Of Science and Faith: Deductive Logic

by Jim Pemberton

In discussing science and faith, the word “reason” is often bandied about without much to say as to what it actually is. Those with any education in philosophy know of the three laws of logic and how to construct syllogisms. That excludes most of the world. So in one short blog article, I intend to lay it out as simply as possible. The reason is that you can’t understand the scientific method without understanding how syllogisms work. Unfortunately, many scientists, while they know how to use the scientific method, don’t understand how it works logically. That’s the reason for discussing it. Hopefully by the end of the next article you will have at least an inkling on how it works and have a leg up on most scientists.

Of Science and Faith

The Three Laws of Logic

There are three important laws of logic that philosophers have discovered over the millennia. They will seem simple at first, and they are. But many simple things get overlooked if they aren’t discussed, and it’s a big deal if these simple things are important.

The first law is called the Law of Identity. The law stated is basically that something is itself. You’re asking yourself why it took a philosopher to figure this out. The fact is that it’s so simple that no one thought to write it down. But it’s important because more difficult things are based on this simple fact and we will forget this simple fact in understanding the more complex thing if we don’t make a note of it. The Law of Identity can be written as a simple formula:

A=A

The second law is built on this fact and is almost as simple. It’s called the Law of Non-Contradiction. This basically means that something is not everything that the something is not. It can be written as this formula:

A≠~A

The tilde (~) means “not”. So you might say this: “A is not not A” Simple?

The third law is only slightly more difficult and is based on the first two. It is called the Law of Excluded Middle. This means that everything must either be or not be. There is no third way where it kind of is, but not really. It can be written as a formula also:

For all A: A or ~A

The three laws are the basis for mathematics. They are also the basis for logic.

Deductive Logic

Deductive logic is the area of logic where the three laws are employed to analyze the logical relationships between things. It is epistemological1 in nature in that it involves the discovery of reality by observing consistent patterns in reality. It isn’t ontological in nature in that it is limited to discovery by relationship rather than by directly apprehending static properties of things.

Since it involves relationships between things, it stands to reason that we need two things rather than one. Thw laws observe two things: A and ~A. For developing syllogisms our two things will be ‘A’ and ‘B’. ‘B’ could be ‘A’ or it could be in the set of ‘~A’. That is that ‘B’ is generally not everything that is ‘~A’, but it is at least one thing that is ‘~A’. Since ‘B’ could be ‘A’, we have at least one kind of possible logical relationship before us:

A=B

This is analogous to the law of identity, but is not exactly the same. This logical relationship doesn’t mean to say that A and B are identical, but that their occurrences are always logically simultaneous. That is, if you experience one of these things, you can be sure that the other one is occurring even if you don’t experience it. For example, we can say that the clock always strikes twelve when both hands are pointing directly at twelve. If the clock is striking twelve, then the hands are both pointing at twelve. If the hands are both pointing at twelve then the clock is striking twelve. By the time the clock is finished striking twelve, we can expect the hands to no longer both exactly point to twelve. Right before the clock strikes twelve, we can expect the hands to not exactly be pointing at the twelve. So we have two things: A=”the clock striking twelve” and B=”the hands pointing to twelve”. (This assumes, of course, that you have a clock that has hands and that the clock also strikes twelve at the right time.)

But there is a far more common logical relationship called a conditional statement. This is most easily explained in terms of causation. That is to say that we notice when something causes something else. Now a conditional relationship may involve two things where one is not a cause of the other. For example, both things may be caused by a third thing. Or there may be some other mysterious mechanism at work. But occurrences of the two can be tested for this relationship. Remember that we are talking about a relationship that is epistemological in nature. So we talk about the relationship necessarily in terms of one thing causing the other, but we use words that remind us how we know something. The two important words that refer to each side of the conditional statement are “sufficient” and “necessary”. That is to say that if we know one thing, it is sufficient, but not necessary to know the other thing. On the other hand, if we know the other thing, it is necessary, but not sufficient to know the first thing. That which is sufficient is called the “antecedent”. That which is necessary is called the “consequent”. The formula looks like this:

A∩B

You would say “If A, then B”
Note that A is the antecedent and is sufficient but not necessary to know B.
Note that B is the consequent and is necessary but not sufficient to know A.

Let me explain the words better. The words “antecedent” and “consequent” can be misleading. Normally when the syllogism represents a causal relationship, there is one thing that is caused and many things that work together to cause it. The thing that is caused is the “antecedent” and one of the causes is the “consequent”. So you can say: “If I know the thing that is caused, then I know one of the things that caused it.” So knowing that thing that was caused is sufficient to conclude all of the things necessary to cause it. But the thing that was caused is not necessary to know the thing that caused it. There would be other ways to determine that.

But you would have problems if you said “I know one of the things that cause something, therefore I know that what it causes happened.” The problem is that one of the other things necessary to cause it might not have happened. I’ll give you an example:

Suppose you have a light in the ceiling and a common light switch wired up in the normal way into the wall such that the idea is to flip the light switch up in order to turn the light on. The light switch being up causes the light to come on. So you would explain the logical relationship this way: “If the light is on, then the light switch is up.” Observing that the light is on, you can conclude that the light switch is up without looking at it. But a blind person could not flip the light switch up and conclude that the light went on. The electricity might be out or the light bulb might be burned out. A rat may have chewed through one of the wires. But for the same reasons you cannot conclude that the light switch is down by observing that the light is off. However, a blind man can conclude that the light is off if he finds the light switch and ensures that the switch is down.

So in relatively short order we have established four logical patterns. Two are valid and two are invalid. The two valid ones are thus:

————————–

If A, then B      (relationship stated)
A                         (observation)
Therefore B2    (conclusion)

————————–

If A, then B
~B
Therefore ~A3

 ————————–

The two invalid patterns are thus:

————————–

If A, then B
~A
Therefore ~B4

————————–

If A, then B
B
Therefore A5

————————–

These patterns are called “syllogisms”. Knowing how to build a syllogism without falling into the invalid patterns is necessary to doing science correctly. You can see that if you have two things and you want to test their relationship, you have to know which one to make the antecedent and which one to make the consequent. If you get them backwards, then your syllogism will be invalid.

In the next article, I will talk about how the scientific method is used to test syllogisms.

 


1Remember that epistemology answers the question, “How do we know?”
2This pattern is called “modus ponens” Latin for “the way of affirming”.
3This pattern is called “modus tollens” Latin for “the way of denying”.
4This pattern is a formal logical fallacy called “denying the antecedent”.
5This pattern is a formal logical fallacy called “affirming the consequent”.

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About jimpemberton

Christian, maverick minister, husband, father, jack of all, master of none. I pay the bills controlling production for a laboratory casework manufacturer.
This entry was posted in apologetics, Indigenous Posts, Series: Of Science and Faith and tagged , , , , . Bookmark the permalink.

7 Responses to Of Science and Faith: Deductive Logic

  1. parsonsmike says:

    Jim,
    I am really enjoying your work.
    So if I say that Jim owns a red car, and there is a red car in the lot, therefore it must be Jim’s, I have made an invalid argument. But which of the two invalid arguments did I make?

  2. jimpemberton says:

    Thanks, Mike.

    Now you have me wondering if I used the example of a red car in a blog article before. I used it in a lesson a couple or few years ago at church and possibly again either in Venezuela or India. But my “red car in the parking lot” example is actually for illustrating an informal fallacy. I introduced only formal fallacies here because of the way that I’m building a foundation for discussing the limitations of scientific discovery. Informal fallacies tend to be thought of in terms of inductive logic rather than deductive logic (although deductive logic provides the foundation for it). Nevertheless, to answer your question, I think I used this example before to talk about “hasty generalization”. There’s often some overlap in informal fallacies, so with modification it could be used as an example for a couple of other fallacies as well.

  3. parsonsmike says:

    Jim,
    I see I have more to learn (-:

  4. Ken Hamrick says:

    Jim,

    I, too, am really enjoying this series. You’re doing a super job on this!

  5. As I look at this article, I am reminded of what I discovered when I was writing my thesis for the M.A. in American Social & intellectual History, namely, that there is a problem with the scientific method. That was in the period 1959-71. When I repeated the fact that there was a problem with the scientific method to a science educator in 2006 and explained that it was in adequate to deal with a situation where both the thesis and the null hypothesis are true or, in other words, that it was too analytical, she looked at me and asked: “How did you know that?” Meaning, I suppose, how did an ignorant preacher have such knowledge. Actually, I picked up on the issue as far back as 1963, when I heard a preacher say, “We are suffering from the paralysis of analysis.” It was in my research in church history that I came across evidence that indicated that the hypothesis and the null hypothesis could both be true (this is not to say that every case of a hypothesis and null hypothesis is true). The point I am trying to make is that a rule might be true and the same could be said for the exceptions. Thus, both constitute the truth. This was a factor in Puritan thought, apparently, inherited from Petrus Ramus, the fellow who gave the western world taxonomy, the person responsible for our use of textbooks and attendance in classes devoted to a particular subjects. The Puritans spoke of contrarieties, seeking to deal with some of the difficulties of Scripture. It is my opinion based on years of study and reflection in Intellectual History and the Bible that there are depths to the scientific method that we are yet to grasp. While logic definitely has a place, it also has its limitations. Consider how the sovereignty of God and the responsibility of man or education and illumination in ministerial qualifications can constitute two poles that are to be in the mind for the purpose of setting up a tension in order for the believer to be balanced, flexible, creative, constant, and magnetic. To put it another way, the tension is a desirable one which enables and empowers the believer to respond appropriately to a given situation. Sometimes the God’s sovereignty must be stressed. At other times, man’s responsibility must be presented. In six years of research, covering more than 250 volumes, I discovered that the fugue of contrarieties came to a climactic time in the life of the church during the Reformation and the First and Second Great Awakenings and in the launching of the modern missionary movement. I always think it a matter of humor that God should have a missionary who had been in India seven years longer than Carey and who actually persuaded the first convert to go all the way in professing his faith in public baptism (a dangerous thing then and even now) and who went insane with joy over the first convert and who was said to be a Hyper Calvinist., one Dr. John Thomas.

  6. jimpemberton says:

    Dr. W,
    That’s a great point about contrarieties. I hadn’t planned on discussing that directly in the coming article about the problems with the scientific method. The fact is that the scientific method so many problems that it would be helpful to categorize them, which I haven’t fully done yet. On the surface there is so much overlap between possible systems of categories that it seems a daunting task to organize them well. Nevertheless, I just listened to two lectures by Dr. Sam Waldron last night that have something to do with this. The first lecture was one wrapping up a class on Early Church History with a discussion on different Trinitarian views. Many of the problems encountered seem to be a result of these kinds of logical contrarieties. The other lecture was in apologetics and started a section on the self-attesting nature of the scriptures. One point is that anything we rely on to validate the authority of the scriptures becomes an authority over the scriptures. The point is that any such contrariety where both sides turn out to be true must have an authority over them in order to validate them. In applying this to the scientific method, there must be some epistemological authority over the scientific method. It isn’t self-attesting. There’s some knowledge required to reconcile a contrariety that supersedes it that is either unaddressed or cannot be known.

  7. Pingback: Of Science and Faith: Resuming the Series | SBC Open Forum

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