Brian Smith

Fundamentals of Logic

142 posts in this topic

One of the fundamental things the science of Logic tells man is that his ideas must correspond to reality. This means when a man makes an argument in support of an idea, that argument must not contradict reality. If an argument does contradict reality, it must be rejected. The reason for this is that existence, not consciousness, is primary.

Now there are two ways an argument may contradict reality: if the claimed premises of an argument contradict the facts a man knows of reality - and/or - if the claimed relationship between the premises (or the premises and the conclusion) of an argument contradict the fact that is the Law of Identity. In other words, the two ways an argument may contradict reality is if its premises are false and/or its logic is invalid. In either case, the fact that the argument contradicts reality proves the argument must be rejected. Again, the reason for this is that reality, not a man's argument, is primary.

So what becomes of the conclusion - the idea - the argument was trying to prove? Does the fact that the argument has been dismissed have any relevance to a continued discussion of that idea?

Of course.

Because the argument has been dismissed, the conclusion is now unsupported. It no longer has its identified connection to reality. As such, the conclusion cannot validly be identified as 'true' or 'false' (or even 'possibly true' or 'possibly false') since these claims require that which no longer exists - an identified connection to reality. This means either a different argument must be presented - or - the conclusion must also be dismissed. Put simply, absent a new argument, the conclusion is nothing. It is what Logic identifies as arbitrary. And "the arbitrary is automatically invalidated". The reason for this is that existence exists - and only existence exists.

Thus, far from being irrelevant to anything a man is discussing, when a man identifies that an argument's premise is false or its logic is invalid, he is identifying the fact that the argument can no longer be asserted, the fact that the conclusion no longer has its identified connection to reality, and the fact that the conclusion must either be given a new argument or itself must be rejected.

Put simply, Logic shows man that finding false premises or invalid logic in an argument actually 'proves' quite a lot. Most specifically, it dictates what a man rationally does with the idea he has been discussing.

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It's hard for me to believe I'm coming down on this side of the argument, given so much of my respect for logic, but the point needs to be made that logic can be used inappropriately; as was well said in the other thread, method can be excessively emphasized over content.

For instance Brian, you are not even concerned whether the conclusion is in accord with reality, and this post is aimed to be about the very basics of logic. According to your post, if we start with the beginnings, and follow the process, we don't even need to worry about whether the conclusion accords with reality or not.

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Considering that Brian has not responded to the logical criticism of his points in the thread he started on Off-Topic issues, I don't understand the point of the above argument by Brian. Both Betsy and myself, as well as others, have amply demonstrated the errors involved in Brian's arguments and statements. Apparent attempts to get around Denying the Antecedent by starting a new thread is something I will not participate in.

So I will just say that I disagree with what Brian has stated above. Logic is a theory of consistency. Correspondence to reality is an issue of truth. One combines logic and truth so that one can verify that one's conclusions are true and valid when the premises are true. Logic alone will not guarantee a statement will not contradict reality. (A dog is a bone; a bone is a cat; therefore, a dog is a cat. Valid, logical reasoning.) "If an argument does contradict reality, it must be rejected" he states. Arguments don't contradict reality. Statements alleged to be true may or may not contradict reality if one can show a) the statement is based on a false premise OR b ) an invalid inference was made. An illogical argument or an untrue premise does not show anything about the truth (or correspondence to reality) of the conclusion. Anything else is a logical fallacy as Betsy and others have apply demonstrated in the 'Off-Topic' thread.

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One of the fundamental things the science of Logic tells man

Aristotle and Ayn Rand said logic is not a science.

Could you kindly provide references for this statement?

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Could you kindly provide references for this statement?

AR: [my italics]"logic is the art of non-contradictory identification".

Aristotle used the identical Greek word, "techne"; I can find the exact passages if you'd like.

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Logic is both an art and a science, depending on the emphasis. The art is the practice of it; the systematic formulation of the laws is science. Objectivism uses both forms.

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Overall, in application, logic is an art. See Betsy's quote on Ayn Rand's reasoning for why it's not a method:

I once asked Ayn Rand why she defined logic as "the art of non-contradictory identification" and, particularly, why she used the word "art" rather than "method." She said that she was using "art" to mean a skill acquired by practice and use.

A method, i.e. science in this case, is something that is inherent in the process, and needs merely grasping by the human mind for perfect application; e.g. the Scientific Method, always used in same way at all times. Art is something different, requiring deliberation and judgment by the user for proper use, given the time and the situation. In science, human judgment is almost a detriment to the objectivity of the result. In art, human judgment is a requirement for the objectivity of the result. Those of you who understand programming computers, will understand that as a perfect example when you reflect on why it is an art and cannot be a science. There are many other spheres of human endeavor that cannot be science, and are art instead. For instance, sculpture, where there is no one perfect way to make the ideal statue. It requires judgment and deliberation by the person, at every step.

Logic is both an art and a science, depending on the emphasis. The art is the practice of it; the systematic formulation of the laws is science.

Yes but every human activity that may be classified as art and not science may have systematic formulation of its laws. For instance, there are plenty of good and important laws in statuary. That doesn't make it a science though.

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Could you kindly provide references for this statement?

AR: [my italics]"logic is the art of non-contradictory identification".

Aristotle used the identical Greek word, "techne"; I can find the exact passages if you'd like.

ewv is correct -- and the reference for my agreement with his position is Leonard Peikoff's Introduction to Logic course. Logic is an applied science.

Free Capitalist, your answers are odd, coming from a champion of induction such as yourself. Even if Ayn Rand said "logic is the art [...]" that is no warrant for your very strong statement that "Ayn Rand said logic is not a science."

Not art is only "non-art"; Not art is not "science." Outside the very loose context of popular parlance, art and science are neither opposites nor exclusives. To hold so would be an invalid deduction.

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Overall, in application, logic is an art. See Betsy's quote on Ayn Rand's reasoning for why it's not a method:
I once asked Ayn Rand why she defined logic as "the art of non-contradictory identification" and, particularly, why she used the word "art" rather than "method." She said that she was using "art" to mean a skill acquired by practice and use.
the fundamental concept of method, the one on which all the others depend, is logic.
(my emphasis)
Hence the method man must follow: to identify the facts he observes, in a non-contradictory manner. This method is logic
(my emphasis)

--------------

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Overall, in application, logic is an art. See Betsy's quote on Ayn Rand's reasoning for why it's not a method:
I once asked Ayn Rand why she defined logic as "the art of non-contradictory identification" and, particularly, why she used the word "art" rather than "method." She said that she was using "art" to mean a skill acquired by practice and use.

A method, i.e. science in this case, is something that is inherent in the process, and needs merely grasping by the human mind for perfect application; e.g. the Scientific Method, always used in same way at all times. Art is something different, requiring deliberation and judgment by the user for proper use, given the time and the situation. In science, human judgment is almost a detriment to the objectivity of the result. In art, human judgment is a requirement for the objectivity of the result. Those of you who understand programming computers, will understand that as a perfect example when you reflect on why it is an art and cannot be a science. There are many other spheres of human endeavor that cannot be science, and are art instead. For instance, sculpture, where there is no one perfect way to make the ideal statue. It requires judgment and deliberation by the person, at every step.

Are you sure Ayn Rand's answer to Betsy's question was not contextual? Neither the question nor the response suggest that logic is not a science or method. All the question says is: Why are you using the word "art"? And Ayn Rand replies, I use "art" in this sense. We should not read more into words than what they actually say.

Furthermore, are you suggesting that Science is not "something...requiring deliberation and judgment by the user for proper use, given the time and the situation"?

I have done a fair amount of programming. It is an applied science or technological field. Art, in the sense Ayn Rand used it, most likely means "applied science." In this sense, mathematics is an art.

Logic is both an art and a science, depending on the emphasis. The art is the practice of it; the systematic formulation of the laws is science.

Yes but every human activity that may be classified as art and not science may have systematic formulation of its laws. For instance, there are plenty of good and important laws in statuary. That doesn't make it a science though.

Please see my comments above.

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Free Capitalist, your answers are odd, coming from a champion of induction such as yourself. Even if Ayn Rand said "logic is the art [...]" that is no warrant for your very strong statement that "Ayn Rand said logic is not a science."

Yes but that expression would sound alarming (which I grant it might) only in the context of the common-place meaning of science as the only reliable process of the human mind, contrasted with the arbitrary or the subjective. I didn't mean to make my statement in that context, but instead in the context of the distinction between art and science, both of which are reliable processes and neither of which is inherently subjective. In that context I would say logic is an art and not science.

ewv is correct -- and the reference for my agreement with his position is Leonard Peikoff's Introduction to Logic course. Logic is an applied science.

I don't know if Dr. Peikoff was speaking in the context of art vs. science controversy. Induction cannot be a science (i.e. a strict and indifferent repeatable process); thus anything based on induction, which is most of what we have in our minds, is more art than science; i.e. more reliant on our judgment to reach the proper conclusion, than on following the appropriate predefined steps. I will grant there's nothing that relies on personal judgment within a deductive syllogism, which is entirely scientific. But combining the syllogisms into something useful does at times involve considerable judgment, and isn't automatic; plus all of induction isn't automatic.

Not art is only "non-art"; Not art is not "science." Outside the very loose context of popular parlance, art and science are neither opposites nor exclusives. To hold so would be an invalid deduction.

This comment requires my own kindly question: if everything shares pieces of everything else, how can we ever define anything? How can we possibly define night as different from day, since even on a darkest night there's still some light available?

The difference is in the fundamentals. Science is something that not only doesn't require personal judgment, but in fact avoids it if possible. That's why double-blind studies in psychology are (properly) considered to be the most scientific, by taking human judgment as far as possible out of the equation. Art, by contrast, is something that depends on judgment, cannot exist without it. Logic cannot exist without people making judgment calls at various steps. The only way to call logic a science, properly so termed, would be by claiming that it consists of one big deductive syllogism, or of a series of necessarily following deductive syllogisms.

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I think that Mercury and Free Capitalist may be missing an important issue in Betsy's question to Rand.

I once asked Ayn Rand why she defined logic as "the art of non-contradictory identification" and, particularly, why she used the word "art" rather than "method." She said that she was using "art" to mean a skill acquired by practice and use.
(my emphasis)

I don't think one can conclude from this that Rand did not think that logic was a science or a method. Betsy's question concerned why logic was defined as an art.

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It's hard for me to believe I'm coming down on this side of the argument, given so much of my respect for logic, but the point needs to be made that logic can be used inappropriately; as was well said in the other thread, method can be excessively emphasized over content.

Why not just say 'It's a matter of semantics, it maybe logically true but it is not factually true. In other words, put less emphasis on logic and more emphasis on the facts.

If my interpretation is correct, than I think I am finally starting to understand what you and the others mean by looking at reality.

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One of the fundamental things the science of Logic tells man is that his ideas must correspond to reality. This means when a man makes an argument in support of an idea, that argument must not contradict reality. If an argument does contradict reality, it must be rejected.

Premises and conclusions, because they are about reality can possibly fail to correspond with, or contradict, something else in reality. Arguments, because they are a method of consciousness, do not themselves correspond with or contradict reality. Instead, a valid argument using true premises proves that the conclusion is true. (An invalid argument proves nothing about the conclusion one way or another.)

Thus, to speak of an argument "contradicting reality" is an error in reasoning known as a Category Error or Category Mistake. (here)

The reason for this is that existence, not consciousness, is primary.

That's why it is a category error. An argument itself can't "contradict reality" any more than it can whistle "Dixie."

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One of the fundamental things the science of Logic tells man is that his ideas must correspond to reality. This means when a man makes an argument in support of an idea, that argument must not contradict reality. If an argument does contradict reality, it must be rejected.

Premises and conclusions, because they are about reality can possibly fail to correspond with, or contradict, something else in reality. Arguments, because they are a method of consciousness, do not themselves correspond with or contradict reality. Instead, a valid argument using true premises proves that the conclusion is true. (An invalid argument proves nothing about the conclusion one way or another.)

Thus, to speak of an argument "contradicting reality" is an error in reasoning known as a Category Error or Category Mistake. (here)

So it is a matter of semantics? Quote provided is taken from the wikipedia site provided.

A category mistake, or category error, is a semantic or ontological error by which a property is ascribed to a thing that could not possibly have that property

(Bold is mine.)

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Free Capitalist, your answers are odd, coming from a champion of induction such as yourself. Even if Ayn Rand said "logic is the art [...]" that is no warrant for your very strong statement that "Ayn Rand said logic is not a science."

Yes but that expression would sound alarming (which I grant it might) only in the context of the common-place meaning of science as the only reliable process of the human mind, contrasted with the arbitrary or the subjective. I didn't mean to make my statement in that context, but instead in the context of the distinction between art and science, both of which are reliable processes and neither of which is inherently subjective. In that context I would say logic is an art and not science.

No, the expression doesn't "sound alarming" in the context of a "common-place meaning of science." The expression sounds alarming, in any context, because (1) it is false [Ayn Rand never said that] and (2) it misrepresents a great thinker whose ideas have world-changing potential. I know that sounds harsh, but I'm sure you'll appreciate my speaking plainly.

ewv is correct -- and the reference for my agreement with his position is Leonard Peikoff's Introduction to Logic course. Logic is an applied science.

I don't know if Dr. Peikoff was speaking in the context of art vs. science controversy. Induction cannot be a science (i.e. a strict and indifferent repeatable process); thus anything based on induction, which is most of what we have in our minds, is more art than science; i.e. more reliant on our judgment to reach the proper conclusion, than on following the appropriate predefined steps. I will grant there's nothing that relies on personal judgment within a deductive syllogism, which is entirely scientific. But combining the syllogisms into something useful does at times involve considerable judgment, and isn't automatic; plus all of induction isn't automatic.

Yes, he was, although I wouldn't use the word "controversy." (There was no public dispute about what Ayn Rand meant by "logic.") Listening to the course would provide you with a first-hand grasp of what he said. I think it was brought up in one of the Q&A sessions.

You are using "science" in one sense (as in "doing science in the lab"). Even the formal sense of your usage describes elements of the Scientific Method, as in "observation" and "experimentation." In this respect, the meaning of "science" is closer to the meaning of "art" or "technique." Science, as used by Dr. Peikoff to classify logic, means "a body of systematized knowledge acquired by systematic study." Induction is a science in both senses, i.e., it is one of the methods by which man acquires knowledge; it is also part of the body of knowledge devoted to the processes by which man acquires knowledge. See the definition and synonyms of science on this page. They help clarify my distinctions.

I have two things to say about your use of "judgment" so far on this thread. First, the sense in which you use the term is not clearly delineated and thus open to misinterpretation. Second, it is related (but not closely) to understanding the usage of the terms "art" and "science" in this discussion of the proper classification of logic.

What do I mean?

Judgment has several meanings, depending on context. In ethics, we speak of "value judgments" and this is closest to what many people mean when they say judgment. They use it to mean roughly "personal emotional appraisal of." But, in epistemology, we use judgment to mean "man's cognitive apprehension and integration of facts." A layman's proposition (or sentence) is a basic judgment. In this respect, judgment does not require a "personal emotional appraisal." These judgments are philosophical. (e.g., "This is a messageboard.")

Then there is the judgment which we make in the context of our productive lives. It is in this context that we speak of a professional (e.g. scientific, medical, actuarial) judgment.

More narrowly, in the context of the law, we speak of legal judgment, which is distinct from the professional judgment of a lawyer.

Art, in the sense of an esthetic recreation of reality, does involve value-judgments (metaphysical and esthetic) as well as basic judgments. But, this is not the sense of 'art" in which Ayn Rand defined logic. She meant it in the sense of "a technical application of a body of systematic rules."

So you can see, scientists use judgment too. In fact, they have to. A biologist who discovers new knowledge of a certain terrible virus must use his professional judgment in properly ensuring his safety during his next series of experiments. His epistemological (basic cognitive) judgment is the judgment upon which his ethical and professional judgments rest. All these lie in a different category from his own esthetic judgment of the virus itself, a judgment which depends on his personality and fascination with the subject.

In any case, that is my understanding of the matter.

Which of the senses of "judgment" above do you mean when you use the term?

Not art is only "non-art"; Not art is not "science." Outside the very loose context of popular parlance, art and science are neither opposites nor exclusives. To hold so would be an invalid deduction.

This comment requires my own kindly question: if everything shares pieces of everything else, how can we ever define anything? How can we possibly define night as different from day, since even on a darkest night there's still some light available?

The difference is in the fundamentals. Science is something that not only doesn't require personal judgment, but in fact avoids it if possible. That's why double-blind studies in psychology are (properly) considered to be the most scientific, by taking human judgment as far as possible out of the equation. Art, by contrast, is something that depends on judgment, cannot exist without it. Logic cannot exist without people making judgment calls at various steps. The only way to call logic a science, properly so termed, would be by claiming that it consists of one big deductive syllogism, or of a series of necessarily following deductive syllogisms.

Please see my comments on "science," "art," and "judgment" above.

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Speaking of fundamental logical errors, a very common one is context-dropping.

For example, the following signature:

"identifying logical errors is problematic" [For whom?] "For non-mind-readers like me..."

"claims about his opponent's alleged errors in logic [are] claims he cannot possibly justify or prove without mind-reading"

"Finding a fallacy in an opponent's argument is irrelevant to anything under discussion."

- B. Speicher

Logic courses are not courses in "mind-reading"

Identifying logical fallacies is not a logical fallacy

Identifying a logical fallacy in an argument invalidates that argument

- B. Smith

The sentence fragment attributed to me is taken waaaay out of context since I was referring to the difficulty of accurately identifying which specific logical error another person may have made in coming to an conclusion.

Arguments belong in postings, not in signatures. In all fairness to the people on both sides of a dispute, it is the only way to keep the context. Posters can -- and should -- give refer-backs to the original posts and those taken out of context can replay and correct an out-of-context or misleading quote.

I suggest Brian change his quote ASAP.

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That should be:

Arguments belong in postings, not in signatures. In all fairness to the people on both sides of a dispute, it is the only way to keep the context. Posters can -- and should -- give refer-backs to the original posts and those taken out of context can reply and correct an out-of-context or misleading quote.

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Arguments belong in postings, not in signatures.
Under protest I will remove the quotes. But I reject the assertion that they are misleading in any way. And I refuse to debate that issue here.

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...a valid argument .... (An invalid argument ...)[Emphasis added]
Apparently it is believed the concepts 'valid' and 'invalid' are properly applied to the concept 'argument' - ie that they identify something about the argument. Unless it is claimed these concepts are applied capriciously - ie Logic applies them arbitrarily - then the assertion that "an argument itself can't contradict reality" is false.

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Premises and conclusions, because they are about reality can possibly fail to correspond with, or contradict, something else in reality. Arguments, because they are a method of consciousness, do not themselves correspond with or contradict reality. Instead, a valid argument using true premises proves that the conclusion is true. (An invalid argument proves nothing about the conclusion one way or another.)
While I disagree with Ms. Speicher's claim that an argument cannot "correspond with or contradict reality", I agree that an invalid argument proves nothing about the conclusion one way or the other - ie it proves neither the conclusion's truth nor it's falsehood. An invalid argument is properly rejected. It is dismissed. As such, it cannot say anything about a conclusion at all.

So, to repeat, what is the status of the conclusion at that point? As previously stated, absent its supporting argument, the conclusion is now unsupported. And, what must one do with an idea which is unsupported? Also as previously stated, either one must provide it a different argument - or one must dismiss it.

Thus, while it is true that identifying a logical fallacy does not identify whether a conclusion is true or false, it does identify that one may no longer rationally consider the conclusion on the previously given basis. In order to validly continue considering the conclusion - ie to continue rationally discussing it any further - one must either give a different argument or dismiss the conclusion as arbitrary.

In other words, "finding a fallacy in an opponent's argument" is incredibly 'relevant' to one's discussion - because it identifies the conditions necessary to rationally continue the discussion. Without either a different argument or the dismissal of the conclusion, any continued 'discussion' of the conclusion is the cognitive equivalent of a parrot squawking.

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I am addressing one issue and one issue only - that the identification of logical fallacies and the dismissal of arguments based upon them is logically valid and logically necessary.

Brian, you're right on almost all counts here, and I acknowledge your pursuit of fallacies, and I certainly try to make sure my arguments don't have them, and try to point them out in posts of others.

However, you missed one important thing, and you still continue to misunderstand it: identification of logical fallacies does, and should, lead to dismissal of arguments based upon them; but not of conclusions.

Betsy summarized it very neatly in the following post: the part where you're right, and likewise where you make a mistake:

If you can't prove something with observation -- like the existence of atoms, for instance -- you must make a valid argument to prove your conclusion is true.

The above are proper and on-topic when dealing with any subject.

Disputing an intellectual opponent's premises or conclusions by pointing to observable facts that contradict them is proper and on-topic for any subject.

Making a valid argument for an alternative conclusion is proper and on-topic when dealing with any subject.

Making an issue of an opponent's logical errors is off-topic because an invalid argument proves nothing whatsoever about the conclusions being discussed. If the logical fallacy is the issue, it should be raised in the Metaphysics and Epistemolgy forum.

Ever line in this quote answers some part of your objection.

It is seen very clearly, in regards to Rick's objections, what the proper role of arguments is, and in what context making a valid argument is absolutely necessary.

Most pertinent to your (Brian's) key objection is the second to last line, which indicates the proper way to argue about true conclusions. Instead of following the second-to-last line, your preferred method is the last line, with all of the problems that result from that.

The approach is incorrect; it raises hostility (perhaps unintended); and overloads the crow and renders posts frequently unreadable.

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it misrepresents a great thinker whose ideas have world-changing potential. I know that sounds harsh, but I'm sure you'll appreciate my speaking plainly.

I do. It was no part of my intention to misrepresent Ayn Rand (or Aristotle, for that matter). I think we understand very different things by the word 'art' and 'science', and I'll open up a new thread to deal with that subject. This distinction between those two words is no longer properly made today, but it existed, and I am sure it was still conceptually available 40-50 years ago; when we get into discussing it and when you see what I meant, I'm confident sure you'll find agreement with my point.

By the way, if science is "a body of systematized knowledge acquired by systematic study", then the making of sculpture is a science too, right? So everything's a science, isn't it?

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