Some Basic Logic

[OldWiseGuy]

Sure, why not. But what if you are born with type 1 diabetes. Or short gut syndrome. My husband is doing an operation on a baby today that is missing part of its intestine. This baby will be a million dollar baby.

If people took better care of themselves it would free up medical resources, reduce wait times, lower insurance and medical costs through increased competition, increase productivity, etc. Everyone wins.

 

[Sam26]

I am not saying to throw out logic.
Rather, that there exists more than one logical framework.
Just make sure you are using the correct one.

Using the correct one? What does that even mean? If you have a question about modern logic specifically, or some disagreement with a particular principle, then state it. There is just no comparison to what we know about logic today and the logic of Aristotle (384-322 BC) for example. Aristotle did some pretty good work in logic over 2000 years ago, and some of it is incorporated into the logic of today. However, the advances that we have made in logic in the latter part of the 19th century, and in the 20th century are far beyond what they knew over 2000 years ago.

You seem to think that because they used a particular kind of logic in the OT, that that supersedes what we know today in terms of logic. If you have in mind some principle of logic that they used that is somehow better, spell it out. In other words, state the particular principle that you're talking about, because all you're doing is talking in generalities.

Thanks,
Sam

 

[Sam26]

Logic: The Basics Post #5

What follows is a summarizing of part of Chapter 2 in Kegley and Kegley's book with some of my own input.

Dimensions of Language

Since logic is concerned with both communication and understanding it will be important to sort through some of the functions of language. This will enable us to focus on the actual argument being presented; and it will help us to seek clarity and precision.

Formal analysis of an argument is not an easy task, since arguments in everyday life are rarely put in a form that is easy to analyze. However, if we want to think rationally, we need to be able to think clearly about what we intend to say; and once we know what we intend to say, then we can concentrate on saying it well.

Keep in mind that language can also be used to persuade without concern for rational arguments. We see this all the time. Sometimes people will appeal to opinions, prejudices, and emotions without concern for rationality.

Remember some of the distinctions that have already pointed out about sentences, and the different ways in which they can be used. Not all sentences make statements. For instance,

1. Is your name John?
2. Stand there!
3. Please don't do that.

These interrogative (sentences that ask a question) or horatory (sentences that exhort or encourage) sentences are not the kind of sentences we will be concerned with. We will be concentrating on statements or propositions that are declarative. For example, "The moon is approximately 240,000 miles from earth", or "It is snowing." What sets these sentences apart from the ones listed above is that you can properly ask about their truth or falsity. Hence, logic is concerned with statements or propositions, and thus with sentences that assert or deny something.

Language is very flexible, and it has many functions. The philosopher Ludwig Wittgenstein identified many of the uses of language in the Philosophical Investigations. The following are some examples:

Giving orders, and obeying them.
Describing the appearance of an object, or giving its measurements.
Constructing an object from a description (a drawing).
Reporting an event.
Speculating about an event.
Forming and testing a hypothesis.
Presenting the results of an experiment in tables and diagrams.
Making up a story; and reading it.
Play-acting.
Singing catches.
Guessing riddles.
Making a joke; telling it.
Solving a problem in practical arithmetic.
Translating from one language into another.

 

[klutedavid]

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.

Hello Sam.

One of the great tragedies of the last 2000 has been the influence of Greek philosophy upon interpretation of scripture. Greek logic falls wildly short of being able to understand God and His word and for this cause when Greek logic is used to understand scripture the reader is filled with all manor of feelings of contradiction. This is one of the great arguments that Messianics have had against the Gentile dominated Church is that they have a Hellenistic view of scripture. Greek logic leaves much to be desired in terms of understanding scripture and tempts man to venture into places that God never intended Him to go. Have you ever wondered why there arose so many heresies in the first 4 centuries? People were trying to understand scripture through the ill equipped framework of Greek logic and all sorts of madness developed.
(Text Sermons, Robert Wurtz II, BLOCK LOGIC: An Introduction to Hebrew Thought)

 

[Sam26]

Hello Sam.

One of the great tragedies of the last 2000 has been the influence of Greek philosophy upon interpretation of scripture. Greek logic falls wildly short of being able to understand God and His word and for this cause when Greek logic is used to understand scripture the reader is filled with all manor of feelings of contradiction. This is one of the great arguments that Messianics have had against the Gentile dominated Church is that they have a Hellenistic view of scripture. Greek logic leaves much to be desired in terms of understanding scripture and tempts man to venture into places that God never intended Him to go. Have you ever wondered why there arose so many heresies in the first 4 centuries? People were trying to understand scripture through the ill equipped framework of Greek logic and all sorts of madness developed.
(Text Sermons, Robert Wurtz II, BLOCK LOGIC: An Introduction to Hebrew Thought)

Hello Klutedavid

As I've said in other posts, logic is not the be all and end all of justifying a belief. Logic is an important tool, and one shouldn't neglect it if one is trying to give a good argument in defense of a belief. The problem is that many in religious communities, Christian or not, have tended to reject logic when it suits their purpose, or if they can't make good arguments. They tend to create self-sealing arguments (fallacies) that reject counter-evidence. For example, saying that the reason that you don't understand a particular Christian argument is that you're deceived, or that the natural man doesn't understand the things of God. Or they might say that you're logic is not God's logic, without understanding the outcome of such statements. To be fair though, there are those in the Christian community that do try to stick with the principles of logic (which is one of several other ways of justifying a belief), and do try to give good arguments in defense of their beliefs.

By the way, some of those ancient Greek writers had some important things to say, so I wouldn't be so dismissive, viz., to lump them into a negative light. Moreover, just because the Greeks believed that X, Y, and Z were true, doesn't mean they were using good logic.

You seem to think of logic as something subjective or relative, as though there aren't objective principles that need to be adhered to. The law of non-contradiction is not a matter of opinion, especially if your goal is the truth. Allowing contradictions into one's arguments or beliefs is an enemy of the truth. It destroys our ability to come to conclusions that are coherent. It destroys are ability to communicate. It destroys all the testimonial evidence of the Bible. Moreover, it destroys any idea of God in terms of God having a nature that we can understand. Basically without the law of non-contradiction one would be reduced to silence.

 

[Sam26]

Not being able to apply the principles of logic is not something that is only applicable to religious people. Just about every belief system is full of people who make the same mistakes in reasoning. The point here is not to pick on anyone's belief system, it's to point out that if you're going to defend your conclusions, then you need to be able to properly reason to a conclusion.

No one is immune from making logical errors. I've met plenty of atheists and agnostics who don't know the first thing about how to construct a good argument. So there is plenty of room for growth for anyone who understands the importance of having the proper justification for an argument or conclusion.

 

[Sam26]

Logic: The Basics Post #6

Now the five general categories of language are the following:

1) Cognitive (Informative) Function.

Language is used to convey information. As the following statements demonstrate.

"There are two desks in my room."

"The Japanese bombed Pearl Harbor on December 7th, 1941."

"Triangles have three sides."
(That triangles have three sides is also an example of an analytic statement. An analytic statement is one in which concept of the predicate is included in the concept of the subject.)
"Bachelors are unmarried men."
"All bodies are extended in space."
"All wives are female."

The one characteristic of these statements is that they can be spoken of as either true or false, i.e., they declare that something is or is not the case. That is not to say that other criteria cannot be applied to statements of information, since one can also ask if the statement is significant or not, or one can ask if it is useful or not.

Logic is not concerned with establishing truth or falsity. Logic simply asks if the conclusion follows from the truth of the premises. Another way to put it is that logic is concerned with the internal relationship between or amongst propositions.

2) Expressive

In these examples language is used to express feelings or emotions.

"I am having a great time at the beach."

"The portrait is beautiful."

"You idiot."

The important point here is that these statements express a feeling, emotion, or an attitude. These phrases are also considered evaluative, i.e., they reveal a positive or negative judgment by the speaker.

3) Evocative or Directive

Language is also used to arouse feelings, emotions, attitudes, and certain kinds of responses or actions in others. Examples of these kinds of statements are as follows:

"Duck!"

"Attention!"

"Please wash your hands before eating."

"Brush your teeth three times a day."

"John Doe for president."

These statements are a bit different from the ones we gave earlier in that they are designed to produce an effect or an action from two perspectives: First, the purpose or purposes of the user of the sentences, and two, the effect the user of language wishes to have or not have (Introduction to Logic, Kegley and Kegley, p. 34).

It is important in the study of logic to distinguish between informative statements and evocative statements. After all logic is concerned with what is being asserted, not with how it is being asserted. As Spock might say, emotional appeals are irrelevant.

Now are not saying that we should eliminate all emotion from our language, but only that we should be careful when formulating an argument that we do not include appeals to emotion, and that we stay away from personal attacks.

I'll next continue with the final two categories of language...

 

[OldWiseGuy]

We should use logic to solve our problems instead of consigning it to the ivory towers of intellectual musings and navel gazing.

 

[Sam26]

We should use logic to solve our problems instead of consigning it to the ivory towers of intellectual musings and navel gazing.

I wish logic could solve our problems, but all it will help you do is learn how to draw proper inferences from statements. Unfortunately we are not immune from other psychological factors that contribute heavily to what we believe. Logic tends not to be the predominate factor in what we believe, nor should it be, but it is important.

Intellectuals are not immune from error, and one shouldn't allow one's feelings or attitudes about those in ivory towers take away from the importance of learning. Learning is a good thing, but knowing what to study, and what to read is also important.

It's important to separate the psychology of belief, from reasons for a belief. However, it's not an easy task.

 

[OldWiseGuy]

I wish logic could solve our problems, but unfortunately all it will help you do is learn how to draw proper inferences from statements. Unfortunately we are not immune from other psychological factors that contribute heavily to what we believe. Logic tends not to be the predominate factor in what we believe, nor should it be, but it is important.

Intellectuals are not immune from error, and one shouldn't allow one's feelings or attitudes about those in ivory towers take away from the importance of learning. Learning is a good thing, but knowing what to study, and what to read is also important.

It's important to separate the psychology of belief from reasons for a belief. However, it's not an easy task.

Thank you for this honest and practical assessment.

 

[Sam26]

Logic: The Basics Post #7

The final two categories of language discussed here.

4) The Evaluative Use of Language

The complexity of the language used to make 'value judgments' is mind-boggling. The contexts of such language includes just about every context imaginable. As you can imagine there is still much disagreement over how to characterize such language. In this brief introduction we cannot even begin to do justice to this use of language, so we will only make a few remarks.

As you probably already know evaluative language makes judgments of what is of value, i.e., what is good, just, and beautiful. All you have to do is to look at some of the arguments on the Internet and you will see the wide variety of views in relation to ethics, religion, politics, language, etc. Some people believe that value judgments are subjective, while others believe they are objective, and still others hold some middle ground. Some examples are as follows:

"Knowledge is good in and of itself."
"Bush is stupid."
"This is a good book."
"This song is beautiful."
"The Iraq war is just."

5) Finally, the Ethical and Aesthetic (pertaining to a sense of beauty, or having a love of beauty) Use of Language

This use of this kind of language raises very important questions about how to interpret statements like, "Torture is wrong." Is it merely expressive, which translates into something such as, "I do not like torture" or "Torture - yuck!" Can it be that these statements are simply directive in nature - for example, "Do not torture!" And finally maybe statements like "Torture is wrong" are assertive-type statements that require us to give good reasons for accepting them (p. 56 and 57 of Kegley and Kegley).

These are very controversial topics, and will not be settled in these short musings

 

[Sam26]

I've mainly been talking about how logic works in terms of statements, i.e., drawing conclusions based on other statements that we believe to be true. However, there is also a logic of syntax, i.e., the rules for governing the way we construct a sentence or text. Moreover, Ludwig Wittgenstein, who was arguably the greatest philosopher of the 20th century, demonstrated that there is also an implicit logic built into the way we use language. This logic is reflected in what he called language-games.

Use in itself doesn't determine meaning, because one can use words incorrectly. And don't confuse context with correct usage either, because one can use a word incorrectly in a particular context. For example, a child pointing to the color blue, as he/she says red, is used in a context, but used incorrectly. Note that there is a correct use of the word red, and usually we know when we see it. Thus, there is a kind of built in logic determined by correct usage.

Philosophers and theologians, among a whole host of others, have notoriously been guilty of not understanding the logic of the correct use of words; and as a result there are a host of philosophical and theological problems that have ensued. This is not only true of philosophy and theology, but it's true of almost all subject matter. This problem is not as simple as it might seem. It's a very difficult problem sometimes to analyze.

We create a kind of reality with our language, i.e., we describe reality in certain ways using language. If we start by not understanding correct usage, then we can create our own (a kind of narrative) world that's not represented by the facts.

As philosophers, many times we are looking for an exact expression of a certain word, but there may not be one exact definition or theory that will take into account all of the different uses of a particular word. An example that Wittgenstein uses is the word game, i.e., there is no one definition that can describe all games. There are a multitude of games, and thus there are a multitude of uses of that term. How we use the term, and the logic behind that use, can tell us more sometimes than a definition or theory. Now some words can be precise, and can be summed in a definition, but not all uses of words can be put into a precise definition that can be expected to describe every possible use.

 

[Sam26]

Logic: The Basics Post #8

Logical vs Non-logical Material

One of the problems in analyzing many arguments is separating the logical material from the non-logical material.

Keeping in mind that logic is concerned with the informative side of language, i.e., with what is being asserted. You need to be able to distinguish between the emotive content and factual assertions; and to be able to translate emotive content into neutral content.

Consider the following two propositions:

1) "Bush is a liar!"

2) "Bush was mistaken."

The first statement is likely to be from someone with a negative attitude, while the second one might be from someone with a more positive attitude. We are not concerned with the attitudes of people. We are more concerned with the factual content. Expressions of attitude indicate a positive, negative, or neutral evaluation of someone or something; and as we said earlier in the discussion we want to focus on the cognitive use of language as opposed to the evaluative use.

You should get some practice reading articles and picking out and separating propositions into the five general categories that we have discussed.

We will conclude this section with the three basic kinds of disagreements.

There are disagreements in attitude, in belief, and verbal disagreements.

Ones attitude has more to do with ones state of mind or feeling about an event or fact, and less to do with what is claimed or asserted.

Disagreements about beliefs, on the other hand, are arguments over the supposed facts. These can be classified in two ways. First, the disagreement can be a real disagreement, in that there is a logical inconsistency in one of the arguments. Second, there can be an apparent disagreement, i.e., both arguments are consistent and the arguments can be resolved.

Finally, there can be a verbal disagreement, i.e., the people arguing are using the same words or phrases but different meanings.

 

[Sam26]

Logic: The Basics Post #9

Some Informal Fallacies

What is a fallacy? Simply put, a fallacy is an argument that does not provide adequate support for its conclusion. Furthermore, an argument that is fallacious is so despite having true premises, i.e., the conclusion would not follow from the premises even if the premises were true.

There are two kinds of fallacies, viz., formal and informal. A formal fallacy is an invalid form of a deductive argument. Hence, it violates a rule of deductive reasoning which is directly related to validity. Informal fallacies are much broader in scope and are not as neatly classified as formal fallacies. However, they generally fall into several classifications, viz., fallacies of relevance, fallacies of neglected aspect, fallacies of ambiguity, or the misuse of language (Kegley and Kegley, p. 115).

Here is an alphabetical list of some of the informal fallacies for your perusal.

1) The first fallacy is called an ad hominem argument (argumentum ad hominem). This fallacy consists in attacking opponents rather than the arguments they make. For example, "We cannot believe what the Secretary of Defense says because he is a neo-con," or "We cannot elect that senator, because he/she is a weak-kneed liberal." These kinds of attacks go on all the time, and they occur on both sides of the political isle.

2) The second fallacy is called appeal to authority. This fallacy happens when one appeals to someone who does not have the required expertise needed to supply the proper reasons or evidence in support of a conclusion. For example, Pat Robertson says that string theory is based on faulty mathematics, or Nancy Pelosi says that our military strategy is flawed. Neither Pat Robertson nor Nancy Pelosi have the proper expertise in the required fields.

3) Appeal to Ignorance (argumentum ignorantiam) is the next informal fallacy. This fallacy bases its conclusion on the absence of evidence. It falsely assumes that if there is no proof, then X is either true or false. Example: Until someone proves there are no unicorns, I am entitled to believe unicorns exist.

4) The next fallacy is called begging the question (petitio principii), and it is one in which the conclusion is just a restatement of one of the premises in one form or another.

For example,

There are good reasons for believing X, therefore, X is justified. What the person is saying is that the argument is justified, because the argument is justified.

P is true.
Hence, P is true.

This can be also referred to as a circular argument.

Of course the arguments can get much more complex when they are separated by other statements. The following example is taken from Kegley and Kegley's 'Introduction to Logic.'

"If men are to survive, they must be fit --indeed, only the fittest survive. And we can verify this by simply looking around and seeing who has survived. Obviously, they have survived because they are fit.

"This argument looks like the following:

Because P is true (men survive)
Q is true (they are fit)
Because Q is true (they are fit)
P is true (men survive)"

One final point about this fallacy. You can have a valid argument, which again has to do with form, and still commit the fallacy.

It takes some practice to get good at recognizing these fallacies, and often times people will claim that you are committing a fallacy when you are not, so you need to know them well.

Deductive Arguments

A good deductive argument must be
(1) valid
(2) sound
(3) cogent

As mentioned before in this thread validity is a quality of good deductive arguments. Validity means that the form of the argument forces you to the conclusion. The correct form is crucial. Therefore, if the premises are true, then the conclusion must follow. Note the following forms:

Premise 1: All X are Y.
Premise 2: b is an X.
Conclusion: Hence, b is a Y.

An argument of this form will lead you to a conclusion that is true provided the evidence, which is in the form of premises, are true. The following is an argument using the above form:

Premise (1) All cats are animals.
Premise (2) Morris the Cat is a cat.
Conclusion: Hence, Morris the Cat is an animal.

 

[Sam26]

These posts are not meant to give you what you need to be good at logic. The purpose of these posts is to give you some basic information about logic, i.e., to give you an idea of what logic is about. If you want to study logic it is best to do it in a formal class. Moreover, it is one thing to read a book on logic, and quite another to be skilled at logic. It takes a lot of practice, and practice in the use of logic is much more than just reading a book.

 

[Dave-W]

Where, in your descriptions of logic, is allowance made for the Divine, the supernatural intervention?
How things work in God's space?
And how that interacts with our own world of existence?

 

[Sam26]

Where, in your descriptions of logic, is allowance made for the Divine, the supernatural intervention?
How things work in God's space?
And how that interacts with our own world of existence?

That is a reasonable question, which I will attempt to answer.

First, logic deals with what follows from certain statements, viz., what conclusions can we reasonably make based on premises or evidence? Thus, when talking about the Divine or the supernatural we use language, and based on statements used in a language we come to certain conclusions. It does not matter if the statements are about God or any other subject, the question is, does your conclusion follow based on those statements. In a broader sense logic is part of the framework of reality, and it does not matter if we are talking about what is metaphysical or not, logic would still apply.

 

[Speedwell]

You seem to think of logic as something subjective or relative, as though there aren't objective principles that need to be adhered to. The law of non-contradiction is not a matter of opinion, especially if your goal is the truth. Allowing contradictions into one's arguments or beliefs is an enemy of the truth. It destroys our ability to come to conclusions that are coherent. It destroys are ability to communicate. It destroys all the testimonial evidence of the Bible. Basically without the law of non-contradiction one would be reduced to silence.

The "law of non-contradiction" is not really a "law" but an axiom of a particular axiomatic formal system. There are possibilities, other logics.

Moreover, it destroys any idea of God in terms of God having a nature that we can understand.

What gave you the idea that God must have a nature we can understand?

 

[Sam26]

Speedwell, thanks for your reply and question. I will do my best to answer it in the following way:

Just about every logic book I have refers to the principle of non-contradiction as the "law of non-contradiction." I have no problem calling it an axiom either. However, some think that the "laws of logic" are pre-axiomatic. I however, don't think that is the case. Where some logicians have probably gone wrong is referring to these laws as "laws of thought."

It may be true that if the Christian God exists, or for that matter if any God exists, we may never fully understand that God. However, there has to be some things that we understand, or we would not be able to even say there is a God, or to even have a belief about God.

In terms of God's nature, most Christians believe that included in God's nature are the concepts of omniscience, omnipotence, omnipresence, holiness, etc. We can generally understand these concepts, and thus we can talk about the concepts in relation to God. Does it mean that we fully understand what it would mean for a being to be omniscient? No. However, we talk about a lot of things that we do not completely understand. For example, we do not fully understand quantum physics, but that does not mean we can not talk about quantum physics in an intelligent way, or that we can not use logic in terms of our statements about the subject.

 

[Sam26]

Logic: The Basics Post #10

Continuing with deductive arguments...

The following are more examples of valid deductive argument forms. Remember validity has to do with the form of an argument.

Form: Modus Ponens -- If X, then Y. X. Hence, Y.

The following is an argument using this form:

Premise (1) If George is human, then George is a person.
Premise (2) George is a human.
Conclusion: Hence, George is a person.

Form: Modus Tollens -- If X, then Y. ~Y. Hence, ~X (~ = not).

Premise (1) If Harry is a cat, then Harry is an animal.
Premise (2) Harry is not an animal.
Conclusion: Hence, Harry is not a cat.

There are other deductive forms. For instance,

Hypothetical Syllogism -- If X, then Y. If Y, then Z. Hence, if X, then Z.

Transposition -- If X, then Y. Hence, if not Y, then not X.

Soundness as has already been pointed out, means that the argument is valid plus the premises are true. The following argument is valid, and it is also sound since the premises are true:

Modus Ponens

If I think, then I exist.
I do think.
Hence, I exist.

The next argument is valid, but not sound.

Modus Ponens

Premise (1) If humans are dogs, then dogs are humans.
Premise (2) Humans are dogs.
Conclusion: Hence, dogs are humans.

This is a valid argument, but is it sound? No. It is not sound, because the premises are not true.

Our third criterion is cogency.

Now there are going to be some here that disagree with this criterion. However, it is very important.

Cogency means that the premise's of a deductive argument are known to be true by the person to whom the argument is given. What this means is that not only is the argument sound, but the premises are known to be true. So although it is enough for a deductive argument to be valid and sound, however, for it to be convincing, one must know the premises are true.

The following is an example of a proof in logic:

"The base of a souffle is a roux.
This salmon dish is a souffle.
Hence, the base of this salmon dish is a roux.
(Dr. Byron Bitar)"

So in order for a proof to work for you, you have to know the premises are true. If you do not know what a 'souffle' is, then you will not know that the premises are true, it will not convince you, even if the argument's conclusion is true.