VERITAS EVANGELICAL SEMINARY

VERITAS EVANGELICAL SEMINARY A research paper, discussing the terms and definitions of inductive and deductive logic, in partial fulfillment of the requirements for the certificate in Christian Apologetics PH504 - Logic BY COLIN BURGESS

TABLE OF CONTENTS INTRODUCTION...3 WHAT LOGIC IS NOT...3 WHAT LOGIC IS...4 WHY STUDY LOGIC...6 HOW TO STUDY LOGIC...7 OBJECTIONS TO LOGIC...7 DEFINITION AND RULES...12 Deductive logic...17 Categorical...18 Propositions...18 Distribution...19 RULES OF CATEGORICAL SYLLOGISMS...19 HYPOTHETICAL SYLLOGISMS...23 DISJUNCTIVE SYLLOGISMS...25 INDUCTIVE LOGIC...26 Probability...28 A Priori...29 A Posteriori...29 Degrees of Probability... 30 CONCLUSION...31 BIBLIOGRAPHY...32

INTRODUCTION In order to do Christian Apologetics, it must be defensible that the truth about reality is knowable, therefore, this brief paper will attempt to communicate the measurable outcome, of defining the terms of logic, briefly defending objections of Christianity and logic and will set forth various logical structures and rules of syllogisms, then will touch base, briefly, on inductive and deductive types of reasoning. This paper being no exception, the importance of proper logical thinking, in writings and talks, will be communicated. There are structures and failures in logical thought, which in order to correct faulty thinking, must be understood. WHAT LOGIC IS NOT Dale Jacquette, in his book on symbolic logic, says it well when he says, 'Logic does not actively seek to give statements about science, history or religion, logic teaches us about logic...' and we must apply logic to these respective fields of epistemology, logic enables us to express our beliefs in logically correct arguments, to avoid formal and informal fallacies, to increase our knowledge by drawing logically correct inferences.' Logic, is not an arbitrary set of conventional rules which we have coined, nor have we observed regularities, or patterns in our thinking and set up the rules of logic around such observations. If this were so, it could not be said that truth exists independent of

our minds which apprehend truth. WHAT LOGIC IS Dale Jacquette, in his symbolic logic text describes logic as, being, the collective name for the principles of correct reasoning and the study of logic investigates these principles, allowing the user to identify the general rules that distinguish good from bad reasoning. Logic is not psychology, it stands in contrast to psychology, which is a descriptive study that offers (at best) cause&effect explanations of how thinking occurs, without making value statements about it. Logic is a prescriptive abstract study, like mathematics, that seeks to establish rules for correct reasoning and to help its user avoid mistaken reasoning. One anticipated outcome of logic would be to discover and justify principles that offer the best account of reasoning, as it should ideally occur. While it it true logic is prescriptive and not descriptive, in that we are not observing human thought then painting rules around how we observe it to function, this definition is not mind-independent enough. True reasoning and thought processes exist independently of our minds, which are just capable of apprehending rational truths, much like, as moral beings, we are capable of apprehending moral truths. These truths would exists, even if no moral, or rational beings existed to use them.

In summary, then: Logic is the study of valid thought Reasoned thought or argument, as distinguished from irrationality. Deals with the methods of valid thinking, to draw a valid conclusion, from a valid premise, avoiding formal and informal fallacies. Principles and rules for determining intelligibility and for drawing proper inferences, including deduction, induction and abduction. The rules of logic, then, are like mathematics, normative, or a necessary truth. It is a necessary truth in every possible universe; there is no conceivable universe that 2+2 would not total a sum of 4, much like in every possible universe, contradictory statements (A = non A) could not be true. Logic is not restricted to dealing with what is actual, rather logic can also deal with what is possible. Logic deals with rudimentary principles that have no prior justification. These principles are unprovable and they are presupposed by first order disciplines, such as the sciences. If these presupposed principles were not valid, such as a the law of non-contradiction, science could not differentiate between the object of study and the non-object of study, the theologian could not differentiate between God and non-god. The sciences, and historians, deal with contingent truths. For instance, the observational fact that 'Ravens are black' is a contingent statement, it could be the case that ravens were pink. A historical event which factually took place is not necessary, but contingent,

those who pursue these forms of epistemology (Bodies of knowledge) must first assume logic to be true, then proceed to study their respective discipline. Logic helps us to evaluate these elliptical truths and to understand them and express them in valid terms. WHY STUDY LOGIC? We already know how to, and do, think. We must use our natural reasoning abilities to master logic, just as one must first enter the water if we are ever going to learn how to swim. The reason it is important for the Christian, to study logic is not just so we may study scripture and assign true propositions to the nature of God, but so we may also be committed to being lovers of truth and all truth is God's truth. Logic deals with the methods of valid thinking. We want to draw a proper conclusion from a premise in order to construct an argument, in the philosophical sense, which is more than emotional expressions of what we feel, or wish to be true. In this case we are assessing arguments for various claims to truth. It is a prerequisite of all thinking, including theological thought. Logic is an inescapable tool, those who deny it cannot avoid using it. It is built into the very fabric of the rational universe.

HOW TO STUDY LOGIC In this paper, logic will be studied by comparing definitions and illustrations of correct reasoning, with recognizable types of logical errors. OBJECTIONS TO LOGIC There are objections to logic, in and out of Christian circles. The following are a summary of only a few: OBJECTION #1 - Rationalism. Some might object by saying this type of thinking makes God subject to our reason, creating a form of rationalism. RESPONSE God is not being subject to our reason, but we are using God given reason to understand God. Some things within Christianity are perhaps outside of our reasoning abilities, but are not unreasonable. Take for instance the Trinity which goes beyond, but not against reason. If we brought God down to our level this would be a mistake and we would end up with a Gnostic form of Christianity, rather God condescends to our level and we apprehend His nature by means of reason. God is ultimately rational, but we as His image bearers express His rationality in a diminished way. Without laws of logic to govern our thoughts we could not even understand special revelation. We could not in any way differentiate between the truth

claims of the Bible as opposed to the truth claims of the Qur'an. When scripture affirms God loves the world. how could we know what love is unless we knew what hate was and were able to distinguish between the two? So there is a difference between rationalism which is saying we bring God down to our level, and being rational which is using reason to understand God as He has revealed Himself to us. OBJECTION #2 Differing types of logic. There are many types of logic, why choose just one?, there is Eastern logic and so forth. RESPONSE There are inductive and deductive types of logic, all of which depend on the law of noncontradiction, because if contradictories are true then thought is impossible. If the objector wishes to say that there is Eastern Logic and Western Logic, why does Western Logic win out over Eastern? The answer is simple: Eastern logic denies the Law of Non-Contradiction, but as demonstrated above, denying this law is self-refuting, the very denial of this law of thought is a backhanded affirmation of it, since the denier is also the user of it. as one must affirm it before denying it. Logic is so clearly what governs our thoughts as much as morality governs our behaviour and the laws of nature govern our universe.

Logic is not some arbitrary/conventional set of rules, which we then subject our minds to, nor is it invented, rather, like all truths it is discovered. There are no two different types of logic which we must choose between, this is a false dichotomy, there is just logic and by this measure of logic other so called logics can be called 'illogical'. There are different types of logic in the sense of there being symbolic logic, or modal logic, but all affirm the necessary laws of non-contradiction and its corollaries. OBJECTION #3 Omnipotence. God is omnipotent, scripture affirms He can do all things (Matt 19:26) so why can t He violate the law of non-contradiction? RESPONSE Of course God can do all things that are logically possible, but He cannot make a married bachelor, or a squared circle because this would be a contradiction in terms and scripture equally affirms He cannot lie (Heb 6:18; 2 Tim 2:13). How then can a perfect God from whom all truth flows make two diametrically opposed terms compatible? Thus the ever annoying Can God make a rock so big He cannot lift it riddle is solved. The question is Can God do the logically impossible? and the answer is No.. To go against His own nature would to stop being God. Can a necessary being stop being necessary and become contingent?

OBJECTION #4 Ontology Some may object to using logic to understand God, because God is a necessary being and is preceded by nothing, but is prior to everything, in the order of ontology. RESPONSE Logic is concomitant, or rather an immediate and lesser consequence of God's necessary existence. It is part of His nature. Therefore, logic is not some arbitrary or conventional discipline, with a strict set of rules, to say how we think we think rationally; God is the ultimate rational being from which all beings derive their rationality. For God to stop being logical, God would have to stop being God, which as a necessary Being would be impossible. It is not by physical limitations that He cannot lie (Hebrews 6:8), rather He is bound by His own nature of rationality, that He cannot lie. God cannot make a married bachelor, a squared circle, or a rock so heavy that He cannot lift it. OBJECTION #5 God and Natural Law. If God can contravene the laws of nature, by means of miraculous intervention, why can't God violate the laws of logic? RESPONSE

First, God did not create the laws of logic anymore than He created Himself, they are concomitant with God's existence. Second, The laws of nature are not immutable, they are descriptive rather than prescriptive. When we make statements about how the world works, via science, we are making statements which are contingent and could be otherwise. While the laws of thermodynamics and gravity make accurate statements about how the present state of affairs operates, there exists a possibility in some possible world, which could have existed as opposed to this one, that these laws are not the case. Therefore, logic describes what is possible, not actual. Logic, as it is with God's nature, is immutable, the laws of nature are not. This will be further dealt with, in the section about Religion and the nature of science. OBJECTION #6 Mysteries of the Christian faith and logic. There are many Christian doctrines which are not fully understandable by our minds, how can we encapsulate the infinite God into our finite minds? RESPONSE While it can certainly be agreed that there are many cases within Christianity which we do not understand fully, such as the 3 in 1 nature of the Trinity, or how infinite God became finite man in the incarnation. It will only be briefly said that truth transcends our

minds and our minds merely apprehend it in part, not in full, but there is no Christian truth which goes against our reason, only above it. We should not ever think that we are compressing an infinite God into our finite minds, rather we are using our finite minds, to finitely know God. While it is true that God cannot be fully known, to the extent He can be known, He can be truly known. DEFINITION and RULES Some basic definitions, of commonly used words, are in order, before the rules can be discussed. 1. Propositions: These can be inadequately defined as true or false sentences, or are units of language that convey complete, true/false, thoughts. The simplest propositions are grammatically analyzed as connecting a subject term (ST) to a predicate term (PT), by means of a copula. While all propositions are sentences, not all sentences are propositions. A non-proposition can be recognized as being interrogative, a question, or a command/request. This definition needs to be built upon, much more can be said. Propositions are complex referential meanings; they are complex in that they contain two, or more, concepts which are consisting of more than one concept and these concepts are related by certain semantic connectives. A proposition may or may not be thought about, believed, or be expressed by language. Every proposition is true or false, for a proposition affirms or denies what a certain state

of affairs obtains. * The locution states of affairs is the most general term for any object or situation of any type, whether empirical or non-empirical. 2. Argument: While arguments are often thought of as a heated exchange, for purposes of logic, an argument is described as a semantic structure (which may be expressed linguistically) with a series of propositions, the complete expression of which is divided into assumptions and conclusions by an inference indicator (Hence, So, Therefore...). An argument's assumptions are the propositions in an argument, (The premises may be assumptions which are provisionally adopted and whose truth-value is problematic or undetermined; in the case of propositions known to be true, they cannot be assumptions in the sense indicated.) which are supposed to be true. By contrast, the conclusions in an argument which its propositions seek to prove as following from the assumptions. Arguments will contain assumptions from which the conclusion follows; conclusions that follow from assumptions and are distinguished by inference indicators. The following are the basic laws of logic, which are inescapable. For instance, to deny the law of non-contradiction is to affirm it, as one must affirm what they are denying. 1) The law of non-contradiction. (A is not non-a).

Let A represent Any proposition. This rule says that 2 diametrically opposed ideas cannot be true at the same time and place. Without this, we could not say that God is not non-god, thus, God would be the devil or whatever is non-god. 2) The law of identity. (A is A). There are properties which are shared between objects, yet there are also properties which differentiate between objects, making them distinct, these are predicates. For instance, both horses and tables have 4 legs, yet there are other properties which make that which is a table not a horse and vice versa. Without the law of identity a subject term would not be identical to itself, but could be something else, such as non-subject term. 3) The law of excluded middle. (Either A or non-a). If this law didn t exist we could not affirm that it is ST, or non-st we are speaking about. When we use the term, we could be referring to both ST and non-st. This is also meaningless. It is by this law that we can say that Christianity is true, or non-christianity is true, it cannot be both. Religious pluralism is false as a logically necessary consequent

of this law. When Jesus says, in John 14:6, I am the way, the truth and the life..., He is affirming the law of excluded middle and is disaffirming all other claims to truth about God. Either Christianity is all true, or all false, by necessity of this verse. Why should anyone accept these 3 laws? Many reject them, at least when drawn out to their final conclusion. Zen Buddhism, for example claims that the Tao goes beyond all categories, including true and false. Fortunately, these fundamental, self-evident laws of thought need no defense against the assertions of Eastern pseudo-logic, (Recall Objection #2) for as soon as one affirms that it is the law of non-contradiction they are denying, they are using it by referring definitively to it. There is no prior justification for these thoughts and they can be held as properly basic beliefs, or foundational truths. Take for instance the law of identity, which says the predicate is reducible to the subject. (A is A), therefore it neither needs, nor admits direct proof. Once one understands the terms, they speak for themselves. Once one knows what triangle, and three-sided figure mean, there is no need to prove that a triangle is a three-sided figure. It is simply seen (by rational intuition) to be true.

There is a way of defending the basic laws of thought as self-evident. They cannot be denied without using them; that is any attempt to deny them is self-destructive. Much like saying all sentences longer than five words are false., which is a sentence and is making a positive claim about the requirements of a false sentence, which it itself satisfies. The example sentence affirms in more than 5 words that all sentences longer than 5 words are false, therefore, this sentence is false if it is true and it is false if it is false, it cannot by its self-destructive nature satisfy itself. Expressed mathematically, this is a positive multiplied by a negative, which is a negative. If the law of non-contradiction is not binding then what is true can also be false. This is self-defeating. If it does not claim to be true, then it is not even in the arena of truth and must be ignored by all who seek truth. In addition to the previously mentioned there are the 'Laws of Rational Inference', by which a conclusion can be properly drawn from given premises.. The two categories for this are 1. Deductive logic, and 2. Inductive logic. The validity of these laws hinges on the law of non-contradiction. If these necessary rational inferences are not valid, then contradiction follows. They are corollaries/immediate consequence of the law of non-contradiction.

DEDUCTIVE LOGIC Deductive logic is correctly drawing or deducing a proposition from others, for example: 1) All of A is inside of B. 2) All of B is inside of C. 3) All of A is inside of C. If all A is not inside the class of C, then contradiction follows, for then B would both be inside C according to the second premise and not inside C. If B is inside C, then A must be inside C, too, since A is inside B. The first premise demands it is necessary 'all of A inside B' and that it would be contradictory to have and not have A inside B. The device by which a proposition is correctly drawn from others is called a 'Syllogism' and these come in three forms. 1. Categorical, 2. Hypothetical, 3. Disjunctive.

CATEGORICAL A categorical syllogism is unconditional. In the cases of these types of syllogisms, if the premise is true the conclusion inescapably follows. They are as follows: 1. All A is C 2. B is A 3. Therefore, B is C. There are clearly no 'if's, and's or but's' in a categorical syllogism, they state the conditions as they are and how the conclusion is inescapable, since the premises are related to each other. However, there are rules for these types of syllogisms which protect the law of noncontradiction. Before attempting to understand these rules, it is important to first lay out some rules. PROPOSITIONS Recall the previous definition of a proposition, which includes a subject and a predicate term, in the format of, 'All (Quantifier) S (Subject) is (copula) P (Predicate)'

The subject can be a universal, or a particular, meaning, it excludes or includes all/some in its class. A universal proposition is said to be strong, while a particular proposition is said to be weak. Between the universals/particulars, in culmination with affirmatives/negatives, four different types of propositions are possible: A Universal Affirmative. (All S is P). E Universal Negative. (All S is not P / No S is P). I Particular Affirmative. (Some S is P). O Particular Negative. (Some S is not P). DISTRIBUTION In A-type propositions the subject is distributed and the predicate remains undistributed, take for instance the proposition 'All S is P', since the quantifier is universal and not particular it is a tautology to distribute the predicate, which is reducible to its subject. Why say '3-sided triangle', when by definition all triangles have 3 sides?! There are two propositions in a categorical syllogism, from which a third is deduced, a subject term (ST) and a predicate term (PT), then a middle term (MT). The subject and predicate are the subject and predicate of the conclusion, the middle term occurs once in each premise, along with one occurrence of the subject and the predicate. When in doubt, think of TOM, and use the rational inference chart,

previously mentioned. Example: All T (MT) is M (PT) O (ST) is T (MT) Therefore O is M. RULES OF CATEGORICAL SYLLOGISMS The following are rules of a categorical syllogism, which it must follow to ensure a valid conclusion is drawn from a valid premise. 1. There must be only three terms. 2. The middle terms must be distributed, at least, once. 3. Terms, distributed in the conclusion, must be distributed in the premises. 4. The conclusion always follows the weaker premise, such as in the case with negative and particular ones. One does not reach an 'ALL' conclusion, from a 'SOME' premise.

5. No conclusion follows from two negative premises. (The two negatives cancel each other out.) 6. No conclusion follows from two particular premises. One cannot draw 'ALL' from 'SOME'. It is invalid to say that because 'Horses are 4 legged animals, all horses are animals, therefore all animals have 4 legs.'. 7. No negative conclusion follows from two affirmative premises. (A positive times a positive invariably equals a positive, never a negative.) A good deductive argument will be both formally and informally valid, it will have true premises which are more plausible than their contradictories.. A logical contradiction can be defined as a proposition that is never true, or that is false under any circumstance. A proposition is logically impossible if and only if it involves a contradiction and is logically necessary if and only if its negation is logically impossible.

FALLACIES OF CATEGORICAL SYLLOGISMS Arguments can have formal and informal fallacies; formal fallacies pertain to the form or the construction of the argument, while informal fallacies pertain to the content. The following are 4 formal fallacies which may be committed and lead to invalid conclusions. 1. Illicit Major - The fallacy where the major term is distributed in the conclusion, but not in the premise. 2. Illicit Minor - The fallacy where the minor term is distributed in the conclusion, but not in the premise. 3. Undistributed middle - The fallacy where the middle term is not distributed at least once. 4. Four-Term Fallacy - Where there are more than 3 terms in a syllogism. Other fallacies that follow are ambiguous middle, and equivocal middle. Being aware of these fallacies and avoiding them, ensures we do not put half a jug of milk into the fridge and pull a full one out, or vice versa and will help us construct propositions corresponding to a true state of affairs, leading to true conclusions.

HYPOTHETICAL SYLLOGISMS If P, then Q If Q, then R If P, then R. If P implies Q, then Q implies R, then P implies R, by means of rational inference. Since P is not established as 1, nor can R be, however, if P = 1, so does R, which hinges on P. A hypothetical syllogism can be recognized by the conditional clause IF, in the hypothetical/possible sense. If P is true, then Q necessarily follows, but only if P is true. Think of A, which stands for 'Any proposition', as being a light switch 0/1. If A = 0 then the room is dark A = 0 Therefore, the room is dark. There are only two ways to draw valid conclusions from a hypothetical syllogism: 1. Affirming the antecedent. (The part of the proposition coming before then. If A = X )

2. Denying the consequent. (The part of the proposition coming after then.) The above example, regarding the lighting situation of a room,, is an example of modus pollens (By way of affirmation), the following will be an example of modus tollens (By way of denial). If A =/= 0 then the room is lit (An equal sign with a strike through it, denotes does not equal. A = 1 Therefore the room is lit. Both syllogisms are examples of affirming the antecedent and denying the consequent. The rules already discussed can be used in conjunction with one another to draw more complicated inferences, for example: If P then Q If Q, then R P If P, then R (This follows from premises 1&2) R (Modus Ponens 3&4).

The conclusion validly drawn from the premises becomes a premise for a further conclusion. DISJUNCTIVE SYLLOGISMS A disjunctive syllogism uses either/or type of reasoning and takes the following form, following from the law of excluded middle: A or non-a Not non-a Therefore, A If one sentence is false the other, by necessity of this rule, is true; while both sentences could be true the alternatives needn't be mutually exclusive, allowing the user to conclude only that if one part of a disjunction is false the other is true. A theological example would be the teleological argument for God's existence. The universe is here by design, necessity, or chance The universe is not here by necessity or chance

Therefore, the universe is here by design. There are two ways to draw a valid conclusion from a disjunctive syllogism: One may deny one of the alternates. An alternate would be the statement on either side of the Or. INDUCTIVE LOGIC In prior deductive arguments examined, the conclusion followed necessarily from the premise, but an argument having a deductive form does not effect the epistemic status of the premises and the conclusion. The difference between deductive and inductive argumentation is not found in which they approach demonstrative proof of a conclusion. A good deductive argument may make a conclusion only slightly epistemically probable, if the premises are far from certain, whereas an inductive argument can give a much greater degree of confidence in its conclusion. Some premises are based on inductive evidence. Inductive arguments require true premises, which are more plausible than contradictories and must be informally valid. The truth of the premises does not guarantee the truth of the conclusion.

What Is Inductive Reasoning? Inductive logic can also be known as Experimental logic as is reasons from a particular, to a general state of affairs. Deductive statements will begin with general observations and employ terms such as ALL, rather than SOME, in the premises, which then funnel down to particular conclusions, for instance, All S is P S1 is S S1 is P Inductive logic begins with any number of particulars, then branches out rather than funnels into general statements about them. In inductivism, the evidence is said to undetermine the conclusion, they render the conclusion plausible or likely, but do not guarantee its truth. It could be said that is one were to examine every particular instance, that one could make a perfect induction given that there are only finite instances to examine, for instance, in my pocket there is a finite space and if I knew how many coins it contained, I could say with total certainty how much change was in my pocket. In order to be totally certain a conclusion was true, we must examine as many cases as

possible to increase the chances of our conclusion being correct, or to tip the scales of probability; given it is difficult to examine all cases, we ought to examine the best cases which represent our subject of enquiry keeping in mind factors, such as differences and similarities, were all incidents isolated from one another and were all possible explanations taken into consideration!? The more related instances that we take into consideration, the greater explanatory power. For instance, the more ravens we observe that are black, we will be able to speak with a greater degree of certainty that all ravens are indeed black. This is called a Hypothetical deductive model. There are certain mathematical and propositional axioms which we must also take into consideration, or there are at least bodies of our knowledge which are not known with absolute mathematical certainty, but are known with a great deal of certainty. When we acquire new information, we must ask how well it squares with what we know already. How well does it explain things than other explanations, or, does it contradict other things known with certainty? PROBABILITY In inductive reasoning, there are two major kinds of probability; a priori and a posteriori. One type of reasoning knows the fire is hot because it sticks its hand in the flame, the

other knows the fire is hot because of observances of fire consuming materials and reducing them to carbon. A priori speaks prior to experience, A posteriori speaks subsequent to experience. A PRIORI This type of reasoning speaks prior to and independent of the facts or experience. To remember this, think of 'prior to the facts'. Mathematical and logical propositions would be examples of this. These are known to be true independent of our experiences and repeated experiences. These could also be known as 'Properly basic beliefs', or 'Self-evident truths', because there is no prior justification for them. Once one has a concept of numerical symbols and mathematical operators, there exists no defence for the coupling of one group of two, with another group of two, equalling four. Once one understands the terms, they speak for themselves. A POSTERIORI This type of reasoning is 'post' facts, it speaks after experience. This is the type of reasoning employed by operation science. A Posteriori probability offers varying degrees of certainty that something is true, based on the examination of the available evidence

done with the guidance of the principles previously mentioned. This type of reasoning will presuppose A priori truths, as mentioned above. DEGREES OF PROBABILITY According to inductivism, there are various degrees of probability, which vary on the type and availability of evidence, which range from virtually impossible, to virtually certain, on the other end, which bars apodictic certainty, (which is debatable in philosophy) but the odds on each end of this scale are either so great, or so small, that they are either ironclad, or unlikely to a nearer degree of probability than not. Apodictic certainty is only possible in deductive logic, and only a perfect induction can provide practical certainty, providing every case was examined.

CONCLUSION Indeed, it would be fallacious to conclude in this portion which was not discussed, or to not conclude anything based upon which was premised in the main body of this paper. We have laws which govern our actions, which are moral laws, we have laws which govern the universe, which are physical laws, there are laws of mathematics and number sets, we also have laws of thought, which we call logic. Truth exists independently of our minds, our minds apprehend truth, therefore, it is important we think about this theory laden universe which we inhabit logically, so our thoughts and statements reflect as accurately as possible the actual state of affairs. These statements must not only contain true content, but must be properly expressed while avoiding various fallacies, so that we may think validly about While making statements about God, doing science/history, or doing apologetics, we must avoid certain fallacies which affect the form or content of our arguments. It does not matter how correct we are, or how incorrect our opponent is, in an argument the soundness of an argument is as important as its validity.

BIBLIOGRAPHY Symbolic Logic Jacquette, Dale. Come Let Us Reason Geisler, Norman; Brooks, Ronald M. Philosophical Foundations for a Christian Worldview Craig, William Lane; Moreland, JP. Biblical Christianity, Truth or Delusion? - Mark Hanna.