Category: Logic

Hello everyone and welcome back to Deeper Waters where we are diving into the ocean of truth! Tonight, we’re going to be continuing our look at becoming a thinking Christian. We started discussing logic some last night and tonight, I’d like to continue that by having us look at terminology.

Words. Words are wonderful things. It is amazing that they can convey information often so well. Those who doubt what I am saying are proving what I am saying as my words to you right now are conveying my thoughts. It could be that some of my thoughts are wrong, to which I’m sure some are, but I would hope that I am at least conveying what is wrong truthfully so it could be corrected if need be.

My wife is one who knows about my usage of words. I have a joy of taking words literally at times to laugh about them. For instance, if we’re going down the highway and I see a billboard that says something like “McDonald’s: Exit now!” I can just say “Well I guess if we want to go we have to drive right off of this bridge!”

In logic, your words are important also. All syllogisms only have three terms. Those are the minor, major, and middle. What’s important is that we be clear on what the terms mean. Terms also does not mean that they are one-word only. They can be, but they do not have to be. I could say “The lamp that is sitting to my right of me as I type on my computer” and have that be a term. “Everything in the kitchen except the kitchen sink” is a term.

Of course, there is a danger that a term could be identical in word and different in meaning. To illustrate this, a simple syllogism.

The edge of a river is a bank.
Banks contain money.
Therefore, the edge of a river contains money.

The premises to this are true. (Although granted that an agnostic friend of mine pointed out to me that the second premise can easily be questioned today) The AAA type proposition is usually valid entirely. However, the problem to this is that the term bank is ambiguous.

In the second premise, when we speak of a bank that contains money, we refer to a place of business that has the responsibility of holding money if need be for your safekeeping. (Again, I do realize that that is questionable today) In the first premise, we are speaking of the edge of a river.

The fallacy then is that while we’re using the same word, we refer to two different things. In essence, this becomes the four-term fallacy. This is also important in informal debate and one reason I try to make sure my opponent and I define our terms clearly. What do you mean by God? What do you mean by good? If you are using the same term and you have a different referent to that term, you’re going to be talking past each other.

God takes words seriously. Let’s make sure we do the same.

Hello everyone and welcome back to Deeper Waters where we are diving into the ocean of truth. We’ve been looking lately at what it means to become a thinking Christian and the next step to take is to learn something about thinking. That means logic. Logic doesn’t just mean right thinking. There are rules to thinking. There are a number of people who think that they are logical and they do not know the first thing about forming a syllogism.

Keep in mind this important truth. Logic is not a tool to discover truth per se. It is a tool to guide your thinking to see if something is true or false, but it itself cannot determine if something is true. It can determine if an argument is false if it is invalid, but that does not mean that the conclusion is false. I will demonstrate this with a few syllogism as I go along. Let’s start with the classic one.

All men are mortal.
Socrates is a man.
Socrates is mortal.

This is a valid syllogism and a true one. The important point with validity is that if a syllogism is valid in its form with true premises, then the conclusion MUST be true. The first sentence is called the major premise because it contains the major term, which will be the predicate in the conclusion. The second sentence is the minor premise as it contains the minor term, the subject of the conclusion. The term showing up in the premises but not the conclusion is the middle term.

Now let’s consider this syllogism.

All angels are rational.
Gabriel is rational.
Gabriel is an angel.

If you are a Christian, you could be quite tempted to immediately say that this syllogism is valid. We can agree with the conclusion, but the argument to get there doesn’t work. Want the proof? Take out Gabriel and put in your name and then tell me if you’re ontologically an angel. (I know some of you are really good people, and I don’t mean an angel in that way.) Gabriel could be the name of your next-door neighbor and while he is rational, he is not an angel.

The fallacy that has taken place is that of undistributed middle. A classic example of this was committed by a poster on Theologyweb with this syllogism. (To this day, he has not admitted it is invalid.)

All basketballs are round.
The Earth is round.
The Earth is a basketball.

The fallacy is called undistributed middle. In logic, there are four types of propositions.

A = All S is P.
E = No S is P.
I = Some S is P
O = Some S is not P.

A term is distributed if it refers to the entire class of which it speaks. In an A term, the subject is distributed. In an E term, the subject and predicate are distributed. In an I term, none of them are. In an O term, the predicate is. A rule is that the middle term MUST be distributed at least once.

Looking at the first syllogism, we find that rational is not distributed as rational is a predicate in both premises that are A premises. Therefore, the syllogism is invalid.

Note also that if you have a term distributed in the conclusion, it must be in the premises. Consider the following:

All snakes are reptiles.
No turtles are snakes.
No turtles are reptiles.

The problem is that reptiles is distributed in the conclusion, but it is not in the premise. Since this is the major term, it is the fallacy of illicit major. To do so with the minor term would be the fallacy of illicit minor.

This has been a brief look. We’ll discuss more tomorrow.

Hello everyone and welcome back to Deeper Waters, where we are diving into the ocean of truth. I’m going to take another look at a logical fallacy tonight and it will be the fallacy of accident. No. It doesn’t mean just making a mistake in your reasoning, though you shouldn’t do that.

We all make generalizations at times. I’m not saying that’s wrong. I don’t really know much of a way that we can avoid it. The problem with the fallacy of accident is that it takes a general statement and treats it as if there could be no exceptions whatsoever to that statement.

A good example of this in biblical studies is the book of Proverbs. We all know of people who have said that the book of Proverbs says X, and they did X, but it did not happen. For instance, not everyone who does good has a long life. Proverbs however are not meant to be ironclad statements of reality that always follows. They are general principles that tend to lead to a desired result. Chances are, if you live life the way you ought to, you will live a longer life.

This is often the case with moral dilemmas. What do you do about the Nazis who come to your door and ask you if you have any Jews? Generally, we would agree that you should tell people the truth. However, this is a case where I would argue that the Nazis do not deserve the truth and it is justified to lie to them. You could lie to them while still believing in the ninth commandment since you realize a valid exception to the rules.

This is another one that skeptics also have a problem with, especially when it comes to miracles. We are told that the laws of nature have no exceptions whatsoever to them. If that is the case, then there can be no miracles. We’ve seen hundreds of cases after all where people die and they stay dead. Why should we believe that a miracle has taken place?

The Christian arguing for the resurrection however is not arguing against the principle that dead people come back to life by natural means. That would be pretty silly. They in fact agree with the principle. If they did not, it would not make a resurrection so incredible. It would be a case of “Well yeah. That guy came back from the dead. It happens every now and then. So what?” Death itself has to be a constant reality for the resurrection to be considered a miracle.

What the Christian is saying that all things being equal, dead people do stay dead, but in the case of Jesus, things are not equal. There is an outside agent interfering that brings about the resurrection. You don’t have to start with the outside agent, namely God. You can argue that Jesus was raised and then from that point determine that there must have been an outside agent and then establish the identity of said agent.

The one claiming there are no exceptions to dead people staying dead is making an a priori judgment. It could be the case that no miracles have occurred, but it is hardly fair to the evidence to assume this prior and then look back and when you see what could be an event that is miraculous, throw it out ad hoc.

Be wary of generalizations. They are not always absolute rules.

Hello everyone and welcome back to Deeper Waters where we are diving into the ocean of truth! I’d like to start tonight a look at the topic of logic, and mainly of logical fallacies. These are fallacies that can often take place in debate. Normally, when we do debates, we don’t come out listing premises and conclusions, even if we have these in our minds. Thus, formal logic will be looked at later. For now, we’re going to look at some informal fallacies that anyone can catch.

A caveat needs to be made at the start. Because a fallacy is used, it doesn’t mean the conclusion reached is automatically wrong. It just means that there is not a good idea given to hold to that view. For instance, if I said “I believe in God because most of the world believes in God so it must be true”, that would be the ad populum fallacy. Now it could be the case, as it is, that God exists, but that is not a valid reason in itself. (I would accept it as evidence however though not an airtight conclusion) Consider also if someone said “I don’t believe in God because Hollywood Celebrity X doesn’t believe in God.” Now it could be, which it isn’t, that God doesn’t exist, but that is not a good reason for disbelieving in God’s existence. As Christians, we want not only good conclusions, but also reaching good conclusions by good means.

I plan to go through a list alphabetically of these fallacies. For all interested, if you have an IPhone or IPad, you can get an application called “Cheatsheet” for a relatively low price that contains each of these. The first one will be the fallacy of accent.

This one can be harder to detect in the online world unless someone uses something like bold, italics, or capital letters. In speeches however, it’s simple to detect. The fallacy takes place when one word or phrase is given an accent as if to highlight what is meant and even go against what was meant.

Suppose you were being interviewed in a man-on-the street interview during the extensive health-care debate we had here in America and were asked what you thought of the Obama proposal. I will use italics to identify which word I am accenting in each sentence.

“I support good health-care policies for all!”

“I support good health-care policies for all!”

The first statement could make you seem like a strong believer in the Obama policy as you wish to emphasize your support of the bill. The second one by contrast could be seen as a challenge to the bill in which you are saying that you support good health-care policies, but you do not see this policy as good.

A great place to watch for something like this would be in fact, the evening news. When a word is emphasized, just watch and see why it’s emphasized. Now not all emphases are wrong. There is a place for emphasis. The goal is to emphasize where you can to make your meaning as clear as you need it to be. There are times you might want to be ambiguous, but if you want to be as clear as you can, watch what you emphasize.

We shall continue tomorrow.