Some Basic Logic

[Sam26]

For those of you interested, I will posts some very basic information about logic or correct reasoning. This should actually be in a philosophy forum, but this seems to be the only place available to post on this subject.


Logic: The Basics

Post #1

I will be using Kegley and Kegley's 'Introduction to Logic' as a guide to some of what I write. I want to make sure I give them credit for much of this material, since much of what I learned came from their book many years ago. It was the book I used in college almost 40 years ago.

Again the source of much of the information in this thread is the following:

Kegley and Kegley, Introduction to Logic, Charles E. Merrill Publishing Company, 1978

Introduction

What is logic? Logic is the study of correct reasoning. Hence, this is why we will using the words 'logic' and 'correct reasoning' interchangeably. Logic forms the foundation of good philosophical arguments, so it seems only fitting that we begin at the foundation. For if our foundation is solid, then we are more apt to build a solid belief system. Beliefs that have a strong foundation are more capable of weathering the onslaught of attacks to the contrary. On the other hand, beliefs that are based on weak premises or weak evidence are less capable of standing up to strong arguments. Good arguments are not based on what we happen to feel at the moment, or what we happen to think at a particular time. Good arguments are independent of what we think or feel.

If logic is the study of good argumentation, then it makes sense that logic would concern itself with how to properly draw conclusions based on the evidence. To put it another way, logic teaches us the proper relationship between good reasons and proper conclusions. While it is true that logic is just a tool - it is a very important tool, you neglect it at the expense of good argumentation.

Logic is not concerned with the thinking process. Thinking processes themselves are the subject of psychology. Psychology studies how people do think, whereas, logic is concerned with how people should think if they want to think logically (p. 5, 6 Kegley and Kegley).

What is an argument? An argument is a set of statements or propositions in which one called the 'conclusion' is supposed to follow from the premises or the evidence. The act of drawing a conclusion based on the evidence is called the act of inferring, or the act of formulating an inference. Therefore, argumentation is discourse containing inference. It should never be confused with the popular notion of the term argument meaning dispute.

Logic is not concerned with emotional content or attitudes. It is irrelevant how you feel about the argument in question, or how you feel about the person giving the argument. For instance, if I say "William is lying" or "Jackie is ignorant," I am expressing attitudes about people. Hence, it is important to distinguish between attitudes and factual assertions. If I say "Abraham Lincoln was the sixteenth president of the United States," we can ask if this statement or proposition is true or false. The latter sentence about Lincoln is a cognitive use of language, and as such it expresses a belief. When someone expresses a belief we often want to know what reasons or evidence they have to support the belief. Attitudes often just express positive, negative, or neutral evaluations toward someone or something.

I will continue...

 

[Sam26]

Logic: The Basics Post #2

Statements, propositions, and sentences

Since logic is concerned with assertions that are justified, logic therefore deals with statements and propositions. I will use the terms statement/proposition interchangeably, since their meaning is nearly the same.

A proposition is a claim that something is or is not the case. For example, "George Washington was the first president of the United States" asserts that something is the case, whereas the proposition "Abraham Lincoln was not the second president of the United States," denies that something is the case. So these kinds of propositions make claims about reality, and about our beliefs. When these kinds of statements are made we can specifically ask about their truth or falsity. Furthermore, we can ask what grounds or reasons one has for making the assertion or the claim.

Keep in mind that statements/propositions are all sentences, however, not all sentences are statements/propositions. Consider the following examples:

1. Who was the third president of the United States?
2. Will you please be seated.
3. Keep quiet!

Each of these are sentences, but none of them assert that something is or is not the case.

 

[Sam26]

Logic: The Basics Post #3

Arguments

An argument uses one or more statements to support a conclusion. The conclusion is supposed to follow from, or be justified by the other statements. These statements can be called variously - evidence, reasons, grounds, or premises. So every argument is made up of two parts, the premises and the conclusion.

For example, I enjoyed the first three movies that Harrison Ford starred in; therefore, I will probably enjoy his fourth movie.

I did well in algebra, geometry, and trigonometry; therefore, I will probably do well in calculus.

These two examples are called inductive reasoning, I will talk more about these kinds of arguments later.

Logical Analysis

To properly analyze an argument the argument must be stated clearly and precisely. One must be able to identify the data used to support the conclusion; and if you do not understand the data that supports the argument, then it is generally considered unwise to criticize it. However, one must not only understand the argument - one must also be able to identify the structure of the argument. In later posts we shall come to see that the structure of an argument is what makes it valid. Hence, structure and validity go hand-in-hand (p. 11, Kegley and Kegley).

Although arguments can be very complex, they can all be put into two basic forms.

1) This is true, therefore, that is true.
2) This is true, so, this is true.

Premises (evidence, grounds, reasons), therefore, conclusion.

Because Bob went to the dance last night with his girlfriend, [thus] Mary, who is Bob's girlfriend, went to the dance also.

I saw a black bird on the first house I passed on Washington street, and on the second, third, fourth, and fifth house, [so] the sixth house will also have a black bird on it.

Keep in mind that arguments given by people in our daily lives are rarely so easy to follow. Arguments can be very complex pieces of discourse, which can presented with any number of irrelevant pieces of information.

Good writing will provide you with clues that let you know that an argument is present. For instance, words like 'because,' 'for,' 'since,' 'in view of,' etc., indicate that what follows is probably a premise; and words like 'therefore,' 'so,' 'thus,' 'it follows that,' and 'hence,' etc., are words that indicate that what follows is a conclusion.

When analyzing arguments one must also be able to tell the difference between a causal explanation which seeks to answer the question why, and arguments which seek to establish the truth of the conclusion based on the evidence (p. 15, Kegley and Kegley).

The following explanatory statements are in the form 'S because R,'
i.e., they are causal explanations.

The man fell off the cliff because his rope broke.

The litmus paper turned red because it was put into acid.

The ice on the sidewalk melted because of the salt.

None of these are considered arguments, because they merely offer explanations. However, that is not to say that we could not put them into argument form. For example...

If litmus paper is put into acid, then it will turn red.
The litmus paper was put into acid.
Therefore, it turned red.

In this instance we took an explanation and turned it into a deductive argument, which is considered a proof in logic (more on proofs later).

Again these are causal explanations intended to show a causal connection between events. So rather than asserting a logical connection between statements, we are offered a non-argument in the form of 'S because T.'

The intention of an argument is to establish the truth of S, and the truth is established by citing evidence. If S is true, then T is true.

 

[Tanj]

Is there any logic behind your decision to reprint a book in post form on a discussion forum?

 

[Sam26]

Is there any logic behind your decision to reprint a book in post form on a discussion forum?

It is not a reprint of a book. The writing is my own except where I might quote specific passages or ideas not generally known. Parts of the outline and some of the ideas I do use, so that is what I'm using as a guide, and why I'm giving credit to Kegley and Kegley. The general ideas of logic are basically the same in any symbolic logic course. The same is true of an algebra course, there are a range of topics covered in algebra that are generally taught in an algebra class, and you might use a specific text in the class as a guide for the class.

Let me repeat, not every idea presented is original with me, hence, the reason to give credit to Kegley and Kegley.

Thanks for the question.
Sam

 

[OldWiseGuy]

I have a very smart nephew who uses such logic in almost all discussions, which of course usually go nowhere except in circles, as he dwells on the process and not the product.

 

[Dave-W]

That is the Aristotelian logic framework. However, that is NOT the framework used in the Bible.

BLOCK LOGIC (An Introduction to Hebrew Thought) - Sermon Index

Judaic Logic

2 Adductive Logic in Torah

http://theologylog.8.forumer.com/a/hebrew-block-logic_post8.html

http://www.hoshanarabbah.org/pdfs/heb_grk.pdf

 

[Sam26]

That is the Aristotelian logic framework. However, that is NOT the framework used in the Bible.

BLOCK LOGIC (An Introduction to Hebrew Thought) - Sermon Index

Judaic Logic

2 Adductive Logic in Torah

http://theologylog.8.forumer.com/a/hebrew-block-logic_post8.html

http://www.hoshanarabbah.org/pdfs/heb_grk.pdf

Logic has advanced much since Aristotle, just as mathematics has advanced. However, I'm not going to rely on logic or math of 2000+ years ago. There are certain principles of logic that apply to any argument, it doesn't matter who, what, where, or when these arguments are given. For example, the law of non-contradiction, which states that "Nothing can both be A and not A." Or, "No statement can both be true and false at the same time and place." If one violates this principle, then any statement can be true and/or false.

 

[Dave-W]

For example, the law of non-contradiction, which states that "Nothing can both be A and not A." Or, "No statement can both be true and false at the same time and place." If one violates this principle, then any statement can be true and/or false.

But that is NOT the logic of the bible. Hebrew Block logic allows for that, if you are working in different blocks.

So if one is to analyze the bible, one should use the SAME logical framework.

 

[Sam26]

I have a very smart nephew who uses such logic in almost all discussions, which of course usually go nowhere except in circles, as he dwells on the process and not the product.

Because one uses logic that doesn't mean that people will agree with you, assuming your using the logic correctly. You could use flawless logic, which in turn means that your arguments are flawless, and still people will find ways to disagree. There is an objective reality to logic that shouldn't be denied. In fact, many Christians accept the idea that mathematics, logic, and a whole host of abstractions are part of the mind of God and built into the universe. This means that they are there to be discovered. I too believe that there is a mind/s behind the creation of the universe, and that, for example, mathematics is part of that mind/s.

 

[Sam26]

But that is NOT the logic of the bible. Hebrew Block logic allows for that, if you are working in different blocks.

So if one is to analyze the bible, one should use the SAME logical framework.

Logic deals with statements/propositions; and the Bible is written using a language that incorporates statements, so yes, the logic we use to draw conclusions based on statements is the same logical framework that should be used to evaluate the Bible. Many if not most Christian apologists would agree with this.

 

[Dave-W]

Many if not most Christian apologists would agree with this.

"Many if not most Christian apologists" are unaware of Hebrew Block logic.

However, Jewish theologians are VERY familiar with it.

 

[Dave-W]

Aristotelian (western, Greek, pagan) logic is fine if you are limited to the natural world. But once you bring God and the super/extra natural into the picture, you have to have a more "mystical" logic framework and system.

 

[Sam26]

"Many if not most Christian apologists" are unaware of Hebrew Block logic.

However, Jewish theologians are VERY familiar with it.

That doesn't matter. Most mathematicians are unaware of certain mathematic views of the ancients, but that doesn't negate what we know about mathematics.

 

[Sam26]

Aristotelian (western, Greek, pagan) logic is fine if you are limited to the natural world. But once you bring God and the super/extra natural into the picture, you have to have a more "mystical" logic framework and system.

I disagree, logic deals with reality, and the language used to describe reality. As long as you are using statements to describe any reality, then you can use symbolic logic or modal logic to draw conclusions based on that logic.

 

[Sam26]

I disagree, logic deals with reality, and the language used to describe reality. As long as you are using statements to describe any reality, then you can use symbolic logic or modal logic to draw conclusions based on those statements.

Now there are limits to logic because there are other ways of justifying beliefs other than using logic. For example, I can use sensory experience (taste) to conclude that my orange juice is sweet. Or I can justify my beliefs based on testimonial evidence, etc.

 

[Sam26]

All of us use logic, i.e. all of us say this is true, therefore this is true. Logic is a way for us to formulate conclusions based on the principles of logic. Everyone has a kind logic that they follow, i.e., a logic that's built into their statements when making an inference. Iran and North Korea have their own logic when it comes to dealing with us. However, the question is whether or not the logic is sound, or whether they have a good understanding of logic.

 

[Sam26]

Logic: The Basics Post #4

The intention of an argument is to establish the truth of S, and the truth is established by citing evidence. If S is true, then T is true.

Why is this important? It is important because we want to be able to distinguish non-arguments from arguments. How do we know when an argument is present? We know an argument is present because the purpose of an argument is to establish the truth of other statements. Explanations are given to answer the question why. Although even explanations can be asserted in argument form, as we saw in the litmus example.

Here are five steps to help you analyze an argument.

1) First find the conclusion, that is, what is the point of what is being claimed.

2) Once you have located the conclusion, then locate the supporting data - the reasons or evidence given in support of the conclusion.

3) Next rule out repetitious statements and emotional content.

4) If there are missing pieces of evidence, then supply what is needed to make the argument a good one. Ask yourself what additional evidence is needed for support. You may also need to ask yourself - what must be assumed in order for the conclusion to follow.

5) Finally, you may also what to look for additional arguments within the context of the main argument, i.e., there may be smaller arguments within the larger context of the statements (p. 17 Kegley and Kegley).

 

[OldWiseGuy]

All of us use logic, i.e. all of us say this is true, therefore this is true. Logic is a way for us to formulate conclusions based on the principles of logic. Everyone has a kind logic that they follow, i.e., a logic that's built into their statements. Iran and North Korea have their own logic when it comes to dealing with us. However, the question is whether or not the logic is sound, or whether they have a good understanding of logic.

This indicates that there is indeed a useful purpose for logic besides being just a game of 'intellectual gotcha'. If so why don't we see more tangible evidence of this logic.

 

[Sam26]

This indicates that there is indeed a useful purpose for logic besides being just a game of 'intellectual gotcha'. If so why don't we see more tangible evidence of this logic.

The way most people use the word logic has little to do with logic itself. For example, someone might say that that isn't logical, but really what they mean is that it is not logical to them.

There is a difference between what you think follows from certain statements, and what actually follows based on the principles of logic. Logic in a lot of ways is like mathematics. For example, in algebra you use variables, and you plug numbers into those variables. In logic you also use variables, but instead of plugging numbers into the variables, you plug statements into the variables.

For example:

Here is a structure of a proof called modus ponens using variables.

Premise 1) If 'P,' then 'Q.'
Premise 2) 'P.'
Conclusion: Therefore, 'Q.'

The following is an example using the statements that can be plugged into the proof.

Premise 1) If 'the Bible is true,' then 'God exists.' (P = "the Bible is true" Q = "God exists.")
Premise 2) The Bible is true.
Conclusion: Therefore, God exists.

This is a proof for the existence of God. It follows necessarily from premise 1.

How do we know the structure is correct? The way we know is by using truth tables. However, I'm not going to give an explanation of truth tables. If you want more information about truth tables there are a variety of classes free on Youtube that explain truth tables.

The problem is that logic generally is not taught in high school, and sometimes it is not required in college. It should be taught starting in the 9th or 10th grade, but unfortunately it is not.

You asked why there is not there tangible evidence of logic. There is, but you have to know where to look. The most tangible evidence is in computer programming. The evidence for logic is also manifested in the use of arguments. However, most people are not that familiar with the logic that is required for formal arguments, which means people generally make poor arguments. Moreover, many people really don't understand what logic is, i.e., they use the word logic, but they use it in a very general relativistic way.