Dr Greg Bahnsen - Critical Thinking: Argument, Logic (Part 1)

All right, we're going to get underway with a course in critical thinking this morning, sometimes called logic. But our considerations will actually be broader than what is usually called logic in university classrooms. And as we get underway, let's have a word of prayer. We are grateful, our Heavenly Father, for your mercies to us every day. We confess that we are unworthy of your love and the blessings that we enjoy. And so we come to you with grateful hearts today that we belong to you. That you have called us out of the world and set your love upon us. And totally by your grace and mercy, you have saved us and made us your own. We thank you that you have given us the gift of your spirit, that we might have new life, that we might be born again. We thank you that that spirit guides us and directs us. We thank you for the word that you have given by your spirit. And we pray that you would help us through this course and in this day, during our discussions, even now, that the Spirit would be with us to think your thoughts after you. That we might please you in all things, and that we might be concerned to be faithful not simply in the things that we say, but in the way that we say them and the way that we reason. We pray that you would make us faithful to you as we learn about thinking and reasoning and argumentation. We ask that this would be done not simply that we would strengthen our intellectual abilities, but that we might better serve you and become better and more effective witnesses for you. We pray that you would not puff us up with pride because of what we learned, or that you would keep us from becoming arrogant or overbearing and arguing with people. We do pray that the skills that we gained through this course might be used for sanctified purposes in the advance of your kingdom. And above all, that we might glorify our Lord and Savior, Jesus Christ, before whom we humbly vow, in whose name we pray. Amen. This is a course in critical thinking. Critical thinking doesn't come natural to people. Although people naturally engage in thinking and criticism. Critical thinking should improve our reasoning ability, should improve our insight into the structure and support weaknesses of arguments that we hear from people. But critical thinking does not stand by itself. It would be impossible to have a course on logic or critical thinking that only dealt with the thinking process or reasoning, whatever you want to call it. Reasoning is always reasoning about something. So we'll be looking at arguments in various forms, fields, history or science or theology, what have you. Ethics, perhaps. But when we look at these arguments, we're going to be Looking at them not so much for the truth of what they contend, what's being maintained in the conclusions. We're going to be studying these arguments for the process by which the conclusion is drawn, to see whether there is good support or poor support for the drawing of the conclusion itself. We'll be studying logic, although as logic is usually understood in university classrooms, we'll actually be doing something broader than just logic itself or deductive reasoning. We're going to be considering the whole field of argumentation, what's involved in analysis. Critical thinking would be the best way to put it, I think. Learning to be critical about the way we think so that we clean our tools of reasoning and debate and then also sharpening the tools of dissecting the arguments of others and understanding whether they are good or bad arguments. And so of course in critical thinking will encompass a number of things. We're going to be looking at the whole notion of argument. That's what I plan to do today. What is an argument? What kinds of arguments are there? What is logic all about? Why is logic important for the Christians? And I'd like to look at the history of logic or reasoning, if you will, in terms of what was it like before the Fall? What has the Fall done to the reasoning process of man? What does regeneration do to the reasoning process of a fallen man, and so forth. So we'll be looking at the general notion of argumentation, but then we're going to turn to a unit on language, because obviously arguments are made in linguistic form. Arguments are not just, you know, facial expressions or even primitive grunts. Arguments are given in sentences. And so we need to know something about the nature of language. A great deal of the difficulty people have in their own reasoning or in trying to understand and dissect the reasoning of others, arises from a misperception of what language is all about and how it works. Then after we have our news on language, we'll be talking about fallacies, common fallacies in reasoning. The kinds of mistakes that are made in what we call natural languages. A natural language stands opposed to a formal language. Mathematics, algebra uses a formal notation, but in English we don't write formal notation. We use words that you can read in the dictionary, put together in the proper syntactic order and so forth. Now there are fallacies that people make in natural languages that are very common. In fact, many university courses, logic, you might be interested to know, focus entirely on informal fallacies, fallacies made in our day to day speech. That's what the book by Morris Engel is All about informal fallacies. However, to understand argumentation to become more critical in our thinking, we should go beyond the common fallacies made in day to day speech. And we begin to look then at a more formalized understanding of arguments. The study of formal reasoning leads finally to putting arguments in symbolic reason form, the same way that algebra uses place markers, X's and Y's and so forth. When we get the symbolic logic, we will have stripped away all of the material content of the premises and arguments, and they will then be symbolized by X's and Y's or S's and P's or whatever it may be. And we'll start looking at the relationship between various things. And there's two specific kinds of formal reasoning that we'll be considering. We'll be looking at what we might call categorical logic, the logic of categories, or it could be called the logic of classes. Logicians have developed refined tools for relating classes to each other, using the quantified expressions some and all, as well as the negation not. And I know that doesn't seem like a whole lot. There's only three words in the English language. We're going to be focusing on all, some and not. But there's a great deal that can be learned because so much of our reasoning has to do with putting things in different categories or classes. If I say all sailors are drunkards, then what I'm saying is that of the class of sailors, everyone in the class of sailors, everyone in that set will be in the set of drunkards. That doesn't mean that all drunkards are sailors, though. Okay, so we have to learn the relationship of plan classes when you have all and some and when not's put in there, that really gets for a real good time in logic. So we'll study category reasoning or class reasoning, and then we'll also study propositional logic. Propositional logic, just to demystify it for you, is nothing more than what I said about category logic or categorical logic. Categorical logic explains how we use the words some, all and not. In propositional logic, we emphasize certain connectives, not between classes now, but between propositions. So what is the relationship between this proposition and that proposition when we use the word and another connective is the word or? And then finally we have a way of connecting propositions in the if then pattern. If this proposition is true, then this proposition is true. Propositional logic, also the negation. And so we are going to, in the end, having studied formal reasoning, mastered the English use of actually the logician's use of the English words some, all, not and, or if then I'm telling you that and I'm glad to see the smiles on your faces. You need to realize, for all. I mean, some of you have looked in the textbook already and it seems, you know, so deep and mysterious. That's all it amounts to. And it can get fairly technical. But you don't need to be intimidated by logicians. Logicians are doing very limited work. They're only dealing with certain words in the English language. Now, they're important words. And these are the words that appear in so many arguments or so many arguments rest upon those connectives or those class relationships that it's good for us to learn that. But it's not the be all and end all of critical thinking. That's just one aspect of critical thinking. So then we're going to have to study language. We have to study fallacies that are made in ordinary speech. Then we're going to study formal reasoning, I.e. passes and then the connections between propositions and. Or if then. And that will eventually become symbolized. That becomes the part that scares many people, symbolic logic. And then we're going to have to look at explanation. We've been talking about analysis and logic, but I hope in this class also to get into the whole notion of explanation and specifically causal explanation. When we say A because of B and B is supposed to be the cause or supposed to offer some causal analysis of why A is the case. That would be the second part of our COFI textbook, which we won't spend a lot of time on. You probably just do some reading. We'll do some discussing of that. And then finally I want to in this course talk about the presuppositional influences on argumentation. That is to get outside of the narrow framework of deductive and inductive reasoning and start looking at the reasoning process or the argument process and how presuppositions affect that, the presuppositions of the field in which you're working or the presuppositions of the worldview that you are using. And we'll talk about also debate, what's involved in debate, proving or disproving and so forth. So we have a lot to cover. And that's why I'm calling this course Critical thinking and not just logic. What is usually in a logic course at the university. It will be part of what we're going to be looking at, but it will not be the whole of it. Well, that. By way of introduction, let's get into Then the subject of argument this morning, which is the agenda for today. What do we mean by an argument? First of all, what it is, and then what it is not. An argument is a group of propositions. That's not the whole definition, but let's just stop at that point and realize that if you have an argument, you have to have a group of propositions, at least two. You might have 200. That would be horrible. But nevertheless, it's a group of propositions. But it's not just any group of propositions. I mean, after all, you could take a sentence from this book and a sentence from that book and a sentence from a third book and just write them all down together. That wouldn't make an argument. An argument is a group of propositions where the truth of one of those propos propositions is asserted on the basis of the evidence furnished by the others. An argument is a group of propositions wherein the truth of one is asserted on the basis of the evidence furnished by the others. So let's go back to this group of propositions we've cut out of reading the book. Now, if we were to say about one of those quotations that it is true and that it is true because we know the other two propositions to be the case, then you'd have an argument. Because then you're saying, here we have evidence for this particular conclusion. Now you are arguing. You're asserting some proposition based on others. Argument is not just in terms of the order of mention of the propositions. It doesn't think. You don't have an argument unless you have premise. Premise, therefore conclusion. That's the way we reconstruct arguments. Many times when you're reading in a book, the conclusion may be the first sentence you read in the paragraph. And then there are other sentences which are supposed to offer some kind of conceptual or causal support for what is being said there. Sometimes, as you'll see in your reading, the argument's not even clearly stated, but it's supposed to be so obvious that you can take it yourself. But where you have a proposition the truth of which is asserted on the basis of others, you have an argument. Not all arguments are good arguments, though. I think our inclination sometimes when we disagree with somebody is to say, well, you haven't got an argument at all. When in fact we want to say is that's a pretty poor argument, or that's a very fallacious argument, or you've not really offered good evidence whatsoever. But an argument is simply a group of propositions wherein the truth of One is asserted on the basis of the evidence furnished by the others. So what we're going to get in arguments will be a sequence statements, and in this sequence, one of the statements will be the conclusion, wherever it's found in the sequence. And the others are supposed to be what is being argued. For now we say that the conclusion in an argument is inferred from its premises. Those statements in the sequence which are supposed to be the evidence bearing statements, whether they're conceptual or a scientific, causal or not. Those statements which are the evidence bearing statements or the premises are supposed to lead to the conclusion. So we say that the conclusion follows from the premises or is inferred by the premises. Now, if I put it this way, maybe I can capture everything we're going to be doing in a little nugget here by just saying logic is the study of that following from relationship. Logic is the study of inferring, looking for good inference patterns and bad inference patterns. Logic does not study biology per se, or astronomy, or literature, or history or theology. Logic is the study of the following from relationship. In any particular field of thought, when a conclusion is asserted on the basis of certain premises, logic studies that inference pattern. Now this has suggested to some people that logic therefore has the same application. And it's just, you know, crystal clear across the board in every field that anybody who knows logic and is going to any field, biology, astronomy, history, literature, theology, and just apply the rules of logic, and that's all there is to, to the analysis of arguments. And I hope that you will not hold that naive of you by the time we get done with this class. Obviously, though logic stresses the form or structure of arguments, there are other things that affect even the evaluation structure of arguments, the field in which you're reasoning, the worldview that you are bringing to bear, and so forth. So I'm at this point just telling you that though logic looks at the formal aspects or the structural aspects of reasoning, that isn't to say that it's some kind of a neutral field of endeavor that everyone will agree on, can be applied across the board to any field without any adjustments. So what is an argument? A group of propositions wherein the truth of one is asserted on the basis of the evidence furnished by the others. Or if you will, it's a sequence of statements where one statement is the point of it all, and the others are supposed to be the basis for making that point point or making that assertion. The conclusion in an argument is said to follow from or be inferred by the premises that are Given. Now we can define argument in this strict way, but we have to recognize that this is not the way the word is always used. Commonly we talk about, you know, boy, they really got into an argument they other night. And when people use the word argument in that fashion, I'm afraid that because Christians know they shouldn't be argumentative in that way, then they have the idea they shouldn't study argument. Or, you know, there's some suspicion about those who are interested in logic and arguing. But you see an argument, technically speaking, it doesn't mean to be nasty or to engage in contention or if you think about it, even in disagreement. You and I might agree on something completely, but we're developing arguments with respect to it and we don't disagree at all. But we still want to have premises that lead to the conclusion. We want to sharpen or strengthen the way in which that is done. So there's no disagreement at all. And yet we're engaging in argumentation. Argument is just having premises that are asserted as leading to a conclusion. And some arguments are good, some are bad. But to be argumentative, when people speak of, boy, they were really going at it, they were really arguing. I think what we should say is they were being very contentious with each other. You know, and of course that isn't a Christian virtue to be contentious, to be argumentative, but it is a Christian virtue to master argument. You don't have to be nasty to master arguments, nor do you have to be socially unscrupulous. You know, the kind of person who's just always cross examining and raising questions and challenging and so forth. Even if it's done politely, you know, people can make themselves social bores by behaving in that fashion. Okay, so this is not a class on how to become a social bore or to be a smart aleck or to show that you know, you know better than others and all that. It isn't a class on nastiness and contentiousness and all that, but it is a class on argument. We're going to be studying the way in which conclusions follow from premises or fail to follow from premises. An argument requires that some proposition is asserted as following from others. This is a new point and it's elaborating on what we've already said. An argument requires that some proposition be asserted. Underline the word asserted. If there's no assertion of something being true, then there's no argument. So if I use the same sentence like this, if the fetus is a human being, then abortion is murder. Is that an Argument. Well, what's being asserted then? Since you think it's an argument, what am I asserting here? I said if the fetus is a human being, then abortion is murder. Have I asserted that abortion is murder? No, I said if the fetus is a human being, abortion is murder. And now if I had said since the fetus is a human being, abortion is murder, then I would have been asserting the conclusion. And since the fetus is a human being, part would have been the evidence or the premise from which I drew that conclusion. So when there is no premise being asserted, where there is no inference being made, where no conclusion is being claimed to be true, you don't have an argument. You might have a conditional statement, an if, then or hypothetical statement, but you don't have anything being a certain. I don't want to go so fast that some of these basic points will be lost in the shuffle because there'll be lots of notes and distinctions we draw over the next couple weeks in this class. Do you all understand this? That you do not have an argument unless somebody's claiming a conclusion? It's true. Now, they don't always have to red flag it by saying, I'm saying this proposition is true. It doesn't always happen that way. And I've already told you, in some cases the conclusion is supposed to can almost, you know, be there silently. It isn't explicitly uttered. But if there isn't some conclusion that is being claimed or certain, then you don't have an argument. Argument. Okay. Another distinction that we should draw is that between an argument and an explanation. Or as you'll see in Coping, maybe that's not the best way to put it. We certainly want to distinguish between a conceptual argument and a causal argument. A conceptual argument. In a causal argument, If I say. All unmarried single men are at risk of AIDS and conclude that therefore all bachelor are at risk of aids, that argument does not rest upon scientific or factual knowledge of the world or any causal relationship. No one's saying there's a causal relationship between this expression, unmarried male and bachelor. That's a semantic relationship. Then there are other types of relationships that are conceptual. We're going to get into that when we study logic. Sometimes we're asserting that these premises lead to that conclusion because of the conceptual ties between the various things that are said in the premises and the conclusion that is different from an explanation. An explanation would be something like this. The bread did not rise because Betty forgot to add the yeast. The bread did not rise because Betty forgot to add the yeast. In that particular illustration, the word because, is not establishing the truth of what went before it. This is going to be somewhat new to people who haven't thought it through. Let's make sure we catch this. When I say the bread did not rise because Betty forgot to add the yeast, I'm not arguing for the truth of the bread did not rise. I am now trying to explain why the bread did not rise. In that sense, I'm taking it for granted that the bread did not rise. And what I'm offering you is a causal connection between two things. The bread not rising is causally. Well, what's causally connected to it as the explanation for it, the reason for it? Well, that explanation for it is that Betty didn't put the yeast in. That's different from an argument in deductive or conceptual reasoning. This is now a more scientific line of argumentation. It was abnormally warm this winter because of the El Nino. Is a scientific explanation to say that it is true that it was abnormally warm this winter because of the truth of the premise that the El Ninos were flowing? Well, that wouldn't be the case. We're not arguing for the truth of something when we say because she didn't put the yeast in or because the El Ninos were flowing. We're trying to explain causally explain. But there are causal arguments. Some are good, some are bad. How about this? I've noticed that there's a high concentration of people who are sick in a certain place. And so I am going to draw the conclusion that that area is responsible for causing illness. Now, the place I'm thinking about is a hospital. There's a high concentration of sick people in a hospital. Therefore, hospitals cause sickness. Look like a good argument to you? Come on now, warm up. You know, that's a silly argument. That's a dumb argument. You know, hospitals don't cause illness. And so causal arguments have to be analyzed, too. Some are fallacious, some are stronger, some are weaker. So we'll be studying argumentation in this class. We know the difference between an argument. We know the difference between an argument and a conditional statement. We know the difference between a deductive argument and an explanation. The word because can be ambiguous. Sometimes the word because signals a relationship between premises and a conclusion that's intended to be deductive. That is, reasons are being offered for the truth of the conclusion. But sometimes because signals a causal explanation of what is taken for granted in the conclusion that a certain event took place. Okay, if we understand what an argument is, let's move on. And ask about what a proposition is. A proposition is what a sentence asserts. Or you can put it this way. It's the meaning of the sentence. A proposition is what a sentence asserts. It is either true or false. It is the sort of thing that can be affirmed or denied. And so questions and commands and exclamations are not propositions. If I say, jay, would you get me a glass of water? I'm not asserting a proposition. I'm making a request. Or if I say, melissa, what did you have for dinner last night? That's not a proposition because I'm not affirming or denying anything. Propositions are what a sentence or a proposition is what a sentence asserts. They can be true or false, affirmed or denied. Now, let's look at what I've just given you and be precise. A proposition is not a sentence then, is it? It's what a sentence asserts. You say, well, what's the difference? Well, let me try to illustrate that difference. The propositions, that meaning of the sentence, despite the sentence form or the language that is used. Here's one sentence, Jesus raised Lazarus from the dead. Here's another sentence, Lazarus was raised from the dead by Jesus. Are those the same sentences? No, they're not, because they use different words, different number of words, different order of words. They're not the same sentence. Are they the same proposition, though? Yes, because they both assert the same thing, just in different way. Moreover, sentences always appear in some natural language. English, Japanese, Greek, what have you. So here's. Here's two sentences for you in two different natural languages. Hesis den hatheos, which is Greek. Here's an English sentence, God is one. Now, it turns out they mean the same thing. Hes eston hatheos is the Greek for what we say in English, God is one. Obviously, they're different sentences. There's not one word that's common, common to the two of them, and yet the proposition is the same. So is this giving you some flavor for what a proposition is? A proposition is that which is asserted by a sentence. It might not surprise you that there are philosophers today who are kind of sensitive about speaking of propositions. They don't particularly like the idea that there are propositions. And why is that? Well, if you're a materialist, you don't believe that there's anything immaterial in the realm of reality. And then you say, well, there are propositions. She can't touch the propositions. You can't smell them, kick them, swallow them. What is a proposition? Proposition becomes something of an Occult entity, right? Something immaterial or spiritual or mental or whatever you want to call it. It's not. Sentences are no problem because sentences are physical. You either see it written on a piece of paper or it's, you know, wavelengths that you hear your eardrum. Sentences are no problem. But when you say that there is some, you have this Greek sentence and this English sentence and they have something in common called the meaning of the sentence, or if you will, the proposition that they both assert. But the proposition is never heard or seen. Then you've got problems in terms of your view of reality. And so you'll find a lot of logicians today trying to dance around the existence of propositions. One has gone so far, Willard Van Orman Quine, Q U I, N E, who is a professor at Harvard and one of the best known philosophers of this century. Quine has gone so far as to try to give a strictly behaviorist explanation of meaning. Meaning is the response to a certain stimulus. This relationship of stimulus and response is the way in which we understand meaning. And the thing which is common, common between Greek and English, the two sentences, or French and German or whatever it may be that we call, we would have called the proposition is just the same stimulus, response. Okay, so there are white dogs is the sort of thing that a person would say in English in the presence of specify these canines that have this color and so forth, and that has the same meaning as the French expression corresponding to it, because people in the presence of these canines with this color would utter that sentence. And so where you have all of the same responses to the identical stimuli, then you have identity of meaning. Now, he's attempted to regiment language and to carry out this program of explaining the meaning of sentences, but I don't think he's been successful. And he creates as many mysteries to be solved as he thinks he's solving. That was an aside. That was a bonus point here. I just want you to know that what I've just said about propositions some philosophers would have some trouble with, but when you're doing logic, it's pretty, pretty hard to get around it. Proposition is that which is common to these English and French and German sentences of a certain same thing. Proposition is what a sentence asserts. Now, statements can sometimes be oblique or ambiguous or open ended. Propositions are not. Here's a sentence that is rather open ended. This weather is my favorite. What does that sentence mean uttered today? Well, I'm looking outside. It's actually changed since we started class, but it might be cloudy weather. When uttered on one day and by one individual, another individual might utter it, you know, on a warm and sunny day. And so the sentence has different meaning depending upon the circumstances under which it is uttered. But we say propositions, that they are not open ended like that proposition asserts some specific thing that is not open to varying interpretations depending on speaker or circumstance. Now then, what's an argument? An argument is a group of these things we call propositions, where one of them is asserted to be true on the basis of the others. Propositions are true or false, but arguments are not true or false. We say that a proposition is true. Well, to give the theological explanation, if it corresponds to the mind of God. The proposition is true if it's what God would say. Another way of putting it is that a proposition is true if it doesn't mislead us as to what is the case. Proposition is true if it asserts what is the case. Propositions can be true, but they can't be valid. Arguments can be valid, but they can't be true. Now, this should be very obvious to you if you just take what we began with. Arguments are groups of propositions that are related in a certain way. And when that relationship is a strong or one that is not misleading. We might say that the argument is valid because the argument asserts the truth of some proposition based on other propositions. And when that is a reliable line of reasoning, when that is a reliable form of inference, then we say that the argument is valid. An argument is valid if its conclusion follows from its premises. So you want to put that in there. Validity is just this. An argument is valid if its conclusion follows from its premises. And thus validity deals with the form or structure of the argument. Truth does not pertain to groups of propositions, but to individual propositions. And so in a group of, let's say, eight propositions, you might have three that are false and five that are true. When we say that an argument is deductively valid, this is moving ahead. Now, when we say that an argument is deductively valid, we mean that it is impossible for its premises to be true and its conclusion to be false. It's impossible for the premises to be true and the conclusion to be false because it's deductively valid. That means the conclusion follows from the premises. And where the premises are all true and the conclusion follows from them, then the conclusion must be true as well. The conclusion is that single proposition whose truth is asserted on the basis of the others, and where the conclusion follows from the premises deductively, with deductive Validity. Then we say it's impossible that the conclusion be false if the premises are true. In a few moments, when we look at something John Frame has written, we'll be talking more about this. Note this down. When we say it's impossible, we're talking here not about physical impossibility. Nor are we even talking about conceivability. We're talking about a kind of necessity or possibility that is un other than imagination or physical constraint. Let me get some thought. What is that? A long one ago I raised the problem that Klein and others struggle with. What's a proposition? We don't want to assert that there's some kind of immaterial thing out there. Now we're into another problem logicians face Log. What is the nature of the necessity of logical inference? What kind of necessity is that if it's not physical necessity? What kind of possibility are we talking about if it's not just imaginability or conceivability? Logic forces us to make some metaphysical commitments. Metaphysics is the study. In philosophy, it's called the study. What philosophers call metaphysics is the study of the nature and limits of reality. What is real? What kinds of things exist? Do angels exist? Do causes exist? Does love exist? Do chairs exist? Do Athens exist? Metaphysics is the study of the nature of reality. What exists. And there are people who don't want to say that this things like propositions or necessity exist. Relationship between propositions I hope that I'm building up for you to what is a pretty strong apologetic for Christianity. That in a sense you have to have a Christian worldview to do logic. If a Christian understands the nature of propositions and necessity in light of the lines of God. But if you throw that out as just Sunday school superstition smart, then the next question is, well, then, what are you doing when you do logic? Back to truth and validity. Validity deals with the necessary relationship between premises and conclusion. To say that an argument is valid is to say that it's impossible for its premises to be true and its conclusion false. So please notice the truth and validity are not related to each other. Are not related to each other in the sense that you can go from the truth of a premise to the validity of the argument, or vice versa. I'm going to give you a series of observations. Five observations. Here you can have true premises and an invalid argument. Your premises can be true and yet your argument is invalid. If Shakespeare wrote Paradise Lost, Shakespeare was a great author. Is that true? Be careful. Is it not true? If Shakespeare wrote Paradise Lost, Shakespeare is a great author. I'm taking it for granted that Paradise Lost is, as most people would say, perhaps the classic in the English language. No, he didn't. But if he did, he's a great author, isn't he? Because whoever wrote it is a good. Is a great authority. So that's true. If Shakespeare wrote Paradise Laws, he's a great author. True premise. Here's another true premise. Shakespeare is a great author. If somebody draws a conclusion. Therefore, Shakespeare wrote Paradise Lost, the argument's invalid, but the premises are true. It's just that they aren't related to each other in a way that gives you the assurance that truth follows in the conclusion. So you can have true premises and an invalid argument. By the way, you can have a true conclusion and an invalid argument. You can have true premises. You can also have a true conclusion, but an invalid argument. All right, Here is an example of that. If today is June 1st, then I am in Hawaii. If I am in hawaii, my name is Dr. Bobson. I'm supposed to be giving you an invalid argument. I'm sorry, let me do this again. If today is June 1st, then I am in Hawaii. I'm going to get my illustrations down. I'm not. I needed three premises to do this. I'm going to make it simpler. Scratch that goes like this. Now, If today is March 31st, then my name is Dr. Bonson. My name is Dr. Bonson. Therefore, today is March 31st. I'll say it to you one more time. I got it right finally. Actually, what I have right is a wrong argument. I finally got a wrong argument stated right. Okay, just kidding. Don't want to mess your minds up. Here. It goes like this. If today is March 31st, then I am Dr. Bonson. Next premise. I am Dr. Bonson. Therefore, today is March 31st. Is the conclusion true? I've made you all. I've spoke to you. Now, is the conclusion True? Is today March 31? Okay, is the argument a valid argument? No, as it has the same form as the Shakespeare Paradise Lost one. We know that's an invalid argument, and yet the conclusion is true. So notice that the truth of the conclusion doesn't prove that the argument's valid. You have many Christian friends, I'll bet, that hold true conclusions in theology into very bad arguments for them. So the truth of the conclusion does not prove that the argument is valid. Moreover, the truth of the premises does not prove that the argument is valid. That's the first point that I made. And now let me comment. Thirdly, you can have an invalid argument then, with either true or or false premises and or true or false conclusion, You could have an invalid argument with either true or false premises or true or false conclusions. That leads to another observation. You can have a valid argument with a true conclusion or true premises. You can also have a valid argument with a false conclusion or false premises. But, and this is the major point, you cannot have a valid argument with true premises and a false conclusion. One thing you need to know about truth and validity is you cannot have a valid argument that has true premises and a false conclusion. If an argument or argument form has true premises and a false conclusion, it's not valid. Let me say it again. You cannot have a valid argument with true premises and a false conclusion. What validity is all about is the impossibility a premises being true and a conclusion being false. So an argument is valid if it enshrines a form of reasoning or a line of thought where the truth of the premises wouldn't necessarily bring the truth of the conclusion. The evaluation of the conclusion is true. That's what a valid argument does. Valid argument says that if the premises are true, the conclusion must be true. It doesn't say that the premises are true though, and it doesn't say that the conclusion is true. It just says that if the premises are true, the argument, the conclusion must be true as well. In this short amount of time, then, we have begun with the elementary concept of an argument, what an argument is. We know that arguments involve premises and conclusions. Premises and conclusions are propositions. We know how propositions are different from sentences. And we know that propositions can be true or false. However, they cannot be valid or invalid. It's arguments that are valid or invalid. And validity simply has to do with the relationship of premises to conclusion, such that you cannot have true premises and a false conclusion if the argument is a valid point or valid as to form. Let's go a bit further. Let's talk about inductive and deductive arguments. Now, Inductive and deductive arguments. In an inductive argument, or what might be called a strong inductive argument, some evidence is offered in the premises for the conclusion that is drawn from them. Some evidence is offered in the premises for the conclusion that is drawn from them. But it's not enough to make that conclusion necessarily true or absolutely true given the evidence that is there. The strength of the conclusion is always affected by the increase in the pool of relevant data that we have regarding it. Okay, so let's say I have a couple of true premises that give Me some reason to believe that the conclusion is true. We'd say, that's an inductive argument. Here's a couple of premises. There's water in the ice cube trays, and the ice cube trays are in the fridge freezer. Therefore, we'll have ice for the party tonight. Okay, now, is that a good argument? We'd say, well, it has some inductive strength to it, for all we know. You can rely on that. For all we know. But now, what if I give you more information? The strength of the argument will be greatly diminished. If I say the refrigerator's not plugged in now all of a sudden, the evidence for we'll have ice tonight doesn't look like real strong evidence at all because now new information has been added. Whenever you have an argument that shows those features, you have an inductive argument where the strength of the conclusion will vary given the amount of relevant information that we have in the premises. So here's an argument. Premise one, there's water in the ice cream trays. Premise two, the ice cube trays are in the refrigerator. Conclusion, we'll have ice for the party tonight. That argument by itself has some strength. But when you add the third premise, the refrigerator's not plugged in, the argument has no strength at all. That's a feature of inductive arguments, that the strength of the conclusion or the strength of the inference varies given the amount of relevant information you have in your premises. In a deductive argument, which is the deductively strong one, a valid one, we have conclusive evidence offered in the premises for the conclusion. In a deductively valid argument, the conclusion is known conclusively, if I can put it that way. The evidence that is offered is conclusive for asserting what we call the conclusion. It's not just probable, given the amount of information that we've considered, it is conclusive. The standard example is all men are mortal. Socrates is a man. Therefore Socrates is mortal. There's no. If you grant the truth of those premises, and what happens with elementary students in logic, they all start thinking of ways to challenge, you know, that Socrates is mortal based on things which violate the premises. But. But if the premises are true that all men are mortal and Socrates is a man, then Socrates is mortal. There's no other information that needs to be taken into account to either weaken or strengthen that argument. And so it is deductively valid. The conclusion is certain. By the way, just as an aside, I told you what we're going to be trying to fly through in this Class. But I just gave you as an example of categorical logic, the relationship of categories. You have the category of Socrates, that's a one member class. You have the category of mortals in the category of men. And so the argument is all men are mortals. That is, all in the category of men are in the category of mortals. Socrates is in the category of men. Therefore Socrates is in the category of mortals. But there are other kinds of category logic, excuse me, other kinds of deductive logic, connective logic, like if, then, or. And propositions related are connected in those ways as well. So inductive argument and deductive arguments. To get back on track here, an inductive argument offers some evidence for its conclusion, but it's not conclusive. It could be strengthened and it could be infirmed by new information added to the premises. In a deductively valid argument, the conclusion follows necessarily from the premises. I need to add another category here, sound arguments. We say that an argument is sound if the premises are true and the argument is valid. We've already said you can have a valid argument with false premises. But where you have a valid argument, the structure is a good, strong structure, if I can put it that way, and the premises are true premises. You've got good content filled into that structure. Then you've got a sound argument. A sound argument has true premises and a valid argument. The argument form is valid, the premises are true, and then we call the whole thing sound. And do you have any questions about argument, proposition, truth, validity, inductive, deductive and sound? We have to start kind of slow with these terms because this is what we're going to be using for the rest of the class. Let's just make sure we understand what we're talking about. Do you have any questions about. Would you say. Yes? Well, it all depends on whether you think the premises are true. And here what you have given us is one of these specimens that we'll look at later. And that is, what do you do when the premise is true, as far as it goes, as we say, then some further analysis is called for. But you see, I'd be willing to accept that statement that all men are mortal, Jesus is a man, therefore Jesus is mortal. And if somebody said, okay, well, that settles it. That's all there is to say in the subject. Oh, no, there's something else too. You know, God is immortal, Jesus is God, therefore Jesus is immortal. And now you got to. What do you do? You got, Jesus is mortal, Jesus is immortal. You say, well, both are true with respect to the two natures that is, he's mortal with respect to his human nature, immortal with respect to his divine nature. You see, logic doesn't give us any problem there, but forces us to be more precise in our theology. Deductive validity, however, is just a matter of if the premises are true and the conclusion follows deductively, then the conclusion must be true as well. If somebody was sensitive to that example that you just gave about Jesus, see, I think the way I've handled it is better. Well, that argument's true, but there's another argument as well. Now, you're going to have to do a third level kind of thing is how you bring these two conclusions together. But if somebody were sensitive, they said, oh, no, I don't want to go into multiple arguments. I want it all in one argument. And I'd say, well, then you probably will not accept the premise Jesus is mortal. You're going to say there's something defective about that premise. It doesn't say everything you want it to say. But I mean, for me, you can't say everything at once. It's true as far as it goes. All right, let's ask now what logic is. And we've said a little bit about it up to this point, but let's try to be a little more focused. We know what an argument is. We know what premises, conclusions are, the difference between truth and validity, deductive and inductive. What about logic itself? Logic, I suppose, could be described as the study of argumentation, the study of argumentation. Logic. Evaluates the arguments that are used, find out which are related, reliable, which are unreliable, which are strong, which are weak. So logic is the study of argumentation. Now, can people argue without studying argumentation? Can people be logical without having a course in logic? I'm waiting for everyone to catch on here. Obviously they can. Can someone paint a beautiful picture without ever taking a course in, you know, art and its analysis? And someone hit a home run without ever taking a course in physiology. Obviously you can. And people can argue without having studied argumentation because people can be logical without having taken a course in logic. What is it we study when we study logic? Well, we study arguments and try to find out which are correct arguments, which are sound, which are misleading. Logic is not the study of thought, nor is it the study of the laws of thought, because thinking is more general than argumentation. If I say, but let's think about lying on the beach in Hawaii. Logic doesn't study that. Nor does logic, say, study the process of thinking in some deviant personality, you know, who you know, whenever you bring up a certain subject, white dogs goes wild, you know, and has to kill people. Psychologists study thinking and the processes of thinking, but psychology is not part of logic or logic part of psychology. Logic is the study of argumentation, that is, the thinking that goes into drawing an inference from certain premises to a conclusion. I wouldn't want to say broadly that logic is the study of reasoning or inference, though, because psychologists study inferences, or if you will, the psychological process of drawing inference to get the focus right. We should say logic kind of studies the end product of inference and what might be rationally reconstructed as premises leading to a conclusion, rather than just, say, the stream of consciousness of somebody going from some premises to another premise called a conclusion. So logic is the study of argumentation, seeking what distinguish between correct and incorrect or sound and misleading argumentation. It deals with more than thought, more than the laws of thought, or even more than reasoning and inference. It specifically looks at the end product of inference, trying to distinguish between sound and unsound, or strong and weak ways of reasoning. Now, we might ask the question, looking at the theology of logic for a bit here, is logic a neutral tool? Is logic something that is not affected by one's theological assumptions, one's basic worldview, one's ethical perspective or lifestyle? Is it a neutral tool? I'm going to suggest that that's like asking whether noses are neutral tools or instruments. When somebody studies the nose and its functions and so forth, will they draw different conclusions for believers and unbelievers? Say, well, believers noses work this way and unbelievers noses work that way. In that sense, believers and unbelievers share noses. I don't mean they have the same nose. They share. They have the same sort of thing we call a nose. Does that mean that they use their noses the same way? No, I just use noses because I think that would be more memorable. Did the fall of man change man's nose? No. I've made you also wary. Nobody will say the obvious things, but think about that. The fall was not something that altered the nose of man. So believers and unbelievers have noses, share noses, and the same kind of thing we call noses. And likewise believe believers and unbelievers share the formal laws of thought, those laws which would guide us as a result of logic. The laws that we come up with guide us into correct thinking and away from incorrect thinking. Those laws are the same for believers and unbelievers. The same with their noses are the same. Or we can put it this way, the laws of thought are somewhat like the laws of morality. Are the laws of morality the same for believers and unbelievers? Well, sure they are. And so believers and unbelievers share the same formal laws of thought. The fall of man into sin should not be seen as somehow metaphysical, nor should it be thought that it altered, you know, the nature of truth and validity and reasoning. The fall was ethical. Man did not stop being a rational creature when he fell into sin. He still uses his reasoning ability or his intellectual. And the way in which he should use it if he would draw good conclusions rather than misleading conclusions. The way he should reason whether he's a believer or an unbeliever is the same. The laws of thought are the same for believers and unbelievers. So there's no difference between Christian logic and non Christian logic if we're just thinking about the formal laws of thought that should guide our thinking or reasoning process. But now, what am I leaving out of the picture here? Well, we said believers and unbelievers have the same noses. Maybe that's not the easiest illustration. They have the same instruments. Let's say hands. Okay, okay. Believers and unbelievers have the same physiology of their hands, don't they? Does that mean they use their hands the same way? No Christian holds up hands in prayer. The Bible says sometimes unbelievers use their hands to murder people. And so though they have, the fall didn't change the nature of hands. What did it change? The use of. Of the instruments God has provided us, meaning noses or hands. Or we can take our illustration of laws of morality. The believer and the unbeliever have the same laws of morality. Doesn't mean they respond to them the same. It's immoral to gossip. Unbelievers gossip. Believers don't. Well, they shouldn't. Okay? They should at least feel bad and confess their sin when they do so. Clearly the response to the laws of morality is going to be different between believer and unbeliever. Even though they are the same laws, the use of their hands and noses and feet and everything is going to be different, even though they have the same physiological features. Apply the same kind of thinking by analogy to logic. Believers and unbelievers have the same laws of thought. The correct way of reasoning is the same for both. But the sinner uses logic for improper purposes. They both have the instrument. They both have the same standard. Maybe that'd be even a better way of putting it. They still have the same standard. Or if you think of logic as one's intellectual capacity. They still have the same instrument or capacity, but sinners will use that capacity in a way that is destructive, contrary to the glory of God and the good of man and the truth of God's word. Whereas believers are going to use their logical abilities or the standards of logic to glorify God, submit to him and serve him. The tool of intellect and the standard of correct thinking is unchanged. It's not different between them, but the use of that tool is quite different. One uses it ethically, the other uses it unethically. And so logic does not then become a neutral common ground between believer and unbeliever for the sake of arbitrating what is the truth. Logic does not provide a neutral common ground for the arbitration of the truth, though the laws of thought are the the same, the standards are the same, and the intellect is the same. By that I mean as a general tool. The fact is logic and intellect will not be used the same by believer and unbeliever. And so it doesn't become something of a neutral umpire between them for deciding on what is the truth. Moreover, now this is a slightly different point than what I've been making. Sin affects one's abilities or powers to a certain degree. We've said the laws of thought are the same between believer and unbeliever. The fall was ethical, not metaphysical. They should reason the same way that they have the same general intellect or tool God's given to them. And yet there's a sense in which the more a person progresses into sin and rebellion against God, the more that affects the abilities or powers that God has given and that are now being abused. Think about a baseball player, baseball player that's a Christian, baseball player that's a non Christian. Now they have the same general kind of body, the same general kind of strength and so forth. But the one tries to lead a life that's glorifying to God and the other doesn't. And let's say for the purposes of my illustration that the unbeliever's lifestyle is one of drunken debauchery night after night after night. You know, now that he's signed on to this professional team and he has this bonus, he has all this call this money. It's just living a life of riot. Now we said that there's no difference physiologically between a believer's body and an unbeliever's body. As a generalization and as two baseball players with roughly the same strength and capability, there's no real difference because of the religious conflict. Now what if the lifestyle of the unbeliever wears down his body, breaks it down? Will not sin then affect, will it not make some difference in the ability of the two? It could conceivably. You see what I'm getting at? Guy who is, you know, not taking care of his body is getting drunk all the time, maybe on drugs, whatever. So sin can have an effect upon ability. And I would suggest that sin can have an effect upon people's reasoning ability too. Sometimes they can get so deep into a lifestyle of rebellion against God that it begins to affect their ability to think clearly, To even take care of themselves, or to watch out in a kind of self preservational way for mistakes and reasoning that they really wouldn't want to make. And so to give you an example, and I'm taking extreme examples just to be clear here, you might have an unbeliever who would be so hateful toward God in the Bible that the unbeliever might support and come up with sophisticated arguments for why Christians should not be allowed to have their own Christian schools because we don't want children, you know, to have to listen to this kind of thing. And then our society is adversely affected. You can just imagine unbelievers, pardon me, coming up with arguments for why Christians shouldn't have the freedom to have Christian schools. Now somebody might point out to him, well, now, but if you reason that way, you have to understand that you're open to the same sort of thing and that believers have the right then to try to influence the civil process and to cut off your perspective from being taught to children. They have the right then to say there shouldn't be any public schools or public schools ought to teach Christian standards rather than allegedly neutral standards. And you'll have unbelievers. You'll have unbelievers who cannot catch the contradiction there. They have become so sickened by their hatred of God, their minds have been so diseased, as it were, that they can't even see that they're cutting off their own right to teach what they want to teach. When they reason this way or another way of putting it, is they don't even see that they are being unfair, that one part of the population is going to tyrannize another part of the population. But even at that, the position of Lord and servant can be reversed in society. So the tyrant might become the Christian tyrant. They can't see that, don't think there's anything wrong in and of itself what they're saying. So what I'm getting At is that the ability to reason clearly can be affected by sin, by a lifestyle of rebellion against God and hatred of his word. Sin can also in a more gross way affect one's reasoning ability or intellectual powers. Just think about drugs. Sometimes people get so heavy into drugs it makes physiological. Does physiological damage to their brain or nervous system or what have you. But even short of that, gross. An example, I'm saying that sin can affect reasoning ability. But all of that was by way of qualification. My more general mark is that reasoning ability per se. Standards of logic are the same between believer and unbeliever. The difference between the believer and the unbeliever is not ability or the standard of logical or illogical thought, but rather the use to which they put their minds, their intellects, the way they use logic. To the Christian, logic's indispensable. To the Christian, it's indispensable. First, in order to carry out the cultural mandate in the broadest sense, God gave man as his task and function in this world, the obligation to subdue this world to the glorious of God. And we will not be able to do what God made us to do. We will not be able to carry out the task God gave us to carry out. If we don't know how to think clearly, we don't know how to reason. Part of subduing the world is, let's say, the medical field that takes care of sickness and disease. And a doctor doesn't distinguish between a horse and a human baby. I mean, I'm using a gross mistake in logic. Then he's not going to be able to be a good doctor and in essence not be able to carry out the cultural mandate that has been given to him. Try writing a symphony where you give up all principles of consistency and logic and so forth. Obviously, the cultural mandate call calls for us to think logically. Moreover, logic is an indispensable tool in terms of knowing God and understanding his word. The Bible does not draw, does not tell us every possible theological truth. Sometimes it tells us various truths and expects us to draw the conclusion, to put things together. So that you don't have a statement in the Bible to the effect that God is triune, but you have all the premises that are necessary to show that God is triune. And so in order to do theology and to know God, we need to use logical abilities. Thirdly, in order to obey God, we need to be able to use logic. God says, don't steal. Here's another premise that you picked up from the world. That car is not my car. In order to obey God, I need to be able to draw the proper conclusion. If I'm not supposed to steal, stealing is taking that which is not mine, that car is not mine. Therefore I'm not supposed to go over there and take that car. Now realize we don't always stop to look at ourselves reasoning like that. It sounds funny to go through that process. But implicitly, when we obey God, we are thinking logically. We're carrying out a premise, you know, from His Word and something we've learned about the world or many things, and drawing an application and living in terms of it. So logic's an indispensable tool for the cultural mandates, an indispensable tool of theology, indispensable tool of ethics and ethical living. Moreover, logic can be a valuable tool in apologetics. Logic can be very useful to us in showing unbelievers the inadequacy of their thinking. Their systems of thought can be very valuable as a tool for an internal critique of the unbelievers worldview. Let me look at the Bible for a few moments just to give you an example of what might be a biblical justification for reasoning and for logic. We can begin with God Himself, Isaiah 1:18, Where God says, through the prophet Isaiah, come, let us read reason together. God engages in reasoning, and if we're going to be godlike, if we're going to follow his pattern of thought, then we should be able to reason as well, is that the Bible calls for consistency in our thinking. Hebrews 6, verse 18, again modeled on God himself, Hebrews 6:18, that by two immutable things in which it is impossible for God to lie, we might have strong consolation, etc. Notice it is impossible for God to lie. God therefore does not utter one proposition and then draw an inconsistent conclusion or utter a contrary proposition to it. God is consistent. Another example, 2nd Corinthians 1:18, 2 Corinthians 1 at the 18th verse. But as God is true, our word towards you is not yes and no. Because God is truthful, then what we say must not be contradictory. It must not be affirmation and denial. Yes and no. God is consistent and true, and so we must be consistent and true. Or consider Matthew 5:37. Jesus says, but let your communication be yes, yes, no, no. That is Jesus says, be clear, be consistent, be sincere in what you say. Let your yes be yes and your no be no. In Matthew 6:24, Jesus says, no man can serve two masters, for either he will hate the one and love the other, or else he will hold to the one who despised the other. You cannot serve God and mammon. You can't serve two masters. You must be consistent. Your yes must be yes. Your no must be no. Or 2nd Corinthians 1:12 another example of how the Bible requires consistency. 2nd Corinthians 1:12 for our rejoicing is this the testimony of our conscience, that in simplicity and godly sincerity, not with fleshly wisdom, but by the grace of God, we have had our lifestyle in the world, and more abundantly to youward for our rejoicing is this the testimony of our conscience in simplicity and godly sincerity. There's no inconsistency, no hypocrisy about what we say and do. So is there biblical justification for logic? Well, God engages in reasoning. Come, let us reason together and we see that God is consistent in what he says. He cannot lie. And therefore our word must not be yes and no. We must be consistent in what we say. Insincere, not hypocritical. We cannot serve two different masters. And we notice it in the Bible that there's a use of reasoning and evidence as well. An example would be Mark 2, verses 6 to 8. Mark 2, verses 6 to 8 is an illustration, one of many, where reasoning is utilized and evidence appealed to. But there were certain of the scribes sitting there and reasoning in their hearts, why doth this man thus speak? Blasphemies. Who can forgive sins but God only? And immediately when Jesus perceived in his spirit that they so reasoned within himself, he said unto them, why reason ye these things in your hearts? Here Jesus challenges their reasoning process, obviously for the sake of the conclusions they're drawing or refusing to draw. But it's interesting. The Bible says that they were reasoning. Jesus perceived the reason. He says, why are you reasoning like that? Look at Matthew 16, verses 2 and 3. He answered and said unto them, when it is evening you say, it will be fair weather, for the sky is red, and in the morning it will be foul weather to day, for the sky is red and lowering. O ye hypocrites, you can discern the face of the sky, but can you not discern the signs of the times?