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Gottlob Frege, The Laws of Logic, and Theism

January 21, 2013 By 3 Comments

FREGE, THE LAWS OF LOGIC AND THEISM

BY MIKE ROBINSON

 

 

Introduction

 

Friedrich Ludwig Gottlob Frege was a renowned logician and mathematician. Significant features of his work can be utilized to advance the notion that the laws of logic are not the product of matter and its supporting capability. Without God as the uppermost mind and the source of logic one weakens, beyond recovery, the justification that one can trust human reason. Frege added that the laws of logic are not “psychologistic,” but logical; they are objective and not subjective. These laws of truth do not come from nor do they only remain in the thoughts of humans. Selected non-theists assert that these laws of logic are not laws—they are not independent and universal. Nevertheless, immutable laws by definition are not subjective and individualistic. Frege was correct; they are unmistakably objective and universal.

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In the beginning was the Logos and the Logos was with God and the Logos was God (John 1:1).

 

FregeFriedrich Ludwig Gottlob Frege (1848–1925) is one of my favorite thinkers. He was a German and is considered a great mathematician, logician, and philosopher. Frege is largely deemed to be the initiator of analytic philosophy and a significant contributor to the philosophy of mathematics. His influence on philosophical issues includes philosophical logic, systems of connotation, linguistic philosophy, philosophy of arithmetic, and mathematical logic. Frege was the originator of axiomatic predicate logic, which he denoted in his book, Conceptual Notation. This was a critical breakthrough in the history of logic. This genius described a system of symbolic logic that moved well beyond Aristotle’s two-millennial-old logic and Frege’s method remains influential to his day. Frege’s subsequent “philosophical masterwork, The Foundations of Arithmetic, drew the attention of both Bertrand Russell and Ludwig Wittgenstein. Frege sought to explain numbers as extensions of concepts while demolishing other theories.”[1]

 

Not everything can be defined (Frege).

 

Frege was a “German mathematician, logician, and philosopher who worked at the University of Jena. Frege essentially reconceived the discipline of logic by constructing a formal system which, in effect, constituted the first ‘predicate calculus.’ In this formal system, Frege developed an analysis of quantified statements and formalized the notion of a ‘proof’ in terms that are still accepted today. Frege then demonstrated that one could use his system to resolve theoretical mathematical statements in terms of simpler logical and mathematical notions. One of the axioms that Frege later added to his system, in the attempt to derive significant parts of mathematics from logic, proved to be inconsistent. Nevertheless, his definitions (of the predecessor relation and of the concept of natural number) and methods (for deriving the axioms of number theory) constituted a significant advance. To ground his views about the relationship of logic and mathematics, Frege conceived a comprehensive philosophy of language that many philosophers still find insightful. However, his lifelong project, of showing that mathematics was reducible to logic, was not successful”[2]

 

Frege’s Logic and the Philosophy of Mathematics

 

Frege birthed contemporary logic by “developing a superior method of formally representing the logic of thoughts and inferences. He did this by developing: (a) a formal system that served as a basis of modern logic, (b) an analysis of complex sentences and quantifier phrases that showed an underlying unity to certain classes of inferences, (c) an analysis of proof and definition, (d) a theory of extensions which, though seriously flawed, offered an intriguing picture of the foundations of mathematics, (e) an analysis of statements about number (i.e., of answers to the question ‘How many?’), (f) definitions and proofs of some of the basic axioms of number theory from a limited set of logically primitive concepts and axioms, and (g) a conception of logic as a discipline which has some compelling features.”[3]

 

Additionally “Frege raised a problem with the traditional account and offered a different understanding of identity statements.” Identity statements are “necessarily true by definition.” Which led to the paradoxical question “how can there be contingent identity statements if identity is necessary?”[4] Consequently, Frege both helped disentangle deep paradoxes while simultaneously, sometimes unwittingly, producing others.

 

Frege was one of the most noteworthy philosophers in the rational maturity of logic. His discoveries and writings regarding the laws of logic and analytic philosophy led the way for the varied schools, forms, and methods of modern logic. One of Frege’s foremost goals was to convert or reduce mathematical truths to logic. He failed in this pursuit, but his work helped develop the modern philosophy of logic.

The laws of logic are not psychological laws of takings-to-be-true, but are laws of truth. They (the laws of logic) are boundary stones set in an eternal foundation.[5]

Frege in his work Begriffsschrift observed that the laws of logic are universal and fixed. These laws are non-mutable laws that rule over all thinking, assessments, discernment, applications, assertions, propositions, predication, theories, actions, and conclusions. He labeled these laws the “laws of truth.” This is a way to name them that helps one understand that these laws govern all true things, not just thinking, but they are imposed on all our actions too. Frege wrote that the laws of truth are “the most general laws, which prescribe universally how one ought to think if one is to think at all.” He thought that the laws of logic must be expressed and applied in a painstakingly precise and methodical manner if the logician is to be consistently logical. Frege, standing on Aristotle’s shoulders, pressed the universality and necessity of the laws of logic.

 

The Christian knows that the laws of truth[6] are universal and necessary. Additionally, they are aspatial, immaterial, immutable, and everywhere in force. Thus they require God, who is aspatial, immaterial, immutable, and everywhere present, universal in knowledge, and necessary, to ground them. Deny God and one denies the only possible foundation for these obligatory laws.

 

Mario Livio in his book Is God a Mathematician? Esteemed the work of Frege by stating that his “program was extraordinarily impressive.”[7] However, many mathematical and logical geniuses are a bit odd. Some scholars, like Ludwig Wittgenstein, did not always understand Frege’s behavior: “I was shown into Frege’s study. Frege was a small, neat man with a pointed beard who bounced around the room as he talked. He absolutely wiped the floor with me, and I felt very depressed; but at the end he said ‘You must come again,’ so I cheered up. I had several discussions with him after that. Frege would never talk about anything but logic and mathematics, if I started on some other subject, he would say something polite and then plunge back into logic and mathematics. He once showed me an obituary on a colleague, who, it was said, never used a word without knowing what it meant; he expressed astonishment that a man should be praised for this! The last time I saw Frege, as we were waiting at the station for my train, I said to him ‘Don’t you ever find any difficulty in your theory that numbers are objects?’ He replied: ‘Sometimes I seem to see a difficulty but then again I don’t see it.’”[8]

 

Frege’s Goal for New Logic

 

Frege’s objective was to “display in a perspicuous way the relationships between concepts and propositions. The goal of the whole of logic is to demonstrate the correctness of deductions without gaps between premises and conclusions, using acknowledged formal and precise rules of inference. Frege’s focus seems initially to have been on determining the correctness (and hence non-synthetic, a priori nature) of mathematical proofs, rather than examining reasoning of all sorts, as had traditionally been the subject of logic.”[9] Additionally Frege’s main interest was to “understand both the nature of mathematical truths and the means whereby they are ultimately to be justified. The appeal to reason: What justifies mathematical statements is reason alone; their justification proceeds without the benefit or need of either perceptual information or the deliverances of any faculty of intuition. The Task: To articulate an experience-and intuition-independent conception of reason.”[10]

 

The Nature and Prominence of Logic

 

In his book Begriffsschrift Frege proposed to reveal the “nature and status” of logic. Logic has normative standing. Logic imposes the standards that have the composition that governs all assessments, beliefs, assertions, suppositions, and inference. Frege rightly insisted that the laws of logic are the “laws of truth.” He states that the laws of logic are “the most general laws, which prescribe universally how one ought to think if one is to think at all.” He thought that the laws of logic must be expressed and applied in a painstakingly precise and methodical manner if the logician is to be consistently logical.

 

Frege further noted that the laws of logic are not “psychologistic,” but logical; they are objective and not merely subjective. These laws do not come from nor do they only remain in the minds of men. Many modern non-theists assert that these laws are not laws; they are not objective and universal. Yet immutable laws by definition are not subjective and must be universal. If one tries to reject the objective universality of the laws of logic, let the person attempt to write one sentence or think one thought or walk one step without utilizing these laws. Frege was correct; they are clearly universal and objective.

 

The Eminence of Frege

 

Richard Mendelsohn writes: “Frege had created … a formal language in which he axiomatized higher-order quantificational logic; derived many theorems of propositional logic, first-order logic, and second-order logic; and defined the ancestral relation. For his work represents a milestone not only in the history of logic and thereby, in the history of philosophy, but also in the history of modern thought, for it was one of the first sparks in a hundred-year explosion of research into the foundations of mathematics, and into the application of mathematical representation of structures other than numbers and shapes.”[11] This son of a theologian was a logical mastermind and a philosophical trailblazer. Mendelsohn adds: “No only did Frege create modern quantificational logic, but he also provided the theoretical framework for many subsequent philosophical developments in logic as well as in speculative philosophy.”[12]

 

Frege An Atheist?

Nearly all logic before Frege was a logic of terms. This “traditional” logic, initiated by Aristotle, had the advantage of … being simple.[13]

Although Frege was the son of a fine theologian[14] he is sometimes claimed by atheists. He may have been an atheist, but a better label would probably be an agnostic or a subtle non-professing atheist in the manner of David Hume. Both men rejected religious commitment and did not display any religious sensibility. Yet contrary to Hume, Frege apparently affirmed an ontological argument for existence which I suppose can be extended to God’s existence (many scholars deny this and affirm the antithesis). Frege pondered the ontological question: “To what then do we refer when we speak of the existence of something?”[15] Oderberg further notes: “No one before Frege talked of an ‘is’ of identity.”[16]

 

Frege’s Ontological Argument for Existence

 

Frege’s Ontological Argument for Existence (OAE henceforth) can be summarized:

The primary premise is that the idea of not existing is mathematically zero. Since a person can ask what a number is, this implies that the person’s existence is higher than a zero. Hence the person is the antithesis of not existing, therefore the person exists.

The Ontological Argument for the Existence of God (OAEG henceforth) was first offered for the Christian God by Anselm. God is “that than which nothing greater can be conceived.” Considering God can be conceived in the mind and He is thought to exist, His existence is greater than not existing. So that “which nothing greater can be conceived” necessarily exists. This argument has been confuted forasmuch as many consider it to be mere play on words (Plantinga has proposed a contemporary and more robust version).

 

To summarize Frege’s OAE: He asserts that one exists because one can conceive of one’s existence, whereupon this existence is greater than zero and not as great as infinity. On the basis of mathematics, existence is that which is greater than zero, and not as great as that which is greater than the infinite (greater than one can conceive). Since you exist and are greater than zero, then you must exist. Frege did not expand this to the existence of God, but that implication seems to follow. Paradoxically the not-religiously-denominated Frege later employs the same wording with reference to the existence of God. He claims that those who assert or reject the existence of God imply that their notion of God cannot be caused by the empirical sense of an object extended in space (there is no immediate perception of God).

 

Frege and Identity Statements

 

Frege argued that within an important operation of the Law of Identity “every object has to be identical to itself.”[17] J.P. Moreland and William L. Craig disclose that Frege viewed identity statements as “statements about language, and they assert that a certain relation holds between the two referring expressions used in the statement, namely, they are coreferring expressions, i.e., they each name the same thing [e.g., car/automobile].”[18] Identity requires and presupposes the Law of Identity even if identity statements can be ambiguous.[19] Frege may not have submitted to theism but he knew that mathematics required a fixed and powerful ground. He wrote: “I compare arithmetic with a tree that unfolds upwards in a multitude of techniques and theorems while the root drives into the depths.”[20] Frege projected in Grundlagen der Arithmetik that there is a “logical inference from n to n + 1.”[21]

 

The Laws of Logic and Thought

The fundamental laws, the laws of thought, [are] those operations of the mind by which reasoning is performed (George Boole: The Laws of Thought).

Livio noted that “according to Frege, even statements such as 1 + 1 = 2 were not empirical truths, based on observation, but rather they could be derived from a set of logical axioms.”[22] Another concern is the meaning of existence and its relation to the ontological status of various items (mental objects, forms, ideas, material objects, etc.). In one passage Frege seems to not just connect existence with self-identity but to equate the two, tossing Aquinas’ distinctions (and countless others) out the ontic window. Additionally, “Frege and Russell were … later to claim that algebra stems from logic.”[23]

 

Frege contended that the laws of truth are not psychologistic, but are necessities of logic; they are objectively true and in force. These laws are not bound to the fleeting subjective opinions or thoughts of men. They are necessarily utilized by all men, but a particular man or set of men (and their particular brains) lack the ontic capacity to ground these laws. Thus I draw from this that only an immutable and universal power source can ground the laws of truth and this can only be God. The always-in-flux cosmos lacks an unchanging nature to ground the laws of logic. Nonetheless, many modern non-theists assert that these laws are not laws; they are not fixed and universal. Yet Frege was correct; they are surely fixed and universal.

Frege published his first revolutionary work in logic in 1879.[24]

Thus the laws of logic are not material laws that may change forasmuch as truth must utilize these principles. Posit them as mere brain accessories or cerebral tools and this will place them in the subjective psychologistic realm. This cannot be true because these laws are objective and necessary. Thus the principles of logic are not mere human conventions or limited to subjective governance. One must be antecedently committed to their independence from the human brain (and the cosmos) and their absolute normative governance. Thus they are transcendent. John Frame observes: “People may very well interpret the expression “law of thought” by analogy with the “law of nature” and then have in their mind features of thinking as mental occurrence. A law of thought in this sense would be a psychological law. … That would be a misunderstanding regarding the task of logic, for truth has not been given its proper place.”

 

The True God Exists

 

Unless I believe in God, I cannot believe in thought (C.S. Lewis).

Change is the condition of life. … But the unchangeableness of God is the negation of all imperfection, it is the negation of all dependence on circumstances, it is the negation of all possibility of decay or exhaustion, it is the negation of all caprice. It is the assurance that His is an underived, self-dependent being, and that with Him is the fountain of light; it is the assurance that, raised above the limits of time and the succession of events—that we might have a rock on which to build and never be confounded (Charles Spurgeon).

God has the ontological heft to account for everything. God, as the One who provides the a priori truth conditions for all things, has the ontic capacity to account for immutable universals (laws of logic, moral law, etc.). Mutable and non-universal entities are devoid of the sufficient attributes that are required, so they are ontologically undersupplied to account for the laws of logic. These laws are invariant universals and are required for communication and knowledge.

Come let us reason together (God: Isaiah 1:17).

God furnishes all the a priori essentials; the necessary epistemic equipment utilized in all thoughts and achievements. God has the ontic attributes of omniscience, immutability, and omnipotence (He has universal reach) enabling Him to be the ground for the universal and immutable laws of truth and ethical necessities (moral law) that are utilized in all thought and action. Any position that rejects the true God as the epistemic (knowledge) base not only leaves an unnerving fissure, but hopelessly fails. Consequently, whatever evidence one discovers must be discerned and processed with the rational implements that arise from Christian theism and the worldview that streams from the true God.

 

The true God is the primordial requirement for all knowledge, proof, evidence, and logic. He is the a priori verity condition for the intelligibility of reality. The immaterial, transcendent, and immutable God supplies the indispensable pre-environment for the use of immaterial, transcendent, universal, and immutable laws of logic (law of identity: A = A; law of non-contradiction: A~~A). Atheistic thought cannot furnish the necessary a priori truth conditions for the immutable universal laws of logic; therefore it results in futility because of its internal weakness. Non-theistic worldviews fall into absurdity inasmuch as they are self-contradictory and lead to conclusions that controvert their own primary assumptions. Without God, ultimately, nothing can make sense.

 

Under Strict Materialism There is No Reason to Trust Human Reason

Van Til warns that “the only alternative to thinking of God as the ultimate source of unity in human experience as it is furnished by laws or universals is to think that the unity rests in a void. Every object of knowledge must, therefore, be thought of as being surrounded by ultimate irrationality.”[25]

If human reason is only the product of matter and its supporting capacity then materialism itself cannot be true. Without God as the highest mind, the source for human reason, one undercuts the reason one can trust human reason.

The laws of logic are potent apologetic tools. However, the Great Logos, Jesus Christ, came to speak and provide the greatest Goodnews: Christ’s death and resurrection atones for the sins of His people. May the reader flee to Christ in faith and find forgiveness, acceptance, and pardon (Titus 3:4-7).

by Mike Robinson: Granbury, Texas. Minister and author.

For a lengthy exposition of Frege’s work and its apologetic applications see my eBook (and Paperback) Aristotle, Frege, The Laws of Logic and Theism HERE

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1. Encyclopedia of Philosophy: http://www.iep.utm.edu/frege/

2. Dictionary of Philosophy: http://www.iep.utm.edu/frege/

3. Encyclopedia of Philosophy: http://www.iep.utm.edu/frege/

4. J.P. Moreland and William L. Craig: Philosophical Foundations for a Christian Worldview, p. 197.

5. Friedrich Ludwig Gottlob Frege: Basic Laws of Arithmetic, p. 13.

6. Laws of Logic: The Law of Non-contradiction (A~~A) and the Law of Identity (A=A). Also known as the laws of reason and the laws of thought.

7. Mario Livio: Is God a Mathematician? p. 186.

8. G. E. M Anscombe: Three philosophers.

9. https://docs.google.com/viewer?a=v&q=cache:93h2Q6MvpQJ:www2.scu.edu.tw/philos/p2/2006-05%2520Frege’s

10. Ibid.

11. Richard Mendelsohn: The Philosophy of Gottlob Frege, p. 2.

12. Ibid, p. 7.

13. David S. Oderberg: The Old New Logic: Essays on the Philosophy of Fred Sommers, p. 33.

14. Mendelsohn, p. 1.

15. Oderberg, p. 211.

16. Ibid.

17. Livio, p. 18).

18. Moreland and Craig: p. 198.

19. Ibid.

20. Frege: Basic Laws of Arithmetic, p. 10.

21. Stephen Hawking, Editor: God Created the Integers, p. 1077.

22. Livio, p. 46.

23. Ibid., p. 182.

24. Ibid., p. 184.

25. Cornelius Van Til: Survey of Christian Epistemology, p. 216.

 

 

 

Suggested Reading

 

 

• Adler, Mortimer (1985). Ten Philosophical Mistakes. St. Martins.

• Aristotle, Metaphysics (1972). Oxford.

• Bahnsen, Greg (1996). Always Ready, Covenant Media.

• Bahnsen (1998). Van Til’s Apologetic, P & R.

• Carroll, Lewis (1989). Best of Lewis Carroll, Castle.

• Charnock, Stephen. ([1684], 2000), The Existence and Attributes of God, Baker Books.

• Clark, Gordon (1961). Religion, Reason, and Revelation, Trinity Foundation.

• Frame, John (1994). Apologetics to the Glory of God, P & R.

• Engel, S. Morris (1994). With Good Reason, St. Martins.

• Frame, John (1987). The Doctrine of the Knowledge of God, P & R.

• Frege, G.F. (1967). Basic Laws of Arithmetic. University of California Press; Second Printing.

• Garson, James (2006). Modal Logic for Philosophers. Cambridge.

• Girle, Rod (2000). Modal Logic and Philosophy, McGill.

• Goble, Lou (2001). The Blackwell Guide to Philosophical Logic, Blackwell.

• Hughes, G.E. (1995). A new Introduction to Modal Logic, Routledge.

• Hunter, Geoffrey (1973). Metalogic, Campus.

• Konyndyk, Kenneth (1986). Introductory Modal Logic, ND Press.

• Lambert, Karel (1991). Philosophical Applications of Free Logic, Oxford.

• Lewis, C.I. (1946). An Analysis of Knowledge and Valuation., Open Court.

• Lewis, C.I. (1969). Values and Imperatives, ed. by J. Lange, Stanford University Press.

• Lonergan, Bernard (1970). Insight, Philosophical Library.

• Plantinga, Alvin (2000). Warranted Christian Belief, Oxford Univ. Press.

• O’Connor, Timothy (2008). Theism and Ultimate Explanation, Blackwell.

• Quine, W.V.O. (1993). Pursuit of Truth, Harvard University Press.

• Ricketts, Tom (2010). The Cambridge Companion to Frege. Cambridge Univerity Press.

• Stern, Robert (2000). Transcendental Arguments and Skepticism, Oxford University Press.

• Strawson, P.F. (1966). The Bounds of Sense, Methuen & Co.

• Strawson, P.F. (1963). Introduction to Logical Theory, Methuen & Co.

• Stroud, Barry (1968). “Transcendental Arguments,” Journal of Philosophy 65.

• Tarski, Alfred (1961). Introduction to Logic. Dover.

• Van Til, (1980). Survey of Christian Epistemology, P & R.

• Van Til, (2007). Introduction to Systematic Theology, P & R.

frege logic book

Filed Under: Apologetics, Christian Philosophy, Transcendental Argument Tagged With: , , , , , , , , , , , , , , , , , ,

Colossal Collection of Many Fine Essays on Frame’s Academic Contribution

May 20, 2012 By 1 Comment

Speaking the Truth in Love: The Theology of John M. Frame (Hardcover)

Speaking the Truth in Love: The Theology of John M. Frame puts the “giant” in “gigantic” since this festschrift honoring Professor Frame is over 1200 pages – Amazing! Subsequently if you’ve only a cursory acquaintance of Dr. Frame, scholar/academician/philosopher/worship leader who has been called Van Til’s second most significant advocate, you may be surprised to learn what a forbearing apologist he is.

Speaking the Truth in Love is teeming with outstanding essays by a variety of erudite apologists, ministers, and theologians. Herein are chapters touching an array of fascinating and diverse topics. For the Presuppositional devotee there are three essential chapters that offer fresh and potent analysis and application of Frame’s employment of Cornelius Van Til’s apologetic commencing with James Anderson, Don Collect and pressed further by Steve R. Scrivener.

Additional chapters (editor is John J. Hughes) have a mix of superb, splendid, captivating, ordinary, tedious, and lackluster writing from first-class scholars such as:

• Wayne Grudem
• Richard Pratt
• Paul Helm
• Vern Poythress
• Bruce Waltke (resigned from RTS due to his defence of “scientific evolution.”)
• William Davis
• William Edgar
• Peter Jones
• Reggie Kidd
• Don Collett (his chapter is his third published revision of his essay on Van Til’s TAG)
* Frame’s most recent reply to Collect’s defense of the Transcendental Argument for God’s Existence (TAG). See my analysis of Reiter’s update on TAG: http://thelordgodexists.com/2012/01/concerning-david-reiter%E2%80%99s-modal-transcendental-argument-for-the-existence-of-god/

• And more mostly fine essays.

An extraordinary chapter includes Steve R. Scrivener’s cogent essay contrasting and intermingling of Frame’s and Van Til’s apologetic while utilizing insights from Greg Bahnsen: fresh, perceptive, remarkable, stupendous, and profoundly contemplative. Scrivener makes use of the work of Frame, Van Til, and Bahnsen as he issues a powerful defense of TAG. He then reformulates the classical arguments in a TA formulation. One may not affirm all of Scrivener’s innovations and amalgamations, but all readers will be challenged and encouraged in the employment of TAG. Scrivener discusses the work of Craig and other non-presuppositionalists as he presses the need of presenting the Gospel as the center of one’s apologetic approach.

Another superb essay comes from the pen of Esther L. Meek on Frame’s epistemology in comparison with Michael Polanyi’s (1891-1976, a European chemist who became a groundbreaking philosopher and epistemologist) epistemic insights. Polanyi asserted that epistemic rights are obtained by central and subsidiary aspects of awareness while fixing on the article at hand while focusing on less important derivative things as epistemic backdrops. Meeks notes that for Polanyi “normative structures such as interpretive frameworks, or even languages, work like hammers… I indwell them, I pour myself into them, to attend beyond me a further focus or project. All knowing involves integrative orientation from subsidiary to focal, from `from’ to `to’ and beyond” (p. 619). Meek’s work in this volume is captivating, enthralling, instructive, and enlightening. A must read for Christians interested in epistemology.

Classical apologist R. C. Sproul acknowledged that “John Frame … has distinguished himself in the fields of theology, apologetics, philosophy, and Christian ethics.”

This massive volume offers several convincing assessments of Frame’s academic efforts regarding the following issues:

• Theology
• Van Til’s apologetic
• Ethics
• Worship
• Ecclesiology
• Classical apologetics
• Evidential apologetics
• Law and government
• Moral absolutes.

A chapter that is well-fitted for a pastor is Bruce K. Waltke’s explication of “Psalm 19: A Royal Sage Praises and Petitions I AM.” Waltke delivers an exegetical gem infused with precision and hearty application. His exposition is laden with exceptional scholarship that makes for a stirring devotional read and will drive many men of letters to their knees in humble thanksgiving (note: Professor Waltke resently resigned from RTS due to his defence of “scientific evolution,” but not “philosophical evolution”).

Two other noteworthy chapters discuss “The Attributes of God Within Frame’s Theology” (Derek Thomas) and Paul Helm on “Frame’s Doctrine of God.”

The price of this admirable book is nearly cut in half since its publication; moreover I would heartily recommend this volume for Christian apologists, philosophers, epistemologists, and ministers of all apologetic schools and disciplines.

See my two of my Books: Truth, Knowledge and the Reason for God: The Defense of the Rational Assurance of Christianity
And One Way to God: Christian Philosophy and Presuppositional Apologetics Examine World Religions http://thelordgodexists.com/books/

and my Apologetic E-books HERE

The Master’s Seminary Here

Filed Under: Apologetics, Book Reviews, Cornelius Van Til, Greg Bahnsen, Presuppositional Epistemology, Transcendental Argument Tagged With: , , , ,

Concerning David Reiter’s Modal Transcendental Argument for the Existence of God

January 4, 2012 By 18 Comments

David Reiter’s Interesting Modal TAG

 

Selected argument forms of Reiter and various comments by Mike Robinson

 

David Reiter (Associate Professor of Philosophy at Erskine College) offers Don Collect’s Causality Transcendental Argument1 (see Reiter’s article for the background exposition and the previous argument forms) constructed from Strawson’s notion of Presupposition:

 

I.

Transcendental Argument (2)

  1. C [i.e., There is causality] presupposes G [i.e., God’s existence]
  2. C

So 3. G.

 

And TA (3):

  1. C presupposes G.
  2. ~C [i.e., There is no causality]

So 3. G.

 

David Reiter observes: “The central and critical point here is that we can validly derive God’s existence as long as the causality premise (there is causality) merely has truth value… This is what makes the transcendental argument (TA) such a daring move in Christian apologetics.”

Reiter argues that the above TA “only establishes the actual existence of God, it does not establish the necessity of God’s existence,” since it lacks a modal conclusion.

 

************************

All the work in complete italics is mine and not Reiter’s.

 

I would like to explore his employment of the term actual; I maintain that when discussing God as actually existing, it seems to point toward God necessarily existing.

 

        •  God is an actual given in a possible world W if, and only if, He has complete omnipresence in W; and

       •  God is omnipresent if He has complete presence in every possible world.

       •  Omnipresence is possibly exemplified. That is, it is possible that there is a God who has omnipresence.

       •  Therefore, possibly it is necessarily true that an omnipresent God exists.

       •  Thus, it is necessarily true that an omnipresent God exists.

       •  Therefore, an omnipresent God exists.

 

When one perceives how the argument works, you might think that asserting or affirming the premise is tantamount to asserting or affirming the conclusion; the astute atheist may assert that he does not believe it is possible that there is a God. But could not a parallel criticism hold of every valid argument? Take any valid argument: after you perceive how it works, you may think that asserting or affirming the premise is tantamount to asserting or affirming the conclusion.

If there are things that transcend the material realm, including God, necessarily; a necessary entity cannot be grounded by a contingent world or series of worlds. In contrast, non-theism rests upon a contingent world or worlds. Consequently non-theism lacks the necessary endowment to underwrite necessary truths.

 

A second possible argument that attempts to move from God’s actuality to necessity:

 

     •   God is actual in a given possible world W if, and only if, He is necessary in W; and

     •   God is actual if He is necessary in every possible world.

     •  Actuality is possibly exemplified. That is, it is possible that there is a God who is necessary.

     •   Therefore, possibly it is necessarily true that God exists.

     •   Thus, it is necessarily true that God exists.

     •   Therefore, God exists.

Logically it’s more than problematic to demonstrate that a necessary being’s existence is impossible; there appears to be modal reasons to affirm that a necessary being, God, by definition, exists.

 

************************************

II.

 

Reiter notes: “Van Til holds that predication is impossible apart from God’s existence. This predication claim amounts to the conjunction of”:

(a)    There is no possible world where some proposition p is true and God does not exist.

(b)   There is no possible world where some proposition p is false and God does not exist.

 

“More compactly, the presuppositionalist claim is as follows:”

  1. There is no possible world where some proposition p has a truth-value and God does not exist.
  2. There is some proposition p that has a truth-value in the actual world (e.g. the proposition Lincoln is the state capitol of Nebraska has the truth-value of true).
  3. So God exists in the actual world.

 

He then offers this analysis: “This is a maximally versatile argument form in the sense that the existence of God follows validly form the truth or falsity of any proposition whatsoever.”

He adds: “But it only yields the actual existence of God—it does not yield the modal claim that God exists in every possible world (i.e., that Necessarily God exists).”

 

Incorporating this supposition then yields the following argument form:

  1. There is no possible world where some proposition p has a truth-value and God does not exist. [Presuppositional Claim.]
  2. For any possible world W, there is some proposition p that has a truth-value in W.
  3. So, For any possible world W, God exists in W.

Reiter apprises: “I call this argument form the form The Transcendental  Argument from Presupposition. This argument is perfectly valid, and it yields the modal conclusion that God exists in every possible world.”

———–

III.

 

Reiter then outlines Sean Choi’s reconstruction of Bahnsen’s TAG and agrees with Choi as he deems it insufficient at proving the conclusion of Christian theism since some other species of theism may be maintained in the same manner.

————

IV.

 

Reiter asserts that “if the goal is to construct an argument for the necessary truth of Christian theism … then the transcendental premise is appropriate and necessary. … let us at this point introduce the general form for a Modal Transcendental Argument, as I shall call it:”

(MTA1) It is necessary that q.

(MTA2) It is necessary that if not-p, then not-q.

So, (MTA3) It is necessary that p.

 

Reiter at that juncture comments: “The important revision here (relative to Choi’s analysis) is that both the granted premise and the transcendental premises are necessary propositions.  … We can now express the Modal Transcendental Argument Form as follows:

 

MTAG1. It is necessary that there is a proposition that has a truth-value.

MTAG2.  It is necessary that if God does not exist, then it is false that there is a proposition that has truth-value.

So, MTAG3. It is necessary that God exists.

 

Reiter completes his proposal: “The overall conclusion of our discussion is that a TA intended to establish the necessity of God’s existence must be purely transcendental—i.e., it must be composed exclusively of necessary truths.”

———————-

———————-

It is essential that the reader studies the complete article to adequately understand the scope and refinement of the author’s exposition.

 

Notwithstanding the philosophical specialization, Reiter’s article is worth reading. It will alert apologists to the philosophical strength of Transcendental Arguments for the Existence of God and the recent objections to them. It will also interest scholars of religion and philosophers working with modal logic. For contemporary presuppositionalists Reiter does not disappoint as he employs high levels of precision, rigor, and innovation that will benefit many readers. The author offers a quick pace sweep from Van Til, Bahnsen, Collect, and Choi. The article develops an innovative view concerning the epistemology and metaphysics of the modality of TAs—truths concerning what is actual, possible or necessary. This framework is then applied to a re-examination of the Transcendental Argument for God.

 

Acquire the journal The Confessional Presbyterian to see the full article inasmuch as it is carefully argued re-evaluation of the relation of necessary existence and transcendental argumentation, casting welcome new light on contemporary discussions. This is a must-read for all thoughtful apologists and theistic philosophers. Bravo David Reiter and Chris Coldwell!

 

Purchase this issue or subscribe to The Confessional Presbyterian at: http://www.cpjournal.com/2011/05/the-confessional-presbyterian-7-for-2011/

 

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1.        David Reiter: The Confessional Presbyterian,  7 for 2011

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see my New E-book Truth and the Reason for God HERE

 

 

 

 

 

Filed Under: Apologetics, Presuppositional Apologetics, Presuppositional Epistemology, Transcendental Argument Tagged With: , , , , , , ,

Logic, Reason, and the Laws of Logic: Definitions and A Christian Theistic Exposition

November 10, 2011 By 5 Comments

Theism, Reason and the Laws of Logic

by Mike Robinson

Definitions are important in communication; perhaps the fallen nature and finiteness of men makes understanding many philosophical issues difficult to fully grasp or defend. It may surprise the reader that very few apologetic works provide clear and explicit definitions of terms logic, the laws of logic, and reason; including many classical and presuppositional apologetic books. Furthermore, regarding some doctrines (the Trinity; Sovereignty; the Incarnation; etc.) conceivably one might have to utilize philosophical and theological distinctions that are so minutely exact and fine that a fallible finite man could under no circumstance, in principle, comprehend them entirely. Thus one must study essential classifications and delineations as one communicates eternal truths with humility.

I. Distinctions I Maintain Between Logic and the Laws of Logic

Logic: “The study of argument [not a quarrel]; a piece of reasoning in which one or more statements are offered as support for some other statement” (S. Morris Engel: With Good Reason).

Logic is: (1) The Science of Argument. (2) A Hermeneutical Tool. (3) A Science of Commitment (John Frame: DKG, p. xi).

Logic is the study of the methods and principles used to distinguish correct from incorrect reasoning (Irving Copi: Introduction to Logic).

The Laws of Logic: Laws of thought and reason that are immaterial, aspatial, atemporal, universal, obligatory, necessary, immutable, and absolute. Some academics identify them as the laws of thought, the laws of truth, or the laws of reason. Various scholars strongly prefer to name them the laws of logic because they are independent of human minds and are ubiquitous throughout all experience. All rational thinking (and communication) presupposes and uses the laws of logic.

The Law of Identity (LOI) is A=A. The most well-known law is the Law of Non-contradiction (LNC): A cannot be A and Non-A at the same time in the same way (A~~A). A man cannot be his own father.

The laws of logic “are basic principles of reasoning” (Frame: CVT).

The laws of logic reflect the nature and mind of the God of the Bible; thus, they have ontological grounding—that is, they are grounded in the very nature of truth itself and cannot be reduced to human convention, opinion or psychology. Without these laws, knowledge and rational thinking are impossible. To deny the laws of logic, one must use these laws in one’s attempt to deny them. Those who deny the laws of logic are participating in a self-defeating endeavor. The Law of Non-contradiction (LNC), the Principle of Contradiction (or the Law of Contradiction) is perpetually necessary and in the words of Aristotle: “One cannot say of something that it is and that it is not in the same respect and at the same time.”

Various scholars assert that the Law of Excluded Middle may have real exceptions.

Allan Bloom stated that “The earliest-known explicit statement of the principle of contradiction, the premise of philosophy, and the foundation of rational discourse” is given in Plato’s Politeia. Therein is where the character Socrates states, “It’s plain that the same thing won’t be willing at the same time to do or suffer opposites with respect to the same part and in relation to the same thing” (all the above are excerpts from my Apologetic Book: Truth, Knowledge, and the Reason for God at: http://thelordgodexists.com/product/truth-knowledge-and-the-reason-for-god-the-defense-of-the-rational-assurance-of-christianity/).

“The law of contradiction [LNC] cannot be thought of as operating anywhere except against the background of the nature of God” (Van Til: IST).

II. Definitions of the Term Logic

Logic: enables us to think in a rational, systematic and orderly way.

Etymological definition: logike is the Greek term that means thought; a treatise pertaining to thought.

Logic real definition: commonly defined as the art and science of correct inferential thinking deals with the laws, methods and principles of correct thinking. Through Logic, we acquire the techniques and skill of thinking correctly whereby our mind is able to proceed with order, ease and without error, when we master the techniques and acquire the skill of correct thinking then we are able to expound our thought orderly, clearly and systematically.

Logic as the study of the methods and principles used to distinguish correct reasoning from incorrect reasoning. Thus it provides us with the techniques for testing the correctness (and also the incorrectness) of arguments (Copi).

Logic real definition as a Science: It is a systematized body of knowledge about the principles and laws of correct inferential thinking. It follows certain rules and laws in arriving at valid conclusions.

Logic real definition as an Art: The art of reasoning. It requires mastery of the laws and principles of correct inferential thinking. Reasoning conducted or assessed according to strict principles of validity.

Aristotelian logic: A particular system or codification of the principles of proof and inference. (http://www.slideshare.net/ulrick04/1a-logic-intro).

III. Additional Definitions of the Terms Logic and Reason

Logic: Removing or preventing contradictions in one’s thoughts or ideas.
Logic is the art of conforming one’s thoughts to the Law of Identity. In one respect, thoughts have to conform to the Law of Identity, as does everything else. This has to do with the nature of thoughts. Ideas have a different nature than memories, which are different from emotions. In this respect, all thoughts conform to the Law of Identity.

In a different respect, though, it requires focused action to conform to the Law of Identity. Ideas have content. This content is generated by the thinker from perceptual data. However, it may be generated incorrectly. Logic requires the content to be clear and identifiable. It requires that no contradiction exist within the idea.

Logic is used in integrating ideas as well. Again, it is the process of conforming to the Law of Identity. What this means in practice is combining information clearly, and without contradiction. It must be combined into a specific, identifiable package, that doesn’t contradict itself.

Logic is the art of non-contradictory identification. It is the mental tool that sets the standard for proper thought. It is the foundation of knowledge. It is the means of understanding and clarity. Without logic, we could not distinguish between the true and the false. We could not throw out bad ideas because we could not judge them as bad. Without logic, our minds would be cluttered with so many absurdities and falsehoods that if there was some truth, it would be lost in the garbage of contradictions, fuzzy thoughts, and non-integrated mental images. (www.ImportanceofPhilosphy.com)

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Reason: Rational capacity, and the ability and proclivity to follow the same in a logical manner. To reason or to use one’s reasons in an orderly manner. The concept of reason is closely related to the concepts of language and logic, as reflected in the multiple meanings of the Greek word “logos”, the root of logic, which translated into Latin became “ratio” and then in French “raison”, from which the English word “reason” was derived. In contrast to reason more generally, language refers not to the thinking as such, but to the communication or potential communication of rational thoughts.
Reason: (1) The ability to understand and explain cogently, based on evidence and according to logical principles; (2) the ability to treat others fairly and decently, unless one is harmed by them.

A. This is a fundamental human capacity, and based on the capacity to represent things symbolically. A cogent explanation is one that is based on true or probable premises and deductively entails what it explains. Science is based on reason, and the test that something is a real science is that it has produced a real technology that works independent of belief in or understanding of the science that produced it.

There are three basic kinds of reasoning, where reasoning involves argumentation of any kind using assumptions and inferences of conclusions:
1. Deductions: To find conclusions that follow from given assumptions
2. Abductions: To find assumptions from which given conclusions follows
3. Inductions: To confirm or infirm assumptions by showing their conclusions do (not) conform to the observable facts.

Normally in reasoning all three kinds are involved: We explain supposed facts by abductions; we check the abduced assumptions by deductions of the facts they were to explain; and we test the assumptions arrived by deducing consequences and then revising by inductions the probabilities of the assumptions by probabilistic reasoning when these consequences are verified or falsified.

B. The term “reason” is used in another sense, that is more related to morals and ethics than to science. In this sense, one is reasonable if one treats others fairly, does not harm them unless attacked, does not deceive them without provocation, and in general behaves towards them according to some schema of values that chart what it is to be virtuous (www.PhilosophicalDicitonary.com).

I do not believe Van Til defines reason anywhere, but it is clear that he views it primarily as a human capacity or faulty. Specially, reason is the capacity of a person to think and act according to logical norms, including the capacity to form beliefs, draw inferences, and formulate arguments (Frame: CVT).

Reason is the power or capacity whereby we see or detect logical relationships among propositions (Alvin Plantinga: Warranted Christian Belief).

Supporting Material on The Laws of Logic

And a Modal Argument for the Laws of Logic

Laws of logic are also known as the laws of truth, thought, and reason (many prefer to designate them the laws of logic since they are ubiquitous throughout human experience). These laws are immaterial, aspatial, atemporal, universal, obligatory, necessary, immutable, and absolute. Some academics identify them as the laws of thought, the laws of truth, or the laws of reason. A few scholars strongly prefer to name them the laws of logic because they are independent of human minds. All rational thinking (and communication) presupposes and uses the laws of logic.

The Law of Identity (LOI) is A=A. The most well-known law is the Law of Non-contradiction (LNC): A cannot be A and Non-A at the same time in the same way (A~~A). A man cannot be his own father.

The laws of logic reflect the nature and mind of the Triune God; thus, they are grounded in the very nature of God and cannot be reduced to human psychology. Without these laws, knowledge and rational thinking are impossible. To reject the laws of logic, one must use these laws in one’s attempt to reject them.

Modal Argument that Maintains the Universality of the Laws of Logic

• A law of logic is universal in a given possible world W if, and only if, it has complete ubiquity in W; and
• A law of logic is universal if it has complete ubiquity in every possible world.
• Universality is possibly exemplified. That is, it is possible that there be a law of logic that has complete ubiquity.
• Therefore, possibly it is necessarily true that a universal law of logic exists.
• Thus, it is necessarily true that a universal law of logic exists.
• Therefore, a universal law of logic exists.

When one perceives how the argument works, you might think that asserting or affirming the premise is tantamount to asserting or affirming the conclusion; the astute physicalist advocate (or anti-universalist) may assert that he does not believe it is possible that there be a universal law. But could not a parallel criticism hold of every valid argument? Take any valid argument: after you perceive how it works, you may think that asserting or affirming the premise is tantamount to asserting or affirming the conclusion.

The ultimate norms for human knowledge are found not in any human mind or minds, or anywhere else in creation, but in the mind of God (James Anderson: Speaking the Truth in Love).

There are things that transcend the material realm, including the laws of logic. A = A (Law of Identity) and A~~A (Law of Non-contradiction) universally; an immutable universal (something that is always true) cannot be grounded by a mutable particular (non-universal) cosmos, which non-theism rests upon. Therefore non-theism lacks the necessary endowment to underwrite the laws of logic.

I employ the expression “a particular” as an individual thing, a specific entity that may be material, abstract, or spiritual. It lacks universal reach forasmuch as it is one finite thing. A material particular cosmos that is mutable lacks universality and immutability required to account for the universal immutable laws of logic; Yahweh possesses these attributes, thus He sufficiently accounts for the laws of logic. The laws of logic must be utilized in everything one does: in all one’s actions and in all knowledge claims. They are inescapable; hence Yahweh is inescapable.

This argument contends that one would have to believe the contrary of the possible, a universal law of logic exists, yet logically it’s not possible to demonstrate that a law of logic’s existence is impossible, thus the law of logic’s existence is logically necessary inasmuch as a law of logic, by definition, is a ubiquitous universal (For more see my Book: Aristotle, Frege, the Laws of Logic, and God HERE

This contention is not a gap dependent argument since it does not ascribe to divine work something which may possibly, in principle, be explained through mutable natural causes. The whole of the natural world is in a state of flux, all natural things change. Thus one cannot argue for a mutable ground to account for the immutable laws of logic. On cannot appeal to individual mutable natural causes to account for immutable universals such as the laws of logic.

In the beginning was the Word (Logos) and the Word was with God and the Word was God (John 1:1).

Belief in God is ultimately, of course, the presupposition that controls even one’s concept of reason itself (John Frame, DKG).

In the E-Book Aristotle, Frege, the Laws of Logic, and Theism, Mike Robinson demonstrates that God is the true foundation for the Laws of Logic and that atheism lacks the necessary substructure to ground these laws of thought. Many noteworthy issues that atheism upholds are tackled with clarity, precision, and thoughtfulness. Throughout this volume the author informs, needles, illumines, elucidates, enlivens, and motivates the reader with powerful truth regarding the laws of logic. This work is accessible, fluid, and loaded with useful arguments for Christian Theism.
Aristotle, Frege, the Laws of Logic, and Theism is not the typical criticism of atheism; it utilizes new ground proclaimed by numerous and diverse apologetic advancements.

or The Paperback HERE

The eternal Logos is a Necessary Truth Condition of Human Knowledge

 In the beginning was the Logos … (John 1:1).

Jesus’ ontology (His being and essence) is a substantial element of Christianity, for He is the great Logos (John 1:1), and logic is an attribute of His being and nature. Christians are a community that can account for reason; as reason comes from the nature of God. The true God is the God of reason. Reason cannot be held over His head in a type of Eurythro Dilemma, but is a reflection of His nature; additionally we must espouse it in submission to His revelation in the Bible. Christians should base their worldview on God’s word and His character. The Laws of Reason (Laws of Logic) have no material content. One cannot put the laws of reason (A = A; A~~A) in a bowl and pour milk over them. The abstract application of reason also has no material content.

The laws of logic are essential (they are immutable universals) and an a priori truth condition for any communication. Logic is the foundational instrument necessary for all utterance, debate, science, mathematics, and learning. Without using the laws of logic, one could not deny that logic is mandatory for communication. The precondition for the laws of logic is God.
Without the transcendent, immutable, and universal in reach God, one cannot justify or account for the transcendent, immutable and universal rules of logic. God is the truth condition for laws of reason.

Also known as the laws of truth (Frege), these laws are an a priori truth condition for knowledge, discourse, and argument. Logic is absolutely necessary for the intelligibility of life and God is absolutely necessary for logic. Thus, the Triune God is, and has to be. And He alone is God. No other named god supplies the obligatory truth conditions for the intelligibility of this world.
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Comments

Jarvis says:

Hi Mike,
Do you recall the bit you wrote using the symbols A~~A? Basically you were showing how to know anything one must presuppose the laws of logic. The idea seemed to be that to know some thing A, one must know that A is itself and is not its negation, or that A is A and that A is not ~A. Is this right?
I’m having a hard time seeing how logic is the precondition for thinking and knowledge. Would you mind showing me how that is true. I know I think, and I know I know; but I don’t see how exactly that means the basic rules of logic (LI, LEM, LNC) are true. You said that one must use them to deny their necessity for thinking and knowledge. I don’t see exactly how that is true. I would appreciate your help!
The heart of my question is how do we show or prove what you write here in your reply:
“Without these laws [the laws of logic], knowledge and rational thinking are impossible. To deny the laws of logic, one must use these laws in one’s attempt to deny them. Those who deny the laws of logic are participating in a self-defeating endeavor.”
I see these as three closely-related conclusions:

1.) “Without these laws [the laws of logic], knowledge and rational thinking are impossible.”
2.) “To deny the laws of logic, one must use these laws in one’s attempt to deny them.”
3.) “Those who deny the laws of logic are participating in a self-defeating endeavor.”

What you were getting at in this bit:
All thought must assert that A~~A.
Whenever one thinks of something, it is not another thing at the same time/way.
The thought that a something is not another thing is knowledge.
All knowledge must distinguish one thing from another
All knowledge presupposes A~~A.
All thought and knowledge presuppose and utilize A~~A.

Is there any more where this came from? In other words, could you elaborate on this? Also, I do not know what A~~A means. Is it a reference to the law of non-contradiction? I am actually a Christian, so yes I affirm all those things. But like Anselm, I am pursing the certainty of what I believe.
 Thanks, again, Mike!
 -------
 
 Jarvis says:
 Hi Mike,
 I hope it is okay if I ask another question. It has to do with paraconsistent logic. As you undoubtedly know, advocates of paraconsistent logic hold there is some proposition P that is compatible with not-P, even if most propositions are not compatible with their negations. In other words, most of reality is rational (not contradictory) but some is irrational (contradictory). But if presupposing the classic law of non-contradiction (that for any proposition P, P is not compatible with not-P) is necessary for any knowledge, as we have been discussing, then that would mean presupposing paraconsistent logic would make knowledge impossible. But how do we show that? It seems the advocate of paraconsistent logic could simply say that the knowledge they do have, for example of paraconsistent logic, their existence, etc., are cases where P is not non-P, but still there are propositions that are consistent with their negations. So they know the things they know because those things are not compatible with their negations, but still the contend there are some things that are compatible with their negations. How can we refute this position and show that no knowledge is possible if paraconsistent logic is substituted for the classic law of non-contradiction? As always, thanks for your help!
 Jarvis says:
 Hey Mike, not sure if you received my earlier post on paraconsistent logic. Anyway, I am trying to see how to refute it. As you undoubtedly know, advocates of paraconsistent logic hold there is some proposition(s) P that is compatible with ~P (in exactly the same sense and same way), even if most propositions are incompatible with their negations. Now the typical response to anyone denying the classical law of noncontradiction is to assert that one must presuppose the law to deny it, making the law undeniable. But this does not seem to work against the advocate of paraconsistent logic. If asked if their very statement, or proposition, affirming paraconsistent logic is true or false, they would say it is true, that in the case of this statement, it is a proposition that is not compatible with its negation. Thus it seems they could say the assertion that paraconsistent logic is true does not presuppose the classical law of non-contradiction (that for any proposition P, P is incompatible with ~P in exactly the same sense and same way); rather, the statement simply presupposes the truth of paraconsistent logic: that most propositions are incompatible with their negations, including this very statement or proposition affirming paraconsistent logic, while nevertheless there are some propositions that are compatible with their negations. How would you refute this?
 ----
 Mike Robinson says:
 There seem to be many problems with the notion of the paraconsistency logic in relation to the LNC.
 1. The asserter must supply and account for the concept of contradiction within his paraconsistent logical (PL) method. I don’t see how this can succeed. It appears impossible, so the system collapses. One can make an assertion, but is there a consistent foundation that has the ontic resources to account for the LNC (or even the principles of PL) that underwrites the assertion? Not with PL.
 2. The PL advocates that I have read seem to confuse negation with contradiction; there’s a clear distinction (Liars paradox, etc.)
 3. It appears that PL examples do in fact utilize P in a different manner; so it fails.
 Logicians differ on PL and other topics, yet in their sundry arguments and systems, the LNC must be utilized: Is PL in fact PL? or is PL its contradiction?
 I hope that helps,
 Mike.
 -----
 Jarvis says:
 Hi Mike, thanks for your response. I really appreciate your correspondence. Let me think over what you have written, and I’ll let you know what I think. Best, Jarvis

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Mike Robinson says:
Jarvis you might want to check out one of my books–two of them discuss the issue at length:
Truth, Knowledge, and the Reason for God

http://www.amazon.com/Truth-Knowledge-Reason-God-Christianity/dp/1432765914

or
Aristotle, Frege, the Laws of Logic and God at: http://www.mikearobinson.com/
or the E-books at: http://www.smashwords.com/books/view/35432
They may assist you in your studies.
Blessings, Mike.
—
Reply
Jarvis says:
Dear Mike, I am struggling to see how we can show that all reality must be rational, that it, that it is not even possible that there is some irrational reality. How can we refute the idea that there may be contradictory realities, even if most reality is not contradictory? I can see that with respect to anything I know (e.g. my own present existence), I must think that thing is what it is (law of identity) and not its negation (law of non-contradiction), but what about the many things that I do not know. What shows that there cannot be something, even one thing, that violates the laws of logic, and so is non-rational and unknowable? In other words, it seems we must show that to know anything one must presuppose not simply that that thing is what it is and not its negation, but that all things must be what they are and not their negation. But it only seems the former, and not the latter, stronger law must be presupposed to know something. So, again, I don’t see how to prove that all reality is rational. Your expert advice on this would be very appreciated. Once again, can you specifically show that to know something we must presuppose that all things are /must be identical to their respective selves and not identical to their respective negations? Thanks, Mike! I hope to hear from you soon! I’m sorry if I am just slow-witted! Jarvis
—-
Reply
Mike Robinson says:
Jarvis:
The foremost notion one should remember is that to affirm anything, including the demise or limitation of a law of logic, one must utilize the law in that assertion.
1. Ask the universal LNC-denier to supply one sentence that fails to be bound to the LNC.
2. Ask them to give you a deductive argument that proves the non-universality of the LNC.
And what are you attempting to achieve in your pursuit (i like this stuff a lot too); so few of the upper few will ever get to this level of LNC skepticism? If they do just, give them a cogent answer, agree to disagree and then press the moral law on their hearts and share the grace of the gospel.

Here is a modal argument that is going into my new book (see the earlier presented Modal Argument in this treatise).
I hope this might assist you a bit, keep up the good work.
Blessings,
Mike
—-
Jarvis says:
Hey Mike,
Thanks for your reply. I especially appreciate you sharing your new modal argument with me. It is really fascinating; I will have to mull it over some more. Again, thanks!
At the beginning of your reply you wrote, “to affirm anything, including the demise or limitation of a law of logic, one must utilize the law in that assertion.” Can you demonstrate this, because I am still having a hard time seeing that it must be true. Specifically, I do not see how it is true of this assertion:
“There may be some proposition(s) P that is compatible with ~P (in exactly the same sense and same way), even if most propositions are incompatible with their negations.”
It seem that if the holder of this position were asked whether the position is true or false, they could say it is true, that in the case of this statement affirming their position, it is a proposition that is not compatible with its negation. In other words, it seem like the person could say the assertion of the truth of their position does not presuppose the law of non-contradiction (that for any proposition P, P is incompatible with ~P in exactly the same sense and same way); rather, the statement simply presupposes its own truth: that most propositions are incompatible with their negations, including this very statement or proposition affirming the position, while nevertheless there are some propositions that are compatible with their negations. Do you see what I’m saying? As always, thanks for your help!
—-
Mike Robinson says:
Jarvis:
It appears that you may be into some possible unnecessary speculation. If I am gathering what you are trying to communicate correctly, I would say that if:
i = an irrational aspect of some reality somewhere at some time; then i = i;
Thus the Law of Identity is still in force; I don’t see how one can escape it.
Perhaps I’m do not fully understand that which you are asserting.
Best wishes,
Mike

—-
Jarvis says:
Mike, it’s so funny that you posted this message today. I actually woke up this morning thinking exactly the same thing you wrote!! I realized that it really comes down to the law of identity: that for something to exist, it must be SOME THING. And then the law of non-contradiction follows: to be some thing is to not be the negation of that thing. And all of this means that no reality can be irrational, for then that reality would not be some specific, or determinate, thing; which is to say it would be nothing, or NO THING. Fantastic!
—-
Mike Robinson says:
Jarvis: excellent point. Also there is so much wrangling within and without paraconsistent schools that one can take a peek from above and see that all the diverse types of PL have to affirm their own perspective while presupposing A=A and deny aspects of other PL types so they must presuppose the LNC in order to do so.
Blessings to you, and stay in touch,
Mike
—-

Suggested Reading

• Adler, Mortimer (1985). Ten Philosophical Mistakes. St. Martins
• Aristotle, Metaphysics. Oxford.
• Bahnsen, Greg (1996), Always Ready, Covenant Media.
• Bahnsen (1998). Van Til’s Apologetic, P & R.
• Carroll, Lewis (1989). Best of Lewis Carroll, Castle.
• Charnock, Stephen. ([1684], 2000), The Existence and Attributes of God, Baker Books.
• Clark, Gordon (1961). Religion, Reason, and Revelation, Trinity Foundation.
• Frame, John (1994). Apologetics to the Glory of God, P & R.
• Engel, S. Morris (1994). With Good Reason, St. Martins.
• Frame, John (1987). The Doctrine of the Knowledge of God, P & R.
• Garson, James (2006). Modal Logic for Philosophers. Cambridge.
• Girle, Rod (2000). Modal Logic and Philosophy, McGill.
• Goble, Lou (2001). The Blackwell Guide to Philosophical Logic, Blackwell.
• Hughes, G.E. (1995), A new Introduction to Modal Logic, Routledge.
• Hunter, Geoffrey (1973). Metalogic, Campus.
• Konyndyk, Kenneth (1986). Introductory Modal Logic, ND Press.
• Lambert, Karel (1991), Philosophical Applications of Free Logic, Oxford.
• Lewis, C.I. (1946). An Analysis of Knowledge and Valuation., Open Court.
• Lewis, C.I. (1969) Values and Imperatives, ed. by J. Lange, Stanford University Press.
• Lonergan, Bernard (1970). Insight, Philosophical Library.
• Plantinga, Alvin (2000), Warranted Christian Belief, Oxford Univ. Press.
• O’Connor, Timothy (2008), Theism and Ultimate Explanation, Blackwell.
• Quine, W.V.O. (1993), Pursuit of Truth, Harvard University Press.
• Stern, Robert (2000). Transcendental Arguments and Skepticism, Oxford University Press.
• Strawson, P.F. (1966). The Bounds of Sense, Methuen & Co.
• Strawson, P.F. (1963). Introduction to Logical Theory, Methuen & Co.
• Stroud, Barry (1968). “Transcendental Arguments,” Journal of Philosophy 65.
• Tarski, Alfred (1961). Introduction to Logic. Dover.
• Van Til, (1980), Survey of Christian Epistemology, P & R.
• Van Til, (2007), Introduction to Systematic Theology, P & R.

Filed Under: Apologetics, Presuppositional Apologetics, Presuppositional Epistemology, Transcendental Argument, Transcendental Argument for the Existence of God Tagged With: , , , , , , , , , , , ,

There is Proof, Proof, Nothing but Proof: Yet God is Required for Proof and Evidence

April 27, 2011 By Leave a Comment

                  

Yes, the Bible reveals to humanity that the Earth hangs on nothing (Job 26:7) and is a sphere (Isaiah 40:22). Scripture declared this thousands of years before telescopes and modern science discovered those facts. God’s word teaches us the proper function of the water cycle (Job 38:12-14), the existence of ocean currents (Psalms 8:8), the solar cycle, and the expansion of the universe (Isaiah 40:22) centuries before modern science found these truths. These evidential facts are consistent with the authority of the Bible. These and other evidences do not give the Bible its authority; it is endued with it because it is God’s word, thus all things are evidence for God’s existence.

          There is Proof for Theism and Theism is the Required Truth Condition for Proof

All science, testing, research, and examination presuppose God and His word. Testing utilizes a number of dynamics such as the laws of logic and induction. A materialistic worldview cannot justify the existence or the use of the laws of reason. They are nonphysical and abstract dynamics that can only come from the nature of the one true God. We have certain knowledge that the God of scripture lives. We do not think He probably exists. Our faith is not just reasonable or plausible. It is impossible for the true and living God not to exist because without Him, we cannot know anything at all. He is the precondition for all knowledge. God must be presupposed as the basis of every element of mankind’s experience, knowledge, and value.

Ponder the following syllogism:

  • The God of scripture is the foundation of all reality or reality is unintelligible.
  • Reality is intelligible.
  • Therefore, God is the foundation of reality.

The consequence of affirming that God does not exist is to assert that the world is unintelligible and unknowable. That proposition is impossible because it is self-smiting. If the world is unintelligible and unknowable, then that statement also would be unintelligible and unknowable, hence it would be self-voiding and false. This consequence leads to the truth that God is the ground and foundation of knowledge. Unless Christianity is true, for it alone furnishes the rational pre-essentials as the epistemic bedrock for immaterial immutable universals, we can know nothing of reality. If we can know nothing of reality, we cannot know that proposition. Unless the God of revelation is and has spoken, human knowledge has no intelligible basis.

Harry Blaimires commented, “The Old and New Testament… No one can pretend it isn’t there. Everyone who is concerned with the meaning of life, and the destiny of the human race will have to take it into account.”

  

God’s word declares that life must revolve around Him. We must have no other gods before Him. All men have a destiny that will find its consummation at the judgment seat of Christ. Self-deceivers can pretend that God does not exist, but God lives. Those, who pretend He has not spoken, live a life that is contradictory and confusing. Their life will end one day and they will give an account for their life. This truth must consistently remain in front of our eyes. We should live and move before the face of God. This is our duty and our joy.

 
There are many professional skeptics and scoffers in our culture who marshal their full-bore nastiness to defend atheism. These men stroke their tobacco stained beards, and try to act sagacious, as they employ their acerbic wit to attack God. They are truth “falsifiers.” They become experts at wishful thinking and self-deception. They have elaborate arguments that instruct the blind how to stay in the dark, while professing to make them wise.

See:

http://www.amazon.com/Letter-Atheist-Nation-Presupositional-Apologetics/dp/1432706322/ref=cm_cr_pr_pb_t

Filed Under: Covenantal Apologetics, Presuppositional Epistemology, Transcendental Argument Tagged With: ,