of abstractions such as Russell’s example of the class of attributes of attributes. Every proposition has a range of significance: “The class of men is mortal” is meaningless since a class of men is not man, no more than “Socrates is human,” means “Socrates is humanity” for humanity is not a thing. Russell concluded that the entire concept of “a class is a member of itself” is nonsensical and a “incomplete symbol.”

 

Logicism attempted to reduce mathematics on the underlying stratum of the “reality of things,” not unlike empiricism, by attempting to turn mathematics into physics (Cassirer, p. 375 ff). For logicism the meaning of number rests on some empirical matter, or “the existence of things,” usurping the autonomy of logic. The Neo-Kantian Cassirer instead argues, "The world of mathematical forms is a world of ordinative forms, not of thing forms (Ibid., p.383).” There is also a purely non-material “functional” meaning of number based not on the existence of things, but on the ordinative form of constructed concepts. The logicist concept of number must be de-materialized and detached from “thing-hood.”

 

"To convince someone of the truth, it is not enough to state it, but rather one must find the path from error to truth."-- Wittgenstein

 

In Cassirer’s first volume of his philosophy of symbolic form addressing language, the evolutionary development of the concept of number is traced from an ancient manual concept such as grasping, pointing, and counting objects; then, to the concept of number having no attributes; and finally, to number as de-materialized pure form. 

The Fuji Islanders treated numbers as a quality of things so that there were different numbers for different classes of things in their language: “…different words are used to designate groups of two, ten, a hundred, a thousand coconuts, or a group of ten canoes, ten fish, etc. (Cassirer, Vol. 1, p. 233 ff).”  For the Brazilian Bakairi tribe numbers were so laden to content that a tribesman could not count on their fingers even a few grains of rice without physically touching them for number had to be translated into a specified body part. Cassirer observed that “…it does not suffice at this stage for counted objects to be referred to the parts of the body; in order to be counted, they must in a sense be immediately transposed into parts of the body or bodily sensations (Ibid., p. 230).” In American Indian languages different numbers represent the same quantity of things as opposed to humans, or to animate and inanimate things. Only later in the evolution of language does number gradually shed material content and become independent of things as pure form. Similarly for Russell, he must also de-objectify reason so that thing-constants and thing-unties give way to the universal unities of mathematical function.

 

Fregean logicism is “Arithmetic with frills.”-Wittgenstein.

 

The inventive mind of Ludwig Wittgenstein understood the problem with Frege’s project of establishing mathematics on logic. Logicism instead based logic on mathematics by smuggling in the concept of number within the concept of class. After the contradiction, logic now appears as an unessential decoration attached to mathematics. Other critics suggest quantitative predicate logic should be promptly return to the humanities department. The problem with sets is that the logician must one way or another individually count the number of members within a class. We say that a dozen is a class of twelve members, but we still must conceptually translate “dozen” into twelve members of a class using natural numbers. In addition to the circularity of using number to define number, mathematician Hermann Weyl argued that simply pairing sets is sorely inadequate for establishing the notion of number. Neither is the fundamental logical idea of identity and difference is enough to derive the concept of number. On this issue, Cassirer writes perceptively: “In their attempts to derive the concept of number from the concept of sets, the logicians have always argued most emphatically against any imputation of a petitio principii; they have pointed out that the sense in which logic speaks of ‘identity’ and ‘difference’ does not include the numerical one and the numerical many, and that it is consequently a decided advance in knowledge if we can reduce the numerical sense to a purely logical sense (Cassirer, Vol. 3, p. 377).” Class-theoretic quantification logic was at this stage of development simply the arithmetic of cookies and pebbles. 

"...numbers have neither substance, nor meaning, nor qualities. They are nothing but marks, and all that is in them we have put into them by the simple rule of straight succession." --Hermann Weyl

Concluding Part III:

 The Depth of Reason

Many of Russell’s beliefs concerning logic originated, or were influenced by the early Wittgenstein such as the theory of logical atomism; that atomic facts are logically independent of one another; picture-theory of propositions; and the tautologous circularity of logical-deductive propositions (Copleston, p. 199 ff). With the exception of the circularity of logic, Wittgenstein abandoned those theories by 1933. After hearing intuitionist Brouwer lecture in Vienna during 1928, Wittgenstein returned within one year to Cambridge as a lecturer with a newly evolving philosophy of language and logic (Barrett, p. 87).

Russell commented that once he realized that logic says no more than “a four legged animal is an animal,” he lost interest in logic. Wittgenstein argued in the Tractatus that there is no symbolism that is able to say anything about it own structure: “3.333 A function cannot be its own argument, because the functional sign already contains the prototype of its own argument and it cannot contain itself.” Logic, in the relatively mechanistic Tractatus, was a discovery disguised by language, but later he viewed logic more as an inventive activity as presented in Philosophical Investigations (1953) moving philosophically toward pragmatism, and conventionalism while being open to a variety of new mathematical systems (Barrett, p. 90-91).”  Wittgenstein liked Goethe’s famous saying, “In the beginning was the deed.” Brouwer similarly concluded that mathematics is "far more an action than a theory (Cassirer, p. 371)." Wittgenstein still held to the view there are limits to language; “7 Whereof one cannot speak, thereof one must be silent.” (video lecture:, “Ludwig Wittgenstein, the Great War and the Unsayable,” by Ray Monk).

“The Tractatus was not all wrong: it was not like a bag of junk professing to be a clock, but like a clock that did not tell you the right time.”--Wittgenstein

Sentential propositional logic (“Socrates is mortal”) is a finite syllogistic system. It is perfectly internally consistent and decidable as true of false. However, quantification categorical propositional logic uses universal quantifiers such as, “Everything has some attribute or other,” whose meaning encompasses a possible infinite manifold of things. It is within quantification logic that the contradiction appears. In his “Principles of Mathematics,” Russell writes: “For publishing a work containing so many unsolved difficulties, my apology is, that investigation revealed no near prospect of adequately resolving the contradiction discussed in Chapter x, [The Contradiction] or of acquiring a better insight into the nature of classes (p. vii).” 

Russell’s first attempt to resolve the contradiction was to construct formal syntactical rules prohibiting the inferential steps that give rise to the contradiction. His newly formulated “Simple Theory of Types,” presented a lexicon of symbols to represent types of attributes on different levels in a hierarchy of abstract idealizations; individuals, then attributes of individuals, then attributes of attributes of individuals, and so on. As a rule, the attribute of one individual cannot be predicated of entities of a different abstract hierarchical type such that  “impredicable” class attributes cannot even be defined to produce a contradiction. "Tâtonnement," is the ugly way logical sausage is made, i.e.,  “groping one’s way moving forward by trail and error.” If one wants to avoid an inference leading to a contradiction, then don’t violate the “limitative theorems.”  Russell eventually realized that he was not dealing with different types of entities, but different types of linguistic functions (Copleston, p. 190).  Mathematics advanced with this insight that “…the validity of a mathematical object is not its construction but its ‘constructability’ (Cassirer, p. 372).” Later, other mathematicians created new functions for better versions of Russell’s first theory of types.

“...in advancing to higher and more general theories the inapplicability of the simple laws of classical logic eventually results in an almost unbearable awkwardness. And the mathematician watches with pain the greater part of his towering edifice which he believed to be built of concrete blocks dissolve into mist before his eyes."-- Hermann Weyl

In contemplation of Russell’s paradox, Cassirer caught sight of the important themes of freedom, possibility, and creativity. He believed, “No mathematical concept...can be gained through mere abstraction from the given; a mathematical concept always comprises a free act of combination, an act of synthesis (Cassirer, p. 361)." Mathematical symbolism is an instrument like a microscope, or telescope that enhance our vision (Ibid., p. 386). Mathematics is not a once completed project. The synthetic function is produced from the creative acts of intuition (experience) and the understanding. Cassirer has been called a Hegelian, in addition to a Kantian philosopher for his view of the essential character of the logos as going through a process of self-alienation, and then intellectual reunification through the act of conceptual synthesis (Ibid., p. 432).

Wittgenstein’s Loophole Metaphysics 

“Vorbei redden (speak past) Gödel.”—Wittgenstein

In 1930 Kurt Friedrich Gödel published his incompleteness theorems that state: “A.) If a logical system is consistent, it cannot be complete. B.) The consistency of axioms cannot be proved within their own system.” Wittgenstein was not alarmed by Russell’s paradox, but instead tossed the ladder of logicism away after he climbed it (see, Tractatus, 6.45). He viewed the inconsistency of logicism the same as the ancient paradoxes such as Zeno’s paradox of motion. If the axioms of a logical system cannot prove themselves, then a “hierarchy of languages,” with multiple logics could say what a logical-scientific structure—like the Tractatus—cannot say about itself. Russell correctly understood that Wittgenstein’s Tractatus has a loophole: “… Mr. Wittgenstein manages to say a good deal about what cannot be said, thus suggesting to the skeptical reader that possibly there may be some loophole through a hierarchy of languages, or by some other exit. The whole subject of ethics, for example, is placed by Mr. Wittgenstein in the mystical, inexpressible region (Tractatus, p. 18 )." Philosophy is just one loophole avoiding solipsism with others being literature, music, art, ethics, and religion.

"Don't for heaven's sake, be afraid of talking nonsense! But you must pay attention to your nonsense."--Wittgenstein, 1947

In addition to scientific positivism, a constellation of other methodologies is required for studying human behavior, language, and cultural history. The objectivating attitude of natural-scientific reductionism blends into culture in a horrible transposition by which human beings are perceived as mere objects while things are seen as possessing human attributes and value (see, “The Objectification of Human Beings And Animistic Commodities”).

In another example of misplaced scientific reductionism, economist Steve Keen has critiqued Neo-classical and Neo-liberal economic theories for treating macroeconomics as applied microeconomics: these two methodologies are on completely different levels of abstraction. Dr. Keen argues that “…psychology is not applied biology, nor is biology applied chemistry…nor is macro-economics applied microeconomics (video lecture: 6:51 min., Debunking Economics: the Failure of Neo-classical Economics with Steve Keen). Keen quotes 1977 Nobel Prize winning theoretical physicist, Philip Anderson's saying of multi-levels of scientific abstraction: “Instead at each level of complexity entirely new properties appear, and the understanding of the new behavior requires research which I think is as fundamental in its nature as any other (video: 6:41 min.)”.

Mathematician Hermann Weyl studied under formalist David Hilbert, but later adopted the views of intuitionist Brouwer in 1919.  By 1928, Weyl changed his views again and moved toward the constructivism of Neo-Kantian Ernest Cassirer's philosophy of symbolic form. Another figure involved in the crisis of Fregean logicism is Neo-Kantian Heinrich Rickert who rejects any effort to establish mathematics in empirical reality, or “the thing-sphere of the countable.” Consequently, he believed it impossible to derive mathematics from logic for even the logical unity of “1 = 1” requires experience (intuition) which is ultimately ‘alogical’ (Ibid., p. 346.)”  Interestingly, Rickert acted as an advisor to a young theology student named Martin Heidegger at the University of Freiburg and approved his doctoral thesis in 1916. Rickert was a strong influence on Heidegger’s interpretation of Kant.

By critically applying a constellation of scientific paradigms to the complexities of human life, we might be able to live in truth, and then live in freedom.

“With mathematics we stand precisely at that intersection of bondage and freedom that is the essence of the human itself.”― Hermann Weyl

The Theological Foundations of Hegel’s Phenomenology of Spirit

The Theological Foundations of Hegel’s Phenomenology of Spirit 

“Life is the union of union and nonunion.”

-Hegel, Early Theological Writings, p. 312.

 (∀x){Lx ⊃ [Ux ⊃ (Ux * ~Ux)]} 

One of the greatest philosophical treasures I have recently found is an introduction to Hegel’s early theological writings contained in a collection of essays titled, “On Christianity: Early Theological Writings,” (1907) by Friedrich Hegel, trans. by T. M. Knox with an Introduction by Richard Kroner, (pdf.). 

After being dismissed from the university at Kiel by the German Nazis in 1934, the Neo-Hegelian philosopher, Richard Kroner, escaped to America to become professor of philosophy at Manhattan’s Union Theological Seminary. Kroner’s introduction to Hegel’s early theological writings (original text pages 1-66) is a condensed overview of Hegel’s Christian theology. Kroner narrates the evolution of Hegel’s thoughts on religion from about 1788 to 1801, which ultimately appears in his most famous written work “The Phenomenology of Spirit,” in 1807. Kroner comments on Hegel’s Phenomenology of Spirit (pdf.) in his introduction to build a larger picture of Hegel’s goal, “to intellectualize Romanticism and to spiritualize Enlightenment (Hegel’s Early Theological Writings, here on as HET, original pagination 21).” 

Dr. Kroner recounts how Hegel was extremely impressed by the philosophical movements of his time including Romanticism and the Enlightenment. The German Romantic poet-philosophers Friedrich Hölderlin and Friedrich Schelling were school roommates with Hegel. Philosophers Kant, Rousseau, and the famous poet Goethe (who was a close friend of Schelling) are also found at the core of Hegel’s fully matured philosophical system.

In these early--and sometimes conceptually contradictory--theological essays Hegel works out the dialectical-philosophical language he needed to write the Phenomenology of Spirit. This appearance (phenomenology) of Geist (Spirit or Mind) is a history of the evolutionary development of human consciousness into higher self-consciousness and truth: that is to say, the process of the Logos becoming incarnate.

Yet even his love for these philosopher-poets did not prevent Hegel from critiquing Romanticism and the Enlightenment and even rejecting some parts, or whole worldviews. Hegel rejected Schelling’s conception of God-substance as the Absolute (Being as an undivided whole) with the one-liner response, “…in the Absolute, all cows are black….” Instead, Hegel formulated the Absolute, the whole of a unified reality, as God-Subject, i.e., immaterial Mind, or Spirit. 

Knox does not mention in his introduction one other similar case involving the theologian--and has always annoyed me--when Hegel rejected Kantian philosopher-theologian Schleiermacher and his doctrine of the connection humans have with the infinite as a “feeling of absolute dependence on the infinite.” Hegel gave the brutal response,  "If religion grounds itself in a person only on the basis of feeling, then . . . a dog would be the best Christian, for it carries this feeling more intensely within itself and lives principally satisfied by a bone." The same sentiment toward theologies of experience exists to this day.

 

Of course Hegel’s counter-argument is not fair to neither Schelling, nor Schleiermacher. Schleiermacher would never claim religious experience is “only on the basis of feeling.” Schleiermacher’s use of the term “feeling” does not mean mere affection, or “sensation,” which is “...the lowest stage in the development of the human spirit,” but rather “feeling, as immediate self-consciousness, is the last and highest stage in the same development.” Feeling is the synthesis of thought and will; it is the unity of our being. (see, Schleiermacher: Personal and Speculative,”Robert Munro, Pub. Paisley, Alexander Grardner, 1903, p.200)(pdf.).

 

Schelling views the entire history of philosophy as a struggle between positive philosophy (historical philosophy) and negative philosophy (for Schelling ultimately meaning religious philosophy).  Schelling writes, “At the end of negative philosophy I have only possible [my emphasis] and not actual religion…It is with the transition to positive philosophy that we first enter the sphere of religion (Frederick Copleston, S.J., A History of Philosophy: Modern Philosophy, Fichte to Hegel, Vol. 7, Part I, Doubleday, 1965, page 170).”

 

Schelling believed there should be an emphasis on a philosophy of nature to compensate for the tendency of thought systems to bypass actual existential being since purely idealist philosophies cannot ever logically deduce the world’s existence, or positive being from negative essences, or concepts. Schelling’s emphasis on philosophy of existence, of actuality continued with Left Hegelians philosophers such as Feuerbach (All theology is anthropology) and Marx (dialectical historical positivism). In 1831 Shelling filled Hegel’s chair of philosophy in Berlin and attempted in his lectures to correct what he believed was Hegel’s overemphasis on the negative philosophy of abstract possibility.

 

The Dialectical Development of Hegel’s Early Theology 

“To eliminate the Kantian element in Hegel's philosophy is like eliminating the Platonic element in Aristotle.”—Professor Knox.

Hegel disagreed with Kant in other areas of epistemology and ethics, but he still remained Kantian at heart through his entire life. The pre-Socratic philosopher of change, Heraclitus, and Immanuel Kant’s Critique of Pure Reason inspired Hegel’s dialectical method presented in the Phenomenology (citing HET,p. 4). However, in that same work (Paragraphs 596-671, or pp. 424-72) Hegel harshly and enthusiastically criticized Kant’s ethical system of Duty (deontological ethics) as only a particular stage of developing human self-consciousness. The reason for Hegel’s rejection of Kantian ethics of duty is that all positive historical aspects of religion is purged leaving behind a abstract moralistic idealism impossible to achieve in existence, “…consciousness has realized that its truth is a pretended truth (Phenomenology, para. 631).

 

Thesis: The "Life of Jesus" as a Kantian Teacher of Ethics

 

Hegel drew his conclusions about Kantian ethics partly by performing a thought experiment in an essay on the “Life of Jesus” that presents Jesus as a teacher, or “the schema of morality” within the categories of Kantian religious moral rationalism. This essay was not meant for publication, and is fragmentary; however, Hegel’s criticism is more clearly expressed in his later mature writings (HET, p. V). Hegel eventually rejected the hypothetical Kantian Christ as non-historical (negative) that eventually devolves into the same pharisaic legalism that Jesus originally tried to liberate his followers. Kant’s pure moral rationalism is negative and rejects all historical (positive) elements as merely accidental, or non-essential to religion (Ibid., p. 5).

 

Hegel was dissatisfied with Christianity in his era that reduced itself to a mass collection of statues, dogmatic doctrines, and superfluous creeds. While still heavily influence by Kantian moral rationalism at the age of twenty-five, Hegel wrote, “In The Positivity of the Christian Religion” (The first two parts written in 1795-96, and part III in about 1800) in which he traces the internal problems of Christian orthodoxy to the historical context it emerged. A strict monastic Judaism, and a brutal Roman Empire were the forces that shaped Christianity echoing through the ages:

 “While Jesus aimed at a purely moral religion and fought against superstition and positivity, he could not help generating a church by positive means. He was bound to connect respect for the holiness of moral law with respect for the holiness of his own person. Thus the seed of ecclesiastical authority and of the positivity of all religious forms and institutions was planted. This is the tragic origin of the Christian church (HET,p. 4).”

Antithesis: Hellenistic Humanism with Kantian Rational Ethics

Hegel idealistically viewed Greek folk religion as one of freedom, “imagination and enthusiasm” as opposed to a inhuman clerical bureaucracy of rules that is “the religion of Enlightenment dominated by reason (HET,p. 3).” Hegel believed religion should be about this world and centered about the Greek notion of beauty, freedom, wisdom, and artistic imagination. Hegel still held onto to Kant’s rational ethics of positive moral action (actualization). 

Then suddenly in 1796 after moving from Bern to Frankfort, Germany, Hegel became more influenced by the Romantic philosophers such as Schleiermacher, Fichte, Schelling, and Holderlin and then published his views in the essay, “The Spirit of Christianity,” reversing his former position by reaffirming the need for a historical (positive) Christianity. Now as a mystic Hegel created a new synthesis of Greek humanism, and Kantian moral philosophy which itself has a deep kinship to Judaism:

“The soul of Greek religion is beauty; the reason of Kantian philosophy is morality. Hegel concluded that ultimate truth was moral beauty, and this truth he discovered in the Gospel. The moral principle of the Gospel is charity, or love, and love is the beauty of the heart, a spiritual beauty which combines the Greek Soul and Kant's Moral Reason. This is the synthesis achieved in The Spirit of Christianity (HET,p. 25).”

 

Synthesis: Pantheism of Love

"What is a contradiction in the realm of the dead is not one in the realm of life." 

--Hegel, HET, p. 261. 

But once again truth is discovered to only be pretended truth. These three worldviews of Hellenism, Kantianism, and Judaism had an other-worldliness. Judaism and Kantianism were “monarchical theism” while Hellenism was polytheistic, pantheistic, combined with Stoicism. Hegel believed, “…Jesus teaches a pantheism of love which reconciles Greek pantheism with Judaic and Kantian theism (HET, p. 10).”

The internal contradiction of Hellenism and Kantianism are synthesized by Hegel with the Gospel of Jesus to create a ”Pantheism of Love,” (ibid., p. 10). The unifying Gospel of love overtakes atomizing alienated reflection. Christ represents now a non-rational ethics, but a more powerful unsystematic non-conceptual “ethics of Love.” Hegel believed that this newly synthesized pantheism of love reconciles the disunity of  “one-sided rationalism, one-sided emotionalism, or one-sided empiricism.” Even in Hegel’s philosophical development we see the same pattern repeatedly emerge beginning with an original organic unity (thesis), then disunity (antithesis) that moves on to temporary reconciliation (synthesis). 

Antithesis: The Pantheism of the Logos 

Unfortunately, love is not enough…to bridge the alienating chasm between life (existence) and thought (essence). The spirit of Christianity has historically continually fallen into the trap of objectifying itself into a dogmatic faith of doctrines and creeds instead of a living community of universal spiritual love. After about 1796 Hegel undergoes yet another paradigm shift that provides a more scientific (methodologically systematic) approach to philosophy that recognizes the dialectical patterns created by the interplay of logical oppositions in thought and actual history. With this new methodology Hegel still retains pre-Socratic Hellenistic influences in the form of Heraclitean cosmology where all things material and immaterial emerge out of conflict and change in accordance to a single Logos, or Reason. The Romantics were seemingly pushed out of the system, but they still heavily influenced Hegel’s thinking within this new synthesis that attempted to unify Romantic spirit with logical analysis.

 “…ultimate unification was to be brought about by a rational rather than a Romantic method. While the Romanticists were content with denying ultimate separation, indulging in pictorial language and paradoxes to give force to their negation….The original unity of all things is for him not the object of a mystical or poetical intuition but a truth discovered by logic (HET, p. 15).”

Yet, this ultimate conceptual unification still contains within it different stages of human mind, or consciousness (Enlightenment, Romanticism, Ethical, Religious) presented in Hegel’s later 1807 Magnum opus, “The Phenomenology of Spirit.” These same familiar internally conflicting frame of minds, or shapes of consciousness are reconstructed by phenomenological description as “self-certain Spirit (para. 166),” “unhappy consciousness (para. 197),” “self-alienated Spirit (para. 487),” and “the beautiful soul (para. 632).” These multiple states of consciousness can be found at anytime among persons in many cultures today, and maybe even especially today. According to Hegel the Logos (Reason) can guide consciousness down the road of historical experience to a conceptual unification of Existence and Essence, the Whole and the Parts, of the Infinite and the Finite. 

Reading and rereading Dr. Richard Kroner’s introduction with these theological texts not only provide endless insights into Hegel’s own thought, but also give insight into other philosophers (Marx and Kierkegaard) who imitated and critiqued Hegelian Absolute Idealism.

The Struggle Against Solipsism

 The Struggle Against Solipsism

”Finite players play within boundaries; infinite players play with boundaries.”—James P. Carse, “Finite and Infinite Games,” p. 10.

The critique of Positivistic ideology is complex and technical, but it can be introduced as a relatively clearer critique of Solipsism. Solipsism can be a “presentation concept” to frame this discussion for critiquing science and technology. One cannot logically and consistently accept—or reject for that matter-- Positivism as the paradigm of scientific objectivity, and then reject a critique of Positivism as too abstract because these abstractions are already contained in Positivism’s methodology.

The critique of solipsism was one of Wittgenstein’s goals in writing the Tractatus by showing the limits of language just as Kant demonstrated the limits of Reason in The Critique of Pure Reason. For Wittgenstein language is only meaningful when connected to the world of empirical facts, just as for Kant we can only know the world of experience through the categorical lens of space and time. Both philosophers critiqued solipsism as a symptom of overly reductionist philosophies.

“The solipsist’s predicament is that, when he denies the existence of everything except himself and the world of his own experiences, he is unable to point to what it is that, according to him, does not exist, because it lies outside his world…he is like a man who carefully constructs a clock, and then attaches the dial to the hour hand so that they both go round together. There is no contrast with anything outside his world…( Ludwig Wittgenstein by David Pears, (Penguin),(1970), p.74).” 

Wittgenstein in showing the limits of factual discourse faced the same problem except he cannot say whether a named object exists or not exist because their names are only names-- the objects are the meaning of a name. So he faces the same boundary as the solipsist: he is unable to name objects that do not exist.

“…only certain things exist, but that they exist is something that cannot be said. It can only be shown, and the solipsist’s mistake is to express it in a factual proposition…. [The Subject, or observer] is only a metaphysical subject, which is a kind of focal vanishing point behind the mirror and what the mirror reflects. So the only thing that he [Wittgenstein] can legitimately say is that what is reflected in the mirror is reflected in the mirror…but this is…only a tautology. It means only that whatever objects exist exist. So when solipsism is worked out, it becomes clear that there is no difference between it and realism (Ibid., p. 74)." 

 

1. The world is all that is the case.—Wittgenstein (Tractatus)(pdf.)

 (∀x)Wx

“For all x, x is the world.” I think this notation captures Wittgenstein’s meaning, but this proposition could be stated in another way just as it could be stated in ordinary language. For example proposition “1” could be symbolized as (x)(Wx ⊃ Cx).  However, the actual case could also be the “world,” so that the expression could be propositionally stated as the following:

 (x∀)[(Wx ⊃ Cx)] ⊃ (x∀)[(Cx ⊃ Wx)]

“If the world is all that is the case, then what is the case is the world.”

But is the predicate nominal  “W =  is the world,” just another object, or is it a constructed unity of relations?  In other words, the capital letter “W” (the predicate, or property constant used in Predicate Logic) is being used to denote both relational and non-relational properties. “All that is the case” include relations. Wittgenstein said, "Situations can be described but not given names." (3.144). Therefore, since a relation cannot be named, it cannot be an object. There are other propositions in the Tractatus that builds states of affairs from the concepts of Objects, states of affairs, and facts (2.01-2.0141), see Wittgenstein On Objects. However, he must have other propositions about states of affairs and facts because the one proposition “The world is all that is the case,” is inadequate in itself.

“...the conjunction (conjunctio) of a manifold in intuition [the many kinds of sense experiences] never can be given us by the senses; it cannot therefore be contained in the pure form of sensuous intuition, for it is a spontaneous act of the faculty of representation [of the self].”—Kant, Critique of Pure Reason, p. 94)(pdf.).

How would the logical expression be written to imply that “the world” is a constructed unity of relations? The logician would say that the expression “for all x,” or (x∀) means whatever it can be expanded or quantified to—a very long conjunction of “ands”, (Wa and Wb) and (Wc and Wd) and (We and Wf), and so on. 

This task would only be possible if 1.) There were a finite number of entities in the real universe. 2.) We had a name for every entity in the real universe. However, the real world has a non-finite number of entities so such as long conjunctions of “ands” would be impossible to complete.

Take for example the proposition “Every Even Number is Divisible by 2.” Writing out the conjunction would be an endless chain of “ands” (symbolized with * asterisk), as in the proposition, [(N1 * N2 * N3….) * (E0 * E2 * E4….)]. The universal quantifier (∀x) “for all x” is necessarily exclusive so that we can only symbolize the even number proposition as the following: 

(∀x)[(Nx * Ex) ⊃ Dx] 

"Every even number is divisible by two.”

Sometimes symbolic logic is so minimalist, and so simple that it is difficult to comprehend. A problem of logical symbolization translates into metaphysics as the problem of solipsism. The symbols of logic can only operate in a finite world of entities; those entities that we can name, and yet this is an operationally impossible task due to computational explosion. What is the name of that which we cannot name? "Noumenon” from ancient Greek νοούμενoν means "something that is thought," or "the object of an act of thought." The shorthand of language and logic excludes much of what we call the world due to reductionist tendencies of symbolic systems. Kant names this existential residuum the thing-in-itself, or Noumenon. Kant is using the term noumenon to mean that the thing-in-itself cannot be known in principle, and not as an object yet undiscovered. Solipsism insists that only one’s own experiences are real, and the appearances, or phenomena represent the whole of the reality, i.e., of what is the case. 

"5.64 Here it can be seen that solipsism, when its implications are followed out strictly, coincides with pure realism. The self of solipsism shrinks to a point without extension, and there remains the reality coordinated with it.

5.641 Thus there really is a sense in which philosophy can talk about the self in a non-psychological way. What brings the self into philosophy is the fact that 'the world is my world'. The philosophical self is not the human being, not the human body, or the human soul, with which psychology deals, but rather the metaphysical subject, the limit of the world--not a part of it (Tractatus)."

This constellation of sixty five essays have at some point or another touched on many of the philosophical issues discussed by Chomsky in the newly posted video below. 

I found another very interesting new video dialogue between Dr. Veveake, Dr. James Carse, at the Stoa hosted by Peter Limberg. I am reading Dr. Carse's book "Finite and Infinite Games: A Vision of Life as Play and Possibility,"(1986) and must say it is a very, very good example of dialectical reasoning joined with phenomenological description. I would place myself on the infinite game player team!

Noam Chomsky: Science, Philosophy, Morality, & Anarchism (Interview)

Playing the Infinite Game During the Meaning Crisis w/ James Carse and John Vervaeke

An Existentialist Interpretation of the Last Scene of Fellini’s Film, “La Dolce Vita.”

An Existentialist Interpretation of the Last Scene of
Fellini’s Film, “La Dolce Vita,” (“The Sweet Life”)(1960)

“It’s a monster! It’s been dead for three days!”—Partygoers shout after discovering a giant bloated stingray fish on a beach.

The dead stingray represents spiritual death, nihilism, alienation, and the state of falleness of a particular state of human consciousness. There are other terms of this mode of human existence the Existentialist philosophers use to describe this shape of consciousness such as the “they,” or “Das Man,” (The ‘averageman’) and as “inauthentic existence.” All these words attempt to name a form of personal consciousness that is not “owned” by itself, but lacking self-responsibility while self-deceptively seeking refuge from the anxious uncertainty characteristic of human freedom in its struggle for complete self-actualization. All of these phenomenological concepts are very abstract and material examples, which this film provides, are very helpful for giving them intelligible content. “Phenomenology” is the science of appearances, or φαινόμενον, the Greek term for “phenomenon” meaning to bring to light, make to appear, to show, combined with λόγος, ”logos” of which one of its meanings is study “of the subject,” as in “anthrop-ology.”

I have written about Heidegger’s philosophy before in a more formal way in the essay, “Dasein Analytic.” Writing about authentic and unauthentic Being requires a different kind of thinking that is richly expressive, which can put living flesh back onto these abstract reductionist concepts that attempt to illuminate the essential structures of human existence. Fellini’s film makes this kind of analysis much easier, fun, and even more relevant.

The film’s main character, Marcello Rubini, is a writer for Italian gossip magazines during the 1960s and is gradually pulled into, but also attracted to, the “sweet life” (“dolce vita”) of wealthy high society circles in Rome. This being one of Fellini’s most famous films, La Dolce Vita, is divided into seven episodes each tracing Marcello’s desperate effort to escape himself ending in the last scene on an Italian beach where he is on the verge of having insight into his own existence. Marcello represents a necessary and essential existential stage of human ‘mind,’ or ‘spirit’ (the German term ‘Geist’ has both meanings) that suffers from the anxiety of human existence. In an effort to escape, he embraces pleasure as an end in itself. Hegel quotes Goethe’s play “Faust” to describe this individualistic hedonistic consciousness aimed at fulfillment of desire as its only purpose in the Phenomenology of Spirit (paragraph 360):

“Instead of the seemingly heavenly spirit of the universality of knowing and doing in which the feeling and the gratification of singular individuality fall silent, the spirit of the earth has entered into it, a spirit to whom the only being which counts as the true actuality is that of the actuality of singular consciousness.

It despises intellect and science 

Man’s highest gifts – 

It has given itself over to the devil, 

And must perish”

A stingray is sometimes called a devil fish. For Heidegger, the character of Marcello would epitomize the average man, or the public “they” of all other human beings. In, Being and Time (1927)(pdf.), Heidegger wrote, “The ‘they’ has its own ways in which to be. That tendency… is grounded in the fact that Being-with-one-another concerns itself as such with averageness, which is an existential characteristic of the ‘they’ (Being and Time, p.164).” Heidegger’s phenomenological analysis of consciousness characterized this hedonistic mind—the spirit of the earth--as the self that allows the average-everydayness of an anonymous public “they” to prescribe “…one's state-of-mind, and determines what and how one 'sees' (Ibid., p. 213).” The concept of “seeing” plays an essential part of the person given over to endless hedonistic search for pleasure in the forms of spectacle, and novelty to achieve some sense of a substantial life; a world in which the subject (person) takes for granted they belong and are freely a part of that world.

Curiosity, Looking, and Seeing of the “They”

 “Even at an early date (and in Greek philosophy this was no accident) cognition was conceived in terms of the 'desire to see’.”--(Being and Time, p. 214)

Heidegger uses other words for special kinds of sight or seeing using his clever etymological kinship studies such as 'Umsicht' meaning “circumspection” for example (Ibid., p.159, Footnote 3). Sight (‘Sicht’) is the ability to see, or vision. On the other hand, seeing (‘Sehen’) is the ability to comprehend, recognize, and understand what is seen. In the English language, sight without seeing can mean, “looking” as when one says, “I am looking for the beacon, but do not see it!” or “I saw him, but did not recognize my old friend.”

These distinctions are important for understanding the particular way that the hedonistic self continually seeks seeing, but without comprehension. This particular “I” consciousness relates itself to the world in a mode of Being called “curiosity.” Heidegger describes this comportment of inauthentic human existence:

“The basic state of sight shows itself in a peculiar tendency-of-Being which belongs to everydayness-the tendency towards 'seeing'. We designate this tendency by the term "curiosity" [Neugier], which characteristically is not confined to seeing, but expresses the tendency towards a peculiar way of letting the world be encountered by us in perception (Ibid., p. 214).”

Historically, science is understood as having its genesis in the desire to see, but within inauthentic Being consciousness distracts itself from the issues of its own existential meaning. Seeing is a release from anxiety for inauthentic Being, but it fails to have understanding and comprehension for the person is only seeking sensation, or merely engaged in voyeurism. Voyeurism is one way consciousness abandons the world by superficially embracing the world.

“When curiosity has become free, however, it concerns itself with seeing, not in order to understand what is seen (that is, to come into a Being towards it) but just in order to see. It seeks novelty only in order to leap from it anew to another novelty. In this kind of seeing, that which is an issue for care does not lie in grasping something and being knowingly in the truth; it lies rather in its possibilities of abandoning itself to the world (Ibid., p. 216).”

This kind of seeing is only one form of an idolatry of perception; another being natural-scientific reductionist empiricism in which perception is assumed to be immaculate, or received as purely objective without acknowledging the shaping influence the grasp of consciousness has on our experience. This school of empiricism then attempts to use its credentials as science to become a philosophy of life leading to the violation of human values with disastrous consequences.

One film reviewer summed up the character of Marcello as "detached." I used the term "alienation" to describe him, but Marcello is too detached to be alienated. All of the characters in the movie are ghosts, including two murdered children, in the sense they have an exterior appearance mirroring an internal struggle for spiritual meaning, for a substantial life, for a happy life.

In this mode of Being existence is “ambiguous” making it “…impossible to decide what is disclosed in a genuine understanding, and what is not (Ibid., p. 217)." Ambiguity is the inability of the self to distinguish between the authentic and unauthentic, between the substantial and unsubstantial in one’s own life, Others, and the world. Ambiguity is ignorance that signifies modal confusion. Like the dead devil fish monster on the beach, Marcello can look, but he cannot see.

Chatter and Idle talk

Heidegger describes as inauthentic the hedonistic individual consciousness oriented toward pleasure, superficial seeing; insincere averageness lacking depth; and endless curiosity that divides itself into infinite individual moments in which the fractured self loses its identity. These attributes are named “existentials,” and refer exclusively to the essential structures of human existence, and not to objects. Heidegger adds yet another existential,” named, “chatter” as a particular degenerated form of human discourse that has no understanding, and is just “Idle talk” based on conventional uncritical opinions functioning as yet another escape mechanism to avoid thinking, risk, and responsibility. Chatter filibusters any real commitment to a meaningful life such as this gossip columnist’s endlessly journey skipping from disconnected media event to media event:

“Idle talk is the possibility of understanding everything without previously making the thing one's own. … Idle talk is something which anyone can rake up; it not only releases one from the task of genuinely understanding, but develops an undifferentiated kind of intelligibility, for which nothing is closed off any longer…idle talk discourages any new inquiry and any disputation, and in a peculiar way suppresses them and holds them back (Ibid., p. 213)."

The Second, “Second Coming”

"The waking have one common world, but the sleeping turn aside each into a world of his own (idios kosmos)." "Hearing they do not understand, like the deaf. Of them does the saying bear witness: 'present, they are absent.’ “--Heraclitus

For the Greek word “idios,” the term “idiot” is formed to mean a private “individual,” and “kosmos” meaning “cosmos” or “world.”

Marcello and his party crowd stumble out of a beach house after enduring a boring night-long half-hearted orgy—I just hate those! They spill out into the beach parking lot and hear men calling out in surprise as they pull a giant string ray fish onto the shore. One fisherman suggested to the exhausted orgy partiers the fish could be sold for a large profit. This last scene’s “Second Coming” of the Devil Fish is as sarcastic as the first scene’s return of Jesus as archaic symbolism.

At first, the party mistake the stingray dragged up in the fishermen’s net as being alive, but the fishermen knew it had been dead for three days. Dead for three days: Lent fasting is during the six weeks before Easter, after the Carnival orgy. This moment carries for Marcello only the possibility of insight into authentic existence: an Either/Or moment of existential decision.

Marcello displays utter disgust and contempt for the alien creature which in turn encourages the others to mock the rotting inhuman corpse with its eyes wide open staring at the crowd; without any empathy, a smirking Marcello takes great pleasure speaking for the crowd declaring, “And it insists on looking.” Marcello is smirking at himself while summing up his own spiritually dead meaningless life.

The hedonistic nihilist mode of Being, “…experiences the double meaning implicit in what it did, viz. when it took hold of life and possessed it; but in doing so it really laid hold of death.”--Phenomenology of Spirit, paragraph, 363.

The hung-over and exhausted Marcello wanders to the side of the crowd, and as he sits down on the beach, he hears a voice calling; a voice in the distance across an estuary where a river divides the beach and pours out into the open ocean. But Marcello is unable to hear the young girl, or understand what she is trying to say to him as the ocean waves drown out her voice.

For Marcello the “…pleasure enjoyed has indeed the positive significance that self-consciousness has become objective to itself, but equally it has the negative one of having reduced itself to a moment…its experience is of a contradiction in which the attained reality of its individuality sees itself destroyed by the negative essence confronting it, which is devoid of reality and content, and which yet is the power which destroys it…the poorest form of self-realizing Spirit….(Ibid., para: 363).”

Marcello is kneeling on the beach facing the angelic young girl as she calls out to him. He does not recognize her as the young waitress named Paola he encountered in a seaside restaurant days earlier. Marcello was working on a book while Paola hummed along with the jukebox. Marcello told Paola she reminded him of an angel in an Umbrian painting. Painter Raphael is the most famous painter of the High Renaissance Umbrian School of Art. “Paola” (Pow-la) is the Italian and Spanish feminine form of the name “Paul” which in this context has a religious meaning pointing to the appearance of Christ symbolizing the Substantial Life.

Scientific and unscientific symbolism shares a common ground in a wonderful synthesis of thought and existence, of Being and consciousness. The two different elements of Language that bears the power of logic, and Mythic-Symbols are unified by metaphor (Language and Myth, Ernst Cassirer, 1948). However, for Marcello all symbolism has lost meaning having been reduced to curious isolated images, and odd trinkets unable to point beyond themselves to truth: without truth, Marcello has no possibility of freedom. This is not a tautology. A person is not truly free if rational decisions of choice cannot be made by independent knowledge. Marcello’s consciousness makes it impossible for him to achieve any Great Awakening.

Marcello suffers forgetfulness, of a sense of loss, and the sense of having a debt outstanding. He is on the spiritually dead side of the mythological river of λήθη (Lethe) meaning “forgetfulness,” or “oblivion.” The souls entering the mythic Underworld of Hades drank from the river Lathe to forget they were dead. The letter ἀ is a negative prefix, or alpha privative. The Greek word for "Truth" is ἀληθείᾳ (a-lethea) that means the negation of forgetting, or “remembering.”

According to Johannine Christology the Logos has a face. Marcello is unable to recognize a substantial life even as it is disclosed to him as the face of the Other.

Parody only reinforces the Holy. This film was understandably criticized by the Vatican, and unfortunately banned in many states for parodying the second coming of Jesus; but below the surface of cultural symbolic imagery the film is actually very religious in its attempt to reach for a spiritual dimension in a negative way; however, it may not have been intended by the film makers. The first words for religion must be words against religion the Christian Theologian, Paul Tillich, counseled religious thinkers.

Great Professors on the Internet

Appendix B 

B1

Husserlian Phenomenology: The Possibility of the Science of Essences

For an in-depth and technical explanation of Edumond’s Husserl’s phenomenological methodology, see Dr. Mark Thorsby’s lectures. Thorsby goes through Husserl's introduction to phenomenology in "Ideas" (pdf) section by section. In "Ideas " (section, 19, or pdf., p. 29) Husserl gives a powerful critique of naturalistic empirical positivistic methodology and its assumptions (Naturalistic Misinterpretations video @ 11 min. 43). He presents a good summary to the different types of phenomenologies. 

I have attended course lectures by Phenomenologist, Dr. Jitendra Mohanty, on Husserl’s critique of psychologism and the epistemological problems of naturalistic scientific empiricism. Dr. Thorsby gives an excellent lecture on this fundamental issue underlying all cognitive science, logic, and mathematics (Part II). Also, he teaches a complete symbolic logic course in another series of free videos on his channel. 

Phenomenology is the most radical form of empiricism for it describes the living stream of experience in meaning-reality; however, no pure phenomenological description is possible.

Mark Thorsby: Part I on Phenomenology: Types of phenomenology.
The Encyclopedia of Phenomenology (Kluwer Academic Publishers, 1997) features separate articles on the following seven types of phenomenology.

1. Transcendental Constitutive Phenomenology: studies how objects are constituted in pure or transcendental consciousness.

2. Naturalistic Constitutive Phenomenology: how consciousness takes in the world of nature.

3. Existential Phenomenology: studies concrete human existence.

4. Generative Historicist Phenomenology: studies how meaning is generated in historical processes of collective experience over time.

5. Genetic Phenomenology: studies the genesis of meanings of things.

6. Hermeneutic Phenomenology: studies interpretive structures of experience.

7. Realistic Phenomenology: studies the structure of consciousness, assuming a real world.

Appendix B2

Don’t forget about the Good Professor, Dr. John Vervaeke! I watch all of his videos. His monthly Question and Answer session for April, 17, 2020 is particularly good because it succinctly contains much of the content of his lectures and discussions during the last few months.

Each video lecture gets clearer and more concise on the themes of idolatrous objectification, self -deception, consciousness, paradigm entropy, the Logos, phenomenological existentialism, Kairos, Wisdom, dialectical meaning epistemology, Being Modes, and Mythic-Poetic thinking. 

I go crazy with excitement whenever he mentions Paul Tillich because his systematic theology unifies all those philosophical methodologies that we have been studying. Dr. Vervaeke incorporates the methodologies of Dialectics (Heteronomy vs. Autonomy), Critical Science (Kantian Criticism), and phenomenology (Heidegger, Tillich) in his scientific studies that require clear expression and terms. The professor's working vocabulary reminds me of the careful use of language by Husserl in his 1913 book introducing phenomenology, Ideas (pdf).

Appendix B3

Dr. Cornel West On Being A Revolutionary Christian 
April 23, 2020

Appendix B4

The Philosopher’s Stone

Dr. John Vervaeke discusses Carl Jung with cognitive scientists and practicing psychotherapist Anderson Todd who also teaches courses at the University of Toronto.

Speaking of synchronicity….

Todd demonstrates the use of all three methodologies of dialectical reasoning, critical philosophy, and phenomenology while discussing Jung and other philosophers. In addition, he integrates historical empirical research of past proto-cognitive science and classic philosophy. In other words, Anderson Todd is way ahead working on rich philosophical grounds.

I first encountered this concept of synchronicity in Fyodor Dostoyevsky’s novel Crime and Punishment as ‘coincidence,’ and never seriously researched the concept further. Todd has an insightful and plausible interpretation of synchronicity. Synchronicity could also be understood as an experience of paradigmatic induction: the formation, or re-enforcing, or a weakening re-interpretation (thus inducted) of an ontological paradigm. Reason always demands coherence and completeness. A ‘coincidence’ is remembered and highly selective, but not meaningless. Coincidence can be a metaphor for transcendence. Is this a paradigmatic circularity any rational person can escape?

Also, I wondered why Isaac Newton spent many years experimenting with alchemy: he was not a gold speculator, but searching for something more valuable—the philosopher’s stone and the elixir of life. Rarely, is this side of Newton discussed. The alchemist is experimentally applying the categories of reason (Spirit) to matter, and attempting the reverse.

I am still holding on to the concept of telos, as “ethical telos,” or the “telos for the divine double,” seeking relevance realization, and transformative experience, which is compatible with historical telos, but not the Cold War trope of deterministic historical teleology.  

Appendix B5

The Book People

That ending scene from Fahrenheit 451 is so frightening, and so beautiful.

Eventually, I will link up each appendix to a specific topic in this strange collection of essays. And I wrote them: you can see all the spelling errors as evidence!

Contemporary books on phenomenology are expensive, and so most of my studies focus on primary sources, free online libraries, and my own small book collection. I have found YouTube’s online lecture series freely contributed by scholars, universities (St. John’s College Nottingham, NYC Union Theological Seminary, Goethe-Institute), and philosophers to be very good quality.

There are online lectures on Husserl, and Heidegger given by some of the scholar mentioned already in the other appendixes: Dr. John Veraeke, Dr. Gregory B. Sadler (I finally made it to Lordship and Bondage in Phenomenology of Spirit), Dr. Mark Thorsby (also goes to primary texts of Husserl and Heidegger with expert commentary), and Dr. Johannes A. Niederhauser.

Since contemporary books on Heidegger are so expensive, and I don’t read the German language, my knowledge of the later Heidegger is relatively weak. Dr. Johannes A. Niederhauser insightfully speaks in the language of the later Heidegger and is particularly helpful explaining his further philosophical development. Heidegger’s complete writings are massive in volume.

Lecturer Eric Sean Nelson, formerly at University of Massachusetts Lowell before locating to China, gives a lecture on the later Heidegger and his studies of non-Western religions. Paul Tillich also was doing the same type of exploration of other religions during the 1950s meeting with Daisetz Suzuki and Shin’ichi Hisamatsu to discuss Japanese Buddhism in New York and Kyoto, Japan at various times (Cambridge Companion to Paul Tillich, p. 254)(pdf).

The later Heidegger thought philosophy should be replaced by discourse. The Ancient Greeks had no word for language, but instead used the term "διάλογ-ος “ meaning “dialogue,” “conversation,” “debate,” or “argument.”

Philosopher Hannah Arendt was alive when phenomenology became a philosophical school of thought, and commented that it was “a time when talking became alive.” I think I know what she meant. 

This lecture by Eric S. Nelson ends at 54 minutes, but the question answer period is excellent also.

Husserl and Heidegger: Phenomenology, Eurocentrism, and Buddhism

Appendix B6

The Swimmer (1968)

 (Full movie)

"The smallest thing could give you away. A nervous tic, an unconscious look of anxiety, a habit of muttering to yourself -- anything that carried with it the suggestion of abnormality, of having something to hide. In any case, to wear an improper expression on your face (to look incredulous when a victory was announced, for example) was itself a punishable offence. There was even a word for it in Newspeak: facecrime, it was called."—George Orwell, Nineteen Eighty Four, Chap. 5

The moral of the film is complete self-deception destroys the concept of Truth itself.

This very literary story was first written by John Cheever as a short story appearing in the The New Yorker magazine in 1964.

“The Swimmer” is about self-deception in American society during the heyday of capitalist growth and the extreme optimism that characterized the American mind. This frame of mind, or the shape of consciousness, in this era of suburban expansion and post-War II domination of the world economy was the Neo-liberal free market ideology beginning to emerge as unquestioned conventional knowledge.

We can see today’s corporate culture, which I have experienced, as motivational positive thinking pop psychology to manipulate people into conformity and to enforce ideological harmony masked by a cheerful fake veneer. This unrealistic optimism is strongly pointed out in the film. However, this consciousness is complete self-deception and delusion. Corporate positive psychology instills a false enthusiasm and happy conformity that denies truth itself not unlike Chinese Maoist revolutionary joyful extremists. Notice the excessive smiling of the characters which we see in North Korea. Excessive smiling has even become a syndrome for some Japanese businessmen. Face crimes are serious in authoritarian environments. Ned Merrill, the movie’s protagonist, is a wealthy, middle-aged advertising man trying to “swim” to his home in suburban Connecticut by skipping to his wealthy neighbors’ swimming pools along the way while ignoring the truth exposing his delusions and unconscious lies with his socialite friends, and ultimately with the film viewers. Ned lives a life of complete contradiction. Listen carefully to the dialogue as the truth will sometimes slip out. 

The dead in the Underworld would drink from the mythological river Lethe in order to forget they were dead.

In ancient Greek, λήθη (Lethe) means “forgetfulness,” or “oblivion.” Those that drank from the river Lethe would become oblivious to their true state of Being. The letter ἀ is a negative prefix, or alpha privative. The Greek word for "Truth" is ἀληθείᾳ (alethea) meaning the negation of forgetting, or knowledge is remembrance (early Plato). 

Most people have heard of Hegel’s famous “Thesis, Antithesis, Synthesis” dialectical tirade of thought and historical change, but what is often not mentioned is that the suffering of self-delusion, or illusion of consciousness struggling with itself. This agony and spiritual internal violence is a central concept of Hegel’s historical account of the evolution of consciousness in time. Because of these internal contradictions Ned is unconsciously forced to seek unity in his fragmented life by swimming in each of his neighbor’s pools until reaching home. His journey isn’t a river as he images for rivers are a unified whole. The swimming pool is the human conception of nature’s Walden pond except that 99.99 percent of impurities are filtered away. Self-deception is easy to embrace because of our desires, but a difficult state of mind to escape. Both Ned, and the film viewers will reach what is known in Hegel’s thought as emerging self-consciousness at the end of Ned’s journey of untruth to truth.

Ned first appears in the film walking alone in a forest nearly naked, only wearing a bathing suit. Is he Adam exiting the Garden alone as post-lapsarian man?  Or is Ned the free Rousseauan “state of nature” good human being that transforms into an impostor by life’s shaping internal and external forces? This analysis could be developed further.

This is not a true story, but as myth it is the truest story.

I chose “The Swimmer” for review because of the current pandemic, but also this film as been interpreted by some as a critique of “postmodernism” which it clearly is not, but rather about the individualist social paradigm in American capitalist society.  Some of the postmodern interpretations make many of the same conceptual errors and fallacies identified in my last polemical essay titled, “The Ayn Randian Propagandistic Trope Concerning Postmodernism.”