Theism, Reason and the Laws of Logic
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)
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.
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.
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
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
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.
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
Mike Robinson says:
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.
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:
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.
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,
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