WHAT EVER HAPPENED TO
TRUE/TRUTH/ Revival of Truth in Our Postmodern Culture (Cultural Consequences
of the Epistemological Paradigmatic Revolution)

**A. Correspondence Theory of Truth**

The dominant Theory of Truth in western thought has been the Correspondence Theory of Truth. The essence of this theory of truth is that Truth corresponds with fact and is both absolute and objective (i.e., the observer does not modify the data in the observation process).

**B. Coherence Theory of Truth**

The Correspondence Theory of Truth is frequently understood
to be in classic opposition to the absolute Idealists who understand truth as
coherence. Essentially, this theory
maintains that the more systematically coherent our beliefs are the truer they
are (see Alan R. White, "Coherence Theory of Truth", __The
Encyclopedia of Philosophy__ 2:130-133).

If a system of thought does not contradict itself, then it is a mark of truth. The classical Aristotlean "Law of contradiction" (two valued logic-propositions are either right or wrong. If they contradict one another, one of them is false. Note also the development of pluralistic-dialogical reasoning which challenges the "Law of the Excluded Middle”). The central weakness of The Coherence Theory of Truth is that it is conceivable to have two coherent systems that are in direct contradiction with each other (eg. Euclidian Geometry and non-Euclidian Geometry; e.g. systematic consistency of paradigm A and its conflict with paradigm B which is also internally consistent (alternative World Views and the possibility of cross-paradigm communication).

**C. Pragmatic Theory of Theory**

Another classical theory which denies the validity of The
Correspondence Theory is the pragmatic theory.
This theory argues that which is "true" is that which "works." The Pragmatic Theory of Truth offers a
"function" attraction for effectiveness that is highly valued in our
Postmodern culture. The essence of this
theory is that it claims that the end justifies the means (cf. a la leaves the
question of morals unattainable unless morals becomes justified by their
effectiveness. This view precipitated
Hitler's genocide and contemporary issue of Biological Ethics and high
technologies capabilities—"Could" vs. "Should." No one has ever empirically seen a
"could" but "effective capabilities" is observable). This theory precludes any rational
adjudication between alternative and/or contradictory moral possibilities (cf.
see Empiricist Rationalist Emotivist in chapter 15 of __The Handbook on Christian
Apologetics__ (Kraeft/Tacelli - IVP,
1994, and my Demise of True Truth, The existence of Alternative Theories of
Theory helps demonstrate that Pilate's question, "What is truth?" is
still an ultimate question.

**D. The Existence of A Pluralism of Views of
"Truth"**

The statement continues to suggest that the question of the nature and availability of reality is still a crucial issue. In our Postmodern culture the question has shifted from "What is truth?" to "Is there truth?"

A cultural addiction to "pop attitudes" toward these
questions is expressed by George Barna's account that 66% of all Americans deny
the existence of absolute truth (Barna, __What Americans Believe__. Regal
Press, 1991, p. 83). What intellectual factors have contributed to this
devaluation of truth? Our Postmodern guru, Peter Berger, has suggested three
dominant sociological trends in our culture that have shaped the demise of “True
Truth”: (1) Secularization, (2)
Pluralism, and (3) Privatization (cf. Berger, __Sacred Canopy__,
Anchor/Doubleday, 1969 and Robert Withnow, __The Struggle for America's Soul __(Eerdmans,
1989). (Berger's criticisms reflect
results, not causes of the loss of Truth.)

**E. Secularization**

Secularization is the process by which "sectors of
society and culture are removed from the domination of religious institutions
and symbols." (Berger, __Sacred Canopy__, p. 107 and Martin Marty, __The
Modern Schism__. SCM, 1969). Richard
J. Newhous declares that we live in a "naked public square." R. J. Newhous, __The Naked Square__.
Eerdmans, 1984. Presently morality and
truth are in the hands of media. The
shaping medium does not ell us what to think but it tells us what to think
about (G. Barna, __The Frog in The Kettle;
What Christians Need to Know About Life in The Year 2000__. Regal,
1990, p. 53). Secularization has removed the truth of the Gospel from the
world's public dialogue. "God is
not a proper topic for conversion but lesbian politics is in our politically
correct culture (Page Smith, __Killing the Spirit: Higher Education in America__
(NY: Viking Press, 1990, p. 5; see also Allan Bloom, __The Closing of The
American Mind__ (NY:

Simon/Schuster, 1987.

**F. Privatization**

Berger defines radical individualization or
"privatization" in the following words: "Privatized religion is a matter of the
"choice" or "preference" of the individual or the nuclear
family, ipso facto lacking in common, binding quality. . . religiosity
secularized sections of modern society." (__Sacred Canopy__, pp.
133,134; compare Berger and Hans Keilner, __The Homeless Mind__. Penguin,
1974, chp 3; see my "Loss of Transcendence in Interpretive Categories in
Our Postmodern Culture").

Oz Guinness defines privatization as that "process by
which modernization produces in society a cleavage between the public and the
private spheres of life and focuses the private sphere as the special arena for
the expansion of the individual freedom and fulfillment (Guinness, The Gravedigger
__File; Powers in The Subversion of The Modern Church__ (IVP, 1983, p. 74;
see also his __Dining with The Devil__; Robert Bellah, et. al. __Habits of
The Heart__; __Individualism and Commitment in American Life__.
Harper/Row, 1985; Phillip L. Berman, __The Search for Meaning: Americans Talk
About What They Believe and Why__. Ballentine, 1990; see my "Changing
Paradigms of Meaning".

Privatization makes the Christian faith (any faith)
"socially irrelevant even if privately engaging." (Theodore Roszak, __Where The Wasteland Ends__.
NY: Anchor, 1973, p. 412; Aburdene, __Megatrends 2000: Ten New Directions for
the 1990s__. NY: Wm. Morrow, 1990).
Berger speaks of the classical role of religion as a "sacred
canopy" covering the contemporary culture.
In our pluralistic, relativistic era the canopy is gone and it has been
replaced by the alternative tent of the security zone.

**G. From Privatization to Pluralism**

"In our culture of the 1990s, Man is confronted with a
wide variety of religions and other reality-defying agencies that compete for
his/her allegiance." (P. Berger, __Sacred Canopy__, p. 127) Four
consequences of the demise of modern thought are (1) moral relativism, (2)
narcissism and autonomous individualism, (3) hedonism, the pleasure principle,
and (4) reductive naturalism (Nature is ultimate reality). This pluralism of
options has produced what Malise-Ruthven calls __The Divine Supermarket__.
NY: Morrow, 1989.

Oden observes, "Modernity is not just a time but a set
of passions, hopes and ideas, a mentality that prevails." (Oden, __After
Modernity— What?__. p. 52 ("The hopes and fears of all the years. .
." The results of world relativism is "What is true for you is true
for you and what is true for me is true for me" (cf. James Patterson/Peter
King, __The Day America Told the Truth: What People Really Believe About
Everything That Really Matters__. NY: Prentice Hall, 1991). The Narcissistic
individual is an autonomous person who alone determines his/her destiny and
accountability. The choices of a narcissistic individual is determined solely
by one's own personal pleasure. The politically correct phrase within the maze
of moral relativism is that "truth is relative." In Greek mythology.
Narcissus upon passing his reflection in the water became so enamored with
himself that he lost thought and fell into the water and drowned. This myth is
resurgent in the I/Me generation. The only concern is for "my personal
pleasure and self fulfillment. "If it makes you happy and it doesn't hurt
anyone else, then it's okay." Any behavior is alright if another's welfare
is not jeopardized.

**H. Reductive Naturalism**

Nature is all there is (ultimate seduction into Capraian
Pantheistic Monism) . This value affirms that the only thing that is real is
empirically verifiable (see further my critique of "Linguistic
Analysis-Verification Principle/Falsification Principle" and its impact on
logic, language, truth, ethics, etc). Any statement that is not verifiable is
noncognitive, i.e., meaningless or declares nothing about Reality. All that
remains is that any non-verifiable statement merely exposes the mental
preference of the speaker/author. (See my "Theories of Language" and
"Idolatrous Absolutes", esp. pp. 26ff. on "Relativity of
Conceptual Schemes," pp. 26-32). Any adjudication between
alternative/conflicting "conceptual schemes" demands transcendence if
the impasse between radical contextualization/Sociology of Knowledge,
skepticism/solipsism is to be avoided) . If the Gospel of Christ is not both
True and Relevant, then biblical exclusivism (Acts 4.12, "no other
name") is politically incorrect and intolerant to our "seeker
friendly" American audience composed largely of Generation X (see all of
Lesslie Newbingen works and __The Gospel in a Pluralistic Society__. Eerdmans,
1989; __Foolishness to The Greeks__. Eerdmans, 1986;

__The Gospel As Public Truth__. Eerdmans, 1991; James E.
White, __What is Truth?__. Broadmans, 1994).

**I. Priests
in The Postmodern Temple: Where the "Gospel" of Lost Transcendence is
preached Euclidian Paradigm; (Classical Paradigm of Proof and Truth)**

1. Axiomatic Method and related uncovering of general mathematics by Greek Mathematicians is closely associated with the development of Greek Philosophy.

2. Elements of Euclid affords us the best source for an examination of the mathematics. Euclid's fundamental presuppositions of Elements I will call the Euclidian Paradigm.

3. The major characteristic of The Euclidian Paradigm is the emphasis on geometrical symbols (see my "From Two-Valued Logic to Multiple-Valued Logic (Deductive to Inductive Logic)

.

4. Euclidian presuppositions are obvious by inspection (egs. place of intuition "seeing" in Husserl, Whitehead and Wittgenstein, et al. in each case).

5. The Axiomatic Method of Euclid comes from geometric form. In this form it has conditioned the thinking and intuition of mathematicians and philosophers alike for over 2000 years (Modern to Demise in Postmodern era).

6. Geometry has been defined and traditionally associated with spatial relationships. Indeed Geometry has been defined classically as the science of space (cf. Newtonian "Absolute space" vs. Einsteinian relativized space and its implications for logic of induction and any empirically based theory of science).

7. A mathematics which is characterized exclusively in geometrical symbolism as the Elements allow one to assume a relationship between mathematical form and the human subject comparable to that observed between space and the human subject (cf. Greek choice of geometric symbols of arithmetic in relationship to "seeing", e.g. Wittgenstein's "Picture Theory" of meaning and observation emphasis in learning and media—visibility/audibility—word/symbol/proposition/myth/symbol, etc., in the absence of "irrational number" symbols.)

8. In the Euclidean paradigm the axioms are basic paradigms about the things the definitions describe which are proved by means of the axioms.

9. Crisis in The Classical Paradigm: On the Road to Postmodernism. Formalistic Developments in the 19th century.

The Elements has four different types of
logical constructs: (1) Definitions, (2)
Postulates, (3) Common notions and (4) Propositions (cf. Prepositional
Logic/Propositional Revelation). After
the rigid formulation of the axiomatic method had occurred in the latter part
of the 19th century, definitions were found to be, in Russell's terminology,
"theoretically superfluous."
In the new axiomatic formal systems, definitions refer only intra-system
in distinction to extra-system reference of definitions in the Elements. In modern/postmodern axiomatic systems, there
is no necessary reference of definition to anything outside the system: this development will lead to the loss of the
concepts of universal and necessary which are essential for the
Christian-scientific paradigm of truth claims,
(cf. Schaeffer's "True Truth" on the foundation of Kant's
radical contextualization- Relativism Relevance). The Euclidean descriptive use of definitions
enhanced the objective status of transcendent mathematical objects. The very form of the axiomatic method
suggested that mathematical relationships are "out there" and
objective to the observer. This confirms
the feeling on the general "thereness" that geometrical figures appear
to have been as they are ingressed in phenomenon/objects. Both the use of geometrical symbolism and
axiomatic method provides a natural "unity" for mathematics. The
whole of Euclidean mathematics is deduced from the firm foundation of a few
unique axioms and intuitively clear definitions. The multiple mathematic development in the
19th century-have contributed to the problem of the unity of mathematics and
ultimately the unity of science movement (cf. crisis in the 'Received View,' i.e.,
Positivism-Scientism)(see my "Demise of Transcendent Explanatory
Modes," esp. the section on Logical Positivism). One of the fundamental
presuppositions in any mathematical philosophy is the assumed relationship
between the constructive ability of the mathematician to create mathematical
relationships and the "objective status" of their relationships prior
to or apart from human constriction of them.
(This development has staggering implication for certain forms of
presuppositionalism, evidentialism in Christian Eristics, assumptions regarding
"proof" derived from coherence and consistency and the
"objectivity" of the scientific enterprise which employs the language
of nature-mathematics to explain scientific truth/knowledge claims). Plato and Aristotle contra Locke, who
affirmed that a natural number is constituted by the activity of the mind, vs.
with that of the later Wittgenstein, who states that the mathematician is an
inventor and not a discoverer of mathematical truth (contra Euclid's Elements
in which care is taken to insure that definitions are not merely verbal but do
actually refer to "existent" mathematical figures - see Aristotle's
Posterior Analytics. 92b, 12; and Euclid's __Elements__. I, 142). The Euclidean paradigm (apriori) has impacted
the Augustian/Reformed theological paradigm, also proofs of God via
Plato/Aristotle/Stoics/Anslem, et al.

In his analytic geometry, Descartes established a correspondence between algebraic equations in two variable and plane geometric curves. By means of his technique, a quantity to any power could be represented as a length of line segment, thus Descartes was able to establish a one-one correspondence between the elements of geometry, line segments so that the addition and multiplication and line segments give line segments just as addition and multiplication of numbers give numbers. Descartes sought to transcend the disciplines of algebra and geometry, i.e., "universal mathematics" (mathesis universalis). Descartes' Kuhnian paradigmatic revolution was grounded on the awareness of the existence of the 'ego', that the clear and distinct ides of the axioms of mathematics are secondary to the clear and distinct idea of our own existence (Descartes, Principle V. I, p. 220), Principle VII 1.1, p. 211 "cannot doubt our existence"). Descartes asserted a fundamental dualism which extended substances are of an ontologically different sort than thinking substances. The human ego may radically transcend both mathematics and the world (cf. Augustinian affirmation of transcendence of the human ego via intuitive subjectivity).

Descarte's two loyalties
were: (1) mathesis universalis and (2) a
transcendent ego which could in no way be described by mathematics, i.e.,
reduced to mathematics. This unresolved problem enters the modern intellectual
arena with critical force in The First Critique of Kant. The problem and its solution is tied closely
to development in 19th/20th centuries mathematics. Kant's answer was vitiated by developments
within 19th century. The problem is
significant for the developments in Phenomenology, Existentialism, and
especially the philosophies of Whitehead (as interpreters of Einsteinian
paradigmatic revolution), Husserl, and Wittgenstein, whose efforts at solution
provide the aspect of their philosophies which radically effect the development
of new theological paradigms.

10.The Fundamental Problem: Transcendence of Object or Ego?
Historically, Leibniz, Pascal and Locke expressed important views on the
fundamental problem. Their gradual
awareness of the transcendence of human subject over mathematics precipitated
their concern for the problem. Pascal is the single philosopher between
Descartes and Kant who took seriously both the radical transcendence of the
mathematician over mathematical system and the necessity of his conforming to
mathematical relationships. In his De
1'espirit aeometriaue. Pascal affirms that he can demonstrate truths already
found " . . .in such a way that the proof will be invincible."
(Pascal, __De L'espirit opometrique__. 2 vols, Paris, 1860, II, p.
335). Pascal's radical shift in __Pensees__
where he acknowledges Montaigne's influence on himself with the words, "it
is not in Montaigne, but in myself, that I find all that I see in him," he
then affirms, not the skepticism of Montaigne, but the transcendence of men
over all mathematical and technical reason.
According to him in the __Pensees__. mathematical and technical
reason is not suited to the study of men.
"The order of thought is to begin with self." (ibid, p.
55) Pascal affirmed that Descartes'
heinous error is the beginning with the self for the purpose of reaffirming
"technical reason" to which man is understood as necessary
subject. "We have an incapacity of
proof" (ibid, p. 127). Yet existential reason, by the grace of God, leads to
truth. "We have an idea of truth,
invincible to all skepticism" (ibid).
We must avoid "two extremes. . . to exclude reason and to admit
reason only" (ibid, p. 90).

Pascal broke with the Euclidean
paradigm in two fundamental ways: (1)
de-emphasizing geometric figures as the appropriate mathematical symbolism, and
(2) he reformulated the understanding of the nature of definition (egs. co-efficients
of binomial expansion, and certain mathematical structures of probability (see
H. M. Turnbull, __The Great Mathematicians__. NY: New York University Press,
1961, p. 89 - e.g. Newtonian "continuum calculus" stating probability
theory; Pascal's definitions of intra system and extra systems are undefined as
primitive terms). The utilization of
literal symbols which does not necessarily point to geometric figures and a
clear understanding of the nature of definition, as Pascal had, tends to
subvert Euclidean assumptions that the mathematician gives the literal
symbolism or undefined terms meaning, if it has any (cf. Carnap, The Vienna
circle and their "Received
View"). The mathematician is
perceived in a different relationship to mathematics then in the Euclidean
paradigm. He is more creator than
discoverer, more transcendent to the mathematical system than conformable to it
(cf. Pascal's technical reason and "reason of the heart"). Perhaps it is no accident that he, the
founder of modern algebra (Pascal), developed an existential stance that is
compatible with the existentialism that developed after modern algebra came
into its own late in the 19th century.

11. From Locke's Constructivism to Kant's Synthetic A-Priori. Prior to further radical development in mathematics, Locke's description of the practical constructive ability of the mind to formulate mathematical ideas found its way into the synthetic part of Kant's synthetic apriori and remains visible in contemporary mathematics in the emphasis of the Intuitionists or constructive methods. Kant's assertion that natural numbers may represent relations more adequately than geometrical symbolism was vindicated by the Berlin school in the 19th century. Locke was also opposed to any conception of an innate apriori. He recognized that many of the claims for apriori innate ideas were based on the assumed authority of the axiomatic method. Both the axiomatic method and the privileged use of geometrical symbolism fell before his criticism. They are "archetypes of the mind's own making, not to be intended to be copies of anything," and are put together "without considering any connection they have in nature." (John Locke, An Essay Concerning Human Understanding. 2 vols, NY: Dover Press, 1959, II, p. 230). Locke did not deny the normativeness of geometry over external things (Berkeley's secondary qualities vs. primary qualities). Hume's transference of the relationship of cause and effect from outside things to inside ideas, the process was complete, the necessary regularity of the objective world as described by a normative mathematics was seen to be untenable. The human mind was seen to create its mathematical ideas to handle other ideas about primary sense data. The Euclidean paradigm was rejected intoto. The human subject was seen to have a natural transcendence over all mathematics (c.f. The transcendent Ego creates vs. discovers reality; thus enters the postmodern maze). The Enlightenment paradigm of autonomous man was now complete! (cf. enters Humanism, secularism, pluralism, narcissism and inevitability of progress, complete animality of man, perfectibility of man, ultimate reality of nature).

Thus the stage is set for the Kantian acceptance of the Euclidean paradigm which affirms that mathematics is pure apriori. Our perception of anything is perception in terms of certain mathematical relationships (cf. theory laden observation-language). Kant's acceptance of the Newtonian philosophy of science/mathematics, i.e., that mathematics has the power to describe the world in a comprehensive and necessary manner. Kant sought to construct a philosophy which would justify Newtonian mechanics and its explanatory power. Yet Kant's use of Locke's emphasis on the constructibility of natural numbers the concept of geometry are also constructed. That a straight line is the shortest path between two points is a synthetical proposition because it joins the concept of "straightness" (non quantity) with quantity concept ("shortness"). Kant's concepts of space and time is the point of his fusion of the problem of how mathematics can be both apriori and synthetic (cf. Kant's and Einstein's views of Space/Time). The categories of space and time are not available to observation. (Kant's Critique of Pure Reason. 'Transcendental Analytic', I, 2,3,4) In Kant's efforts to fuse empiricism and rationalism, he failed to account for the necessary laws of the activity of consciousness which can never describe adequately the essential character of our object of consciousness.

**J. Lost Transcendence in Our Postmodern Culture**

Laugrange's masterpiece, __Me'caniaue
analytiaue__. was published in Paris in 1788. His work was thoroughly in the
Newtonian tradition, yet he broke with the Euclidean paradigm by producing a
system of mechanics without the use of geometric symbolism (contra Newton's use
of geometric figure). Beginning with the work of Weierstrass calculus developed
without any concept of infinitesimal and without Newton's concept of nonlimit.

1. Augustine Louis Couchy (1789-1857) introduced a
rigor in mathematics that separated the 18th and 19th centuries' analysis. He shifted the focus of attention from
geometric figures to the properties of the real numbers. The final blow to geometric intuition came at
the hands of Weierstras (1815-1897). He
produced an example that showed a direct contradiction in intuition involving
the classical Newtonian concept. He
demonstrated the existence of a continuous curve which at no point possesses a
derivative. He generated a contradictory conclusion that a curve is being
generated by a moving point which at no time has a definite velocity. The new formal
device allowed the presentation of a curve that could not be pictured
geometrically. The astonishing thing about the curve is that though incapable
of geometrical representation it was found to describe the Brownian movement
(Biologist show work was contra positivistic mechanical model of cause and
effect relationship between two or more events). With the breakdown of the
Euclidean paradigmatic intuition (geometric symbolization) natural numbers
became the new "received view"). So ends the paradigmatic revolution
between Euclidean geometric intuition and the coming of natural numbers as the
norm. This fundamental shift in intuition from geometric figures to that of the
natural numbers further upset the Euclidean paradigm concerning the
relationship of the mathematician constructive ability to that, the objectivity
of mathematical relations. In the Euclidean paradigm mathematical relationships
were considered to be objective and out there. A natural number, however, may
be thought of as crated by the act of counting. As Dedekind (of the Berlin
school) affirmed, "numbers are the free creations of the human mind"
(R. Dedekind, __Essays on The Theory of Numbers__. E.T. NY: Dover, 1963), p.
31.) Mathematics thus appear to be merely a radically subjective creation of
the human intellect (contra Russell's Logische).

2. As numbers replaced The Euclidean paradigm, it too was later found to be inadequate as the content for the whole of mathematics, and there occurred a shift to logic as the primary content (Russell, whitehead, Principia Mathematics). The question of which mathematical content is most appropriate for the ground of mathematics has profound consequences toward the development of our foundationaless postmodern culture. Is there any content at all that is sufficient to ground the whole of mathematics? The results of the new mathematics is that the Euclidean paradigm has been completely dislodged. No longer are there assumed mathematical objects which one seek to pattern by schematic mathematical devices. No longer is there an assumed unity to mathematics. There are a pluralism of different mathematical systems and a pluralism of different mathematical contents; therefore, mathematics is no longer a universal paradigm of proof/demonstration and truth. Goedel's incompleteness theorem has shown the impossibility of formulating one all inclusive mathematical axiomatic system, thus the demise of The Unity of Science Movement and the "Received View" (Positivism) of the nature of scientific knowledge and its progress. Definitions in this system no longer point to mathematical objects; they are simply shorthand devices for handling other symbols. In short, the Euclidean paradigm has been weighed and found wanting.

3. New Mathematical Paradigms: (a) Constensive (content rather than method) and (b) the formal (method rather than content). (Kant's emphasis--constructivism of the transcendental ego. Historicity of all reality in the Sociology of Knowledge thesis. Issues remain - transcendence of mathematics over the mathematical form and an emphasis on the objective and normative status of mathematical objects. Consequences of answers to these questions are vitally important in postmodern philosophical/theological development.)

**K. Three
Philosophies of Mathematics: Prophets of Lost Transcendence (1) Husserlian
Phenomenology/Existentialism; (2) Alfred North Whitehead's Process Philosophy,
and (3) L. Wittgenstein's Philosophy of Mathematics/Language.**

The first two men were mathematicians. Each was involved in the fundamental problem with regard to the relationship of mathematicians to mathematical form.

1. The fundamental starting point of all forms of existentialism is the position that existence precedes essence. Classical Western thought has presupposed that what is given to men in his experience is an ordered set of qualities (relations, etc.). These qualities as structured in certain ways make up all the objects of human knowledge. A critical question for existentialist/non-existentialist distinction is whether "existence" is itself one of the qualities (egs. forms, categories, space, time, etc.). Hegel's paradigm opens Western thought up to: (1) Sociology of Knowledge (loss of Schaeffer's True Truth); (2) Cultural Relativism; (3) Structuralism; (4) Contextuaiism; (5) Indigeneity; (6) Loss of Authorial Intentionality in hermeneutics, homiletics, communication, theories, etc.. Into the Hegelian maze enters Quine, Rorty, et al all prophets of Lost Transcendence (radical shift from reason/rationality and language as vehicle for "True Truth"). Kant's transcendent became an immanent transcendent in Hegel's phenomenology. The term "existentialism" has meaning, however, only if that which is understood to precede essence is first of ail human existence. The mathematical philosophies of Husserl, Whitehead, and Wittgenstein share three characteristics in common: (1) Mathematico-existentialism is the viewpoint that mathematics is considered to be grounded in human existence, the primary "where" of mathematics is human creativity; (2) Mathematico-existentialism is the full recognition of mathematical relationships as objects of some sort. Though mathematical relationships are grounded in human existence, their objectivity and apartness from individual human subjectivity cannot be rationally denied (cf. objectivity of mathematical relationship - Kant's Idealistic tradition /Dewey's Instrumentalism /Bridgeman's operationalism /Wittgenstein's Language Game, etc.). in the process of 20th century scientifico-philosophico development (the two cultural paradigm), Christianity and Science have been reduced to Language Games, and neither are or can be necessarily universally true.

Edmund Husserl's influence on
both Roman Catholic and Protestant Theology through his students Heidegger,
Sartre and Bultmann reflects the fundamental presuppositions of Heidegger. Husserl was a mathematician turned
philosopher. After 1883 Husserl returned
to Vienna to study with Franz Brentano, an ex Roman Catholic priest. Brentano's position was that the true method
of philosophy is none other than that of Natural Science, eg.. The Vienna
Circle 30 years later. Husserl moves
toward objectivity and the Euclidean paradigm.
The whole realm of formal ontology, which is pure logic and includes the
"mathesis universalis" is the science of "object in
general." (Einstein/Whitehead:
Process Philosophy. Whitehead like Husserl,
was a mathematician. Breakdown of
Logical Positivism after World War II: Demise of Transcendence in both
Mathematics and Scientific Enterprise) (Husserl's
influence on J. Wach, __Comparative Study of Religion__, NY: Columbia,
1958). For Wach, Durheim, et al,
"norms and values were to be explained historically, psychologically, and
sociologically" (Wach, pp. 1-6).

2. Whitehead's, A Treatise on Universal Algebra
two years before Husserl's __Logische Hntersuchunaen__ (1898/Hafner 1960).

3. Whitehead grounds unity in generalized geometry
and developments position from Treatise to that of __Principia Mathematica__
where, as with Husserl, he seeks the unity of mathematics in logic. In the
Euclidean paradigm "space" and geometric representation has been
understood to form the ground and unity of mathematics, whether in terms of
geometric construction of Euclidean or Kantian categories.

4. The heart of the issue is, how do we explain the fact that we perceive "the material world" if only by Russell's "between points of space" and "instants of time." (see Russell's critique of Leibniz, London, 1958). Perception is capable of seeing "beyond" space and time or else there is neither universe nor macro or micro worlds.

5. Developments during 1900-19lO—Russell and
Whitehead's __Principia Mathematica__. Vol I, 1910; the other two were
published in 1912 and 1913; (for the influence of Piano and Goedel on
mathematical paradigm, see my "Mathematical Foundations of 20th Century
Philosophy/ Theology")

6. "Mathematics is the science concerned with the logical deduction of consequences from the general premises of all reasoning."

7. Wittgenstein's __Tractatus__ became the standard
work of the movement called Logical Positivism and had characterized the nature
of mathematical propositions as "tautological."

8. Goedel's "Incompleteness Theorem"
strikes at the root of the fundamental motivation of __Principia Mathematica__.
the desire to reconstensivize mathematics into a unified whole. Goedel's
theorem proves that such a goal is impossible to attain.

9. Whitehead's influence on theology (e.g.s.: Thornton, Wieman, Temple, Hartshorne, Cobb, Ogden) is extensive. Whitehead's principle of organism is impersonal. To mistake process (or organism) with God or to call it Personality, is an example of the error of "misplaced concreteness."

10. Wittgenstein, unlike Husserl and Whitehead, was not a professional mathematician. His concern was, is the foundation of mathematics the ground of all knowledge and communication, namely Logic. Wittgenstein's Vienna Circle - the German movement: Schlick, Waismann, Neurath, Zilsel, Feigel, Juhos, Reider, Carnap, Kraft; the American movement: Moris, Langford, Lewis, Bridgman, Wage, Reichenbach, R. V. Mises; the English parallel movement! Russell, Popper, Ayer ("Verification Principle"), Flew ("Falsification Principle").

11.
Two Basic Sources of Logical Positivism/Empiricism are: (a) New Symbolic Logic
of __Principia Mathematica__ and (b) Empiricism. Empiricism differs from the
old empiricism of Mill and Spencer in that it does not require mathematics to
be empirically verified. Mathematics is independent of experience; and gives no
knowledge of reality. The propositions of mathematics are not synthetic but
analytic, i.e., tautologous. All knowledge of matters of fact, all scientific
knowledge, etc., must come from empirical sources. Unity of Logical Positivism
Movement based in agreement/disagreement with __Tractatus__ (Wittgenstein’s
critique of his __Tractatus__ in his __Philosophical Investigation__ also
destroys credibility of Logical Positivism per se.

12.
Wittgenstein's solution is the "Language Game", i.e.. Logic and
Mathematics are exclusively a creature of man's invention. The Language Game is a form of social
activity where different players have different parts (__Philosophical
Investigation__, p. 39).

13. Ordinary language is not one unified interrelated homogenous whole, but a vast motley of different language games. Ordinary language and technical language (mathematics) are a part of ordinary language. Both are to be understood in terms of language games, e.g. intuitive crises and contradiction in mathematics over ambiguity of words (polyvalence vs. univocity) or symbols. Wittgenstein says that "the mathematician is an inventor, not a discoverer." (Renards. p. 167) Compare with Kuhn's paradigm, "Incommensurability Thesis".

14.
Tractatus. Verification Thesis, and hostility to theology, ethics, and
aesthetics. __Philosophical
Investigation__ and concern for Analysis of Religious Discourse is crucial
for Ayer's __Language, Truth. and Logic__; John Wisdom (1920/1944) parable
of the gardener; The Death of God period of the 1960s, all "seeing"
is within context of some language game -objectivity and tacit knowledge of
Polanyi.

**L. Language, Truth and Logic in Our Post Christian
Culture**

(A. J. Ayer, __Language, Truth and Logic__. 1936) Ayer set forth the main tenets of Logical
Positivism. Most postmodern philosophers
and theologians reject evaluating religious beliefs on empirical grounds. In the positivistic mode, only empirical and
observational methods in the hard sciences are the paradigm of and the basis
for ail genuine knowledge. It is logical
in that it conceives of philosophy and theology as the Analysis of Language in
general and of meaning in particular.
Ayer's charge that all classical Christian truth claims (God, Ethics,
Aesthetics, etc.) are not merely false, they are meaningless, i.e.,
non-cognitive, (see my "Meaning of
Meaning in Our Postmodern Culture and my "Theories of Language" esp.
the critique by Pike, Nida, Chomsky.
One's language acquisition in the empirical mode). The Verification Principle precludes Truth
Status to all non-verifiable propositions—theological, moral, aesthetic,
economic, political, etc. (__Ayer. Language,
Truth and Logic__. Dover Press, 1936),
pp. 35-45. Ayer's work has unsettled the
Christian apologetic mode for six decades.)

Flew challenged Ayer with the Falsifiability Thesis. The essence of this thesis is that any statement put forth as a genuine truth claim about the world must satisfy the requirements of falsibility, that is, it must exclude something. There must be some fact or set of facts that, if shown to be true, would count against the truth of the statement and force the speaker to withdraw it as mistaken. Flew’s attacks on Ayer brought the downfall of British Linguistic analysis/Logical Positivism (cf. see my "C. S. Lewis' Literary Apologetic Mode", a critique of his use of "Falsifiability Thesis).

J. L. Austin and Ludwig Wittgenstein seemed to provide the
tools for the recovery of religious discourse.
Austin's work revealed that language functions in more than a
truth-stating function. Truth stating is
only one function. (Flew/MacIntyre, __New
Essays in Philosophical Theology__ (NY: MacMillan, 1955, pp. 97-108)

Braithwaite recovered the premise that the primary use of religious assertion is ". . .to announce allegiance to a statement of moral principles. What is essential is the story rather than empirical propositions presented by the story as corresponding to empirical facts."

R. M. Hare also set forth a non-homiletics descriptive
analysis. He, too, rejects the view that religious language consists of
empirical assertions to account for its meaning. This emphasis precipitated the
resurgence of myth as a communication force. Science Fiction and media in the
1960's, cf. Joseph Campbell and Star Wars. If religious language does not set
forth empirical assertions that must satisfy the requirements of falsibility
then there can be no prepositional assertions that are candidates for truth
claims. The cost of Austin/Wittgenstein's influence in religious discourse was
devastating. Wittgenstein ultimately recovered Kierkeggardian reinterpretation
of religious discourse. Consequently classical Christian apologetics is
pointless and non-cognitive, i.e., meaningless. Christians must not deny the
importance of the Ayer/Flew crisis. Ayer, Flew and Wittgenstein, et al, deny
that religious discourse-is empirically meaningful (cf. C.S. Lewis use of
"falsifiability thesis" in __Letters to Malcom__. 1964, p. 32; __Miracles__.
1974; __God in Dock__. pp. 39-40). What evidence would be required for
rational belief in God's existence? What evidence would be required to falsify
belief in the Judaeo/Christian God?

**M. Priests in The Loss of Transcendence
Temple: Quine and Rorty The Developments in:**

1. Historicism

2. Intentionality

3. Sociology of Knowledge

4. Limitations of Language

5. Hermeneutics (From Epistemolgoy-Truth
to Relevance)

6. Dialogue
(Relations/Revolution/Muiti-Culturalism/Political Correctness attempting to
bridge over Relativism/Rationalism), i.e., Piaget, Kohlberg, Rorty, Quine, et. al.
See Thiel, __NonFoundationalism__.

Dr. James D. Strauss