We Should Have A Logic Area In Here!!!

[nimble]

I think to actually have a section devoted to deductive logic would be really neat. We could find arguments in news, TV, and even boards, and replace the argument with variables and critique the arguments. I think that might be a good addition to the site.

[DavidOdden]

I think to actually have a section devoted to deductive logic would be really neat. We could find arguments in news, TV, and even boards, and replace the argument with variables and critique the arguments. I think that might be a good addition to the site.

I think that would be a really bad idea. Offhand, I can't think of anything of value that you can derive from deductive logic and the replacement of words that refer to concrete concepts with the ultimate floating abstraction, the capital letter variable (standing for arbireary predicates) and the lower case variable (usually restricted to the letters i, j, k, x, y and z). If you know of some case where some good might come from such an exercise, perhaps you could bring it out.

I do think that some discussion of logic (not just "deductive logic") is quite appropriate, but there's an area for Epistemology topics already.

[AndrewSternberg]

When I was listening to my copy of Peikoff's "Introduction to Logic" course, it would have been useful to have such a section to practice it more.

Just becuase induction is more important than deduction, one shouldn't abanden deduction as something that neccesarily leads to floating abstractions. I think deduction in an inductive context is still very important.

I don't think nimble was advocating 'symbolic' logic games. He might have just been talking about 'real' logic excercies that can sometimes be aided with symbols, like those found in the excercise booklet that comes with Peikoff's course.

Automatizing deductive reasoning in a setting like the one nimble is talking about would certainly train you to be quicker on year feet in your thinking while in an everyday life context. Is this not a value?

[nimble]

I think that would be a really bad idea. Offhand, I can't think of anything of value that you can derive from deductive logic and the replacement of words that refer to concrete concepts with the ultimate floating abstraction, the capital letter variable (standing for arbireary predicates) and the lower case variable (usually restricted to the letters i, j, k, x, y and z). If you know of some case where some good might come from such an exercise, perhaps you could bring it out.

I do think that some discussion of logic (not just "deductive logic") is quite appropriate, but there's an area for Epistemology topics already.

Are you serious? First off, variables have value. In fact, Aristotle was the first to notice that (the man who invented logic). Second, we use variables because words dont refer to concretes so well. They are often imprecise and distracting from the argument. Third, deductive logic is MUCH more important than inductive. ALL OF MATH rests on deductive logic, ever used a proof before?

Lastly, I want to hit on this again. How is a variable a floating abstraction? It can represent a term as efficiently and more clearly than words can. Whats the difference between calling a Banana a banana or just calling it B? You still refer to the same thing, it just takes letters out to make it more clear. Or in math, we don't write the word variable everytime we use a variable, instead we use x or y or any letter, so that it makes the equation clearer.

[DavidOdden]

Are you serious? First off, variables have value.

Extremely serious. For starters, I have no idea what you mean by the "value" of a variable. Just to make sure this doesn't go way off the rails, I'll assume you mean specifically "referent". Now then, what is the referent of "y", or of "a", or "y"? Even if I put it in context, for instance "P(x,y)" or "Q(j,k)", you can't tell me the referent of x, y, j or k.

In fact, Aristotle was the first to notice that (the man who invented logic).

In Latin, this is referred to as argumentum ad vericundam.

Second, we use variables because words dont refer to concretes so well. They are often imprecise and distracting from the argument.

Are you serious? You're telling me that you think you understand the referent of "y" or "x" better than you understand the referent of "cow" or "Earth"?

Third, deductive logic is MUCH more important than inductive. ALL OF MATH rests on deductive logic, ever used a proof before?

Pardon me while I snooze though this part a bit. I've done enough deductive proofs in my life to know why they aren't any use to understanding man's method of reasoning. If you'd like to retract your suggestion and make an alternative proposal about a mathematics section, please feel free. I take it that you consider mathematics to be the only important form of knowledge? Your implicit argument -- "Mathematical methods are essential to understanding the universe; mathematical methods cannot be discovered by any means other than symbolic deduction; therefore symbolic deduction is the most inportant method of gaining knowledge" does not go through, for more than one reason. If that isn't your argument, you can say what your argument really is.

Lastly, I want to hit on this again. How is a variable a floating abstraction? It can represent a term as efficiently and more clearly than words can.

If so, tell me what does "b" represent, and what does "x" stand for?

Whats the difference between calling a Banana a banana or just calling it B?

I assume that you're not familiar with Rand's discussion of the conventional nature of names, i.e. it doesn't matter how you pronounce the name of the concept <banana>, from ITOE. Pronunciation is not at issue: what is at issue is that "b" can stand for cow, horse, electron, pink elephant, knife, legislation, containment or anything else that exists. Variables don't have fixed values. Variables are bad, for serious discussion, because they don't have fixed value, and therefore con't refer to anything in particular. The only way to narrow down what you're talking about is to delimit the referent of "y" with... words.

Now let me offer a ray of hope. So-called "deductive logic" is typically understood to be FOP logic like they teach in university-level Logic 101: that's the stuff I'm talking about, which spends too much time going essentially nowhere. Inductive logic is formalizable, and from a syntactic POV is as "deductive" as basic 101 Logic. Real logic is not pure deduction (i.e. question-begging).

[nimble]

Are you familiar that the ONLY difference between inductive logic and deductive logic is that the structure of inductive arguments are flawed? How is induction better?

[nimble]

Just so that my argument is clearer. Here is an example of an inductive argument.

99% of people get sick

I am a person

Therefore I get sick.

It is flawed because it leaves room for error.

Deductive Argument

All life uses respiration

I am alive

Therefore I use respiration.

Its the same form of the argument, only difference is that deductive leaves no room for error. How can it be worse?

[DavidOdden]

Just so that my argument is clearer. Here is an example of an inductive argument.

99% of people get sick

I am a person

Therefore I get sick.

That's not a valid inductive argument. You have to derive the conclusion from particulars, so for example "Fred has gotten sick", "Bill has gotten sick" (etc.) plus "No person (over the age of 3) has not gotten sick". From that you can derive the conclusion "100% of people get sick (some time in their lives)". If you know of particular people who have actually never been sick, that fact is sufficient to block the conclusion that you must get sick sometime (assuming, contrary to fact, that you haven't ever been sick).

It is flawed because it leaves room for error.

What do you mean, it "leaves room for error"? If you're saying that observing consistent correlations is not equivalent to knowledge of causality, that's correct. The essential failure of all of these formal modes of reasoning is that they don't come to proper grips with "Therefore". The formal deductive approach sees the connection as being magical: but the proper way to look at the question is in terms of causation. A proper argument (inductive or deductive) would focus on whether being human causes sickness (and it does not). You can come up with a valid argument framed in terms of causality, if you'd like.

Deductive Argument

All life uses respiration

But that's false, so the rest of the argument is trash.

I am alive

Therefore I use respiration.

Its the same form of the argument, only difference is that deductive leaves no room for error. How can it be worse?

Sound deductive arguments can't be in error, but to be sound, you have to already know the answer that you're 'arguing' to: the deduction does not provide you with any information. The truth of the premises cannot be derived deductively -- they have to be arrived at inductively. Deductive arguments "leave room for error" because the premises may be false.

[nimble]

actually inductive arguments are not derived from particulars. Thats a common misconception. And that arose from a misinterpretation/mistranslation of philosophic works.

Inductive argument is defined as "claims to support its conclusion only with some degree of probability: one of two classes of arguments"

[nimble]

EXAMPLE 3-1

All Republican presidents have been in favor of a strong military.

President Bush was a Republican president.

It follows that President Bush was in favor of a strong military.

EXAMPLE 3-2

John is on the softball team and has short hair. Dan is on the softball team and has short hair. Kenji is on the softball team and has short hair. It seems likely that all the members of the softball team have short hair.

EXAMPLE 3-3

All members of the softball team must have short hair. Jay has short hair.

Therefore, Jay must be on the softball team.

EXAMPLE 3-4

If Hansen is the serial murderer, then his fingerprints would be on the gun. His fingerprints were on the gun. Therefore, it is clear that Hansen is the serial murderer.

EXAMPLE 3-5

Most presidents of the United States did not die in office. Therefore, it is doubtful that the twelfth president of the United States died in office

Example 3-1 is a valid deductive argument. The author is not attempting to persuade us that it is only likely that Bush was in favor of a strong military, but rather that the conclusion follows conclusively from the premises. Example 3-2 is an inductive generalization. From the particular cases of a few members having short hair and being on the softball team, the author generalizes that all the members of the softball team are likely to have short hair. Example 3-3 is an invalid deductive argument. Although the word "must" can be ambiguous, suggesting either high probability or conclusive necessity, it appears that the author of this argument is attempting to provide conclusive evidence for the conclusion, thinking that the premises are sufficient for knowing that Jay is on the softball team. If the author intended only something like "Jay is probably on the softball team" for the conclusion, then we would have to appraise this argument by inductive standards. But the tone of the argument appears to be deductive, even though the inferential claim fails from this perspective.

Number 3-4 (invalid deductive) is a good example of how easy it is to turn an apparent deductive argument into an inductive argument. As the argument is presented, the phrase "it is clear that" indicates that the author thinks that the premises provide conclusive evidence for the conclusion. They don't. It is possible that the premises are true, but Hansen is not the serial murderer. This could be a classic case of circumstantial evidence. There are many ways Hansen's fingerprints could have been on the gun. He could have picked up the gun shortly after the shooting or touched the gun in some way prior to the actual murder in which the real murderer used gloves, leaving only Hansen's fingerprints on the gun. Suppose in discussing this situation with the author of the argument, after reminding him of these possibilities, he backs off from his initial claim. He tells us that he meant it is reasonable to tentatively suspect Hansen, to bring him in as a prime suspect for questioning. If so, we would then appraise the author's argument based on inductive standards. How strong is the evidence, his fingerprints on the gun, for the conclusion that Hansen is the serial murderer? What other kinds of evidence are needed to strengthen our confidence in the conclusion?

Example 3-5 shows that it is a misconception to believe that deductive arguments always move from general premises to particular conclusions and that inductive arguments always move from particular premises to general conclusions. Although this is often the case-3-1, 3-2, and 3-3 fit this alleged rule-it is not always the case. Although 3-5 has a general premise (a statement about most presidents) and a particular conclusion (a statement about the twelfth president), the nature of its inferential claim is inductive. Because the premise states only that "most" presidents have not died in office, it is impossible to conclude with certainty that the twelfth president of the United States did not also die in office. The nature of the premise indicates that only probability is generated for the conclusion and that no attempt is made to provide certainty for the conclusion.

~Indiana Univ. Press

[nimble]

PS- Example 3-2 is an inductive argument (not necessarily strong or weak). And example 3-3 is an invalid deductive argument (fallacy of affirming the consequent).

[Evangelical Capitalist]

actually inductive arguments are not derived from particulars. Thats a common misconception. And that arose from a misinterpretation/mistranslation of philosophic works.

Inductive argument is defined as "claims to support its conclusion only with some degree of probability: one of two classes of arguments"

Is that a dictionary definition? If so, it's not even a very good one. Here's one (from m-w.com) that's closer to what we're talking about here:

induction: inference of a generalized conclusion from particular instances

Deduction is the opposite process: deriving a particular conclusion from generalizations. Those generalizations are the result of inductive reasoning. The process of conceptualization, on which your mathematics is based, is an inductive process, i.e. it generalizes from particulars. That is why induction is more important that deduction.

[nimble]

Is that a dictionary definition? If so, it's not even a very good one. Here's one (from m-w.com) that's closer to what we're talking about here:

induction: inference of a generalized conclusion from particular instances

Deduction is the opposite process: deriving a particular conclusion from generalizations. Those generalizations are the result of inductive reasoning. The process of conceptualization, on which your mathematics is based, is an inductive process, i.e. it generalizes from particulars. That is why induction is more important that deduction.

I guess we are disagreeing on a definition. If that's the case, then I suppose we have no argument here.

[BurgessLau]

I guess we are disagreeing on a definition. If that's the case, then I suppose we have no argument here.

Does not the question then become: Which is the better definition?

Unless of course, one believes definitions are arbitrary -- that is, it doesn't matter where we start because our only concern is with coherence, not objectivity.

That, of course, would be a recipe for rationalism, wouldn't it?

[nimble]

Does not the question then become: Which is the better definition?

Unless of course, one believes definitions are arbitrary -- that is, it doesn't matter where we start because our only concern is with coherence, not objectivity.

That, of course, would be a recipe for rationalism, wouldn't it?

I think you are generalizing too much, and coming to poor conclusions. Definitions are not arbitrary, they help to link a term to its referent concept or object. However, when a difference in defintion arises, it means that we are referring to different concepts or objects. However, the subjective part is which one is to be used? If you call a banana a jookie, and I call it a banana. We are referring to the same physical object, but whose term is better? Truthfully it doesn't matter, as long as we both understand the referent that the terms refer to.

In the opposite example, when you call something a banana, and so do I, yet we have different definitions, then one of us is referring to a different thing in reality. Which term is better suited for which concept is really irrelevant. As long as we recognize we are differing in defintion, then we can sort it out and just rename one of the two concepts that we used the same word for.

So, either you need to label your concept of induction differently or I do. It really doesn't matter who concedes to the change in label. The only reason I believe mine is better is because your definition of inductive was derived from a false translation of greek to english. The only reason you think your definition is better is because it is lexical, and that is not a valid reason for usage.

If being lexical is all that mattered, then there would be no problem with conceding that America is a democracy, when it is really a constitutional republic. Its only because people no longer see the difference, that people have been able to make the two terms one and the same. But I think giving something credit simply because people commonly use it that way today is a poor policy.

*lexical definition=what a word means today, by general consenus (BAD WAY TO DEFINE THINGS)

[DavidOdden]

actually inductive arguments are not derived from particulars. Thats a common misconception. And that arose from a misinterpretation/mistranslation of philosophic works.

Inductive argument is defined as "claims to support its conclusion only with some degree of probability: one of two classes of arguments"

I see. Somehow, somebody gave you the wrong definition of inductive reasoning, so that would explain why you have a bad opinion of it. Some free things you can look at briefly to understand induction are this or this. Most dictionaries (cf. EC's extract from Webster's) will explain the term if you're not familiar with it, though not in great depth. Rather than obsess about the definition of induction, you should simply ask youself, how can the premises of a formal deduction be proven in the first place? The other question you should ask yourself, but seem to have to interest in answering since you've skipped over this issue even after I've brought it to your attention, is what of value do derive from the process of deduction? Your usage of "induction" is non-standard, and while it's your legal right to call a banana a jookie, I won't understand what you're saying.

[Thoyd Loki]

Just so that my argument is clearer. Here is an example of an inductive argument.

99% of people get sick

I am a person

Therefore I get sick.

It is flawed because it leaves room for error.

Deductive Argument

All life uses respiration

I am alive

Therefore I use respiration.

Its the same form of the argument, only difference is that deductive leaves no room for error. How can it be worse?

What book are you getting this from? Or are you making this up? This is a complete misunderstanding of logic on many points.

First, your concept of what an inductive argument is is simply wrong. And here I will quote a real dictionary "The process of inferring or verifying a general law or principle from the observation of particular instances;" (Oxford English Dictionary Fifth Edition)

"The Aristotilian term (Greek script) of which it is the translation [induction], signified generally the process of establishing a general proposition not by deduction from a wider principle, but by appeal to the particular instances, or kinds of instances, in which its truth is shown." ( An Introduction to Logic, H.B.W Joseph page 378)

Induction is not screwed up deduction. They are different in form and in kind. There is also no formal structure of induction as you have rationalistically done in your example. Your example of an inductive argument is an example of a bad deductive argument.

It is invalid this way: Your argument goes, structually like this.

Some A is B

All C is A

All C is B

No argument like this is valid as you stated it. You would have to show (and the bubble diagrams they use in introduction courses are helpful to visualize this) that the class of C is both all in the class of A as well as all in the class of B. This form of argument cannot do this. Therefore even as a deductive argument, it is out.

Also looking up the etymology of the words induce and deduce (and the others) will give you a clearer picture of the differing nature of these to forms of logic.

[nimble]

The stuff I quoted above is from "An Introduction to Logic" produced at Indiana University. We obviously have different sources.

[Bowzer]

Reasoning through probabilities is the predominant view of induction in universities these days. It is also known as Bayesian reasoning after an eighteenth-century clergyman named Thomas Bayes. Bayes proposed a statistical theorem that fits modern rationalists' gloves as well as the infamous black glove of death fit O.J.'s hand. And philosophers use this theorem not to kill ex-lovers but to kill inductive reasoning, indeed reasoning as such.

Plain and simple fact is, Bayes' theorem has nothing to do with reason and nimble's out-of-this-world ramblings on what he thinks induction is just summarize this view at best.

Reasoning through probabilities is the predominant view in the universities but so what!? It's thoroughly false and quite ridiculous. Objectivists do have a different source than you, nimble, it's called reality.

[nimble]

Reasoning through probabilities is the predominant view of induction in universities these days. It is also known as Bayesian reasoning after an eighteenth-century clergyman named Thomas Bayes. Bayes proposed a statistical theorem that fits modern rationalists' gloves as well as the infamous black glove of death fit O.J.'s hand. And philosophers use this theorem not to kill ex-lovers but to kill inductive reasoning, indeed reasoning as such.

Nice parallel, but did you notice the rhetoric you just produce, no argument was put forth.

Plain and simple fact is, Bayes' theorem has nothing to do with reason and nimble's out-of-this-world ramblings on what he thinks induction is just summarize this view at best.

Way to make an assertion without providing evidence for your theory. And also, nice ad hominem.

Reasoning through probabilities is the predominant view in the universities but so what!? It's thoroughly false and quite ridiculous.

Keep running with that straw man.

Objectivists do have a different source than you, nimble, it's called reality.

Is that so? I am absolutely confident that all of my views are tied to reality, and that my being is capable of interpreting that reality. How is my source any different than yours?

[DavidOdden]

The stuff I quoted above is from "An Introduction to Logic" produced at Indiana University. We obviously have different sources.

Come on, get serious. There is no such thing as "Introduction to Logic" produced by Indiana University. Indiana University does not "produce" works. Specific people of units at IU do. Does this have an actual author -- what's the name? Is this published by Indiane University Press? What is the ISBN number? Is this a handout for some class you're taking? What is the class -- what department, what specific course? Who is the instructor? What authority does he cite to support his totally erroneous notion of induction? I hereby challenge you to substantiate the implication that anyone in the world, other than you, is this confused about induction. Are you merely saying "Some drunken jackass wrote this nonsense, and they were physically located at IU when they committed this crime against the name of logic"?

I believe that all of your erroneous assertions about induction have been thoroughly refuted, so all you seem to have left is evasion.

[nimble]

I hereby challenge you to substantiate the implication that anyone in the world, other than you, is this confused about induction.

I accept this challenge

Reasoning through probabilities is the predominant view of induction in universities these days. It is also known as Bayesian reasoning after an eighteenth-century clergyman named Thomas Bayes.

[source]

Nice parallel, but did you notice the rhetoric you just produce, no argument was put forth.

Way to make an assertion without providing evidence for your theory. And also, nice ad hominem.

Keep running with that straw man.

Is that so? I am absolutely confident that all of my views are tied to reality, and that my being is capable of interpreting that reality. How is my source any different than yours?

nimble,

the flaw of the probability theorem is in assuming that whatever was calculated as most probable solution, is taken as that which is a solution. The theorem is guilty of the kind of induction you propose with your definition. Something has 99% probability, therefore it will happen. In mathematical logic, that's not true. It's not even 99% true because in mathematical logic there is no such thing.

I've written a few days ago a blog entry I named "Odds for Success." I suggest you read it.

[nimble]

nimble,

the flaw of the probability theorem is in assuming that whatever was calculated as most probable solution, is taken as that which is a solution. The theorem is guilty of the kind of induction you propose with your definition. Something has 99% probability, therefore it will happen. In mathematical logic, that's not true. It's not even 99% true because in mathematical logic there is no such thing.

I've written a few days ago a blog entry I named "Odds for Success." I suggest you read it.

What do you mean? Mathematical logic is deductive, and I agree that deductive logic is valid. It's inductive logic that is invalid, but let me read your blog. And I'll post again after my class today.

(oh and definition of valid="if the premises are true, then it is logically impossible for the conclusion to be false." Definition of invalid="if the premises are true, then it may still be possible for the argument to yeild a false conclusion."

[Free Capitalist]

Nimble, here's what's going on. You were shortchanged in your Logic class, although unfortunately the corrective process was muddled by your stubbornness in face of knowledgeable authority here.

When I took a Logic class 3 or so years ago, we also had to buy an Introduction to Logic book, maybe it's the same one as what you have (hardcover, pinkish tint, mathematical graphs splashed across the page, I forget the author). I was likewise taught that Induction is *defined* as logic of probabilities, whereas Deduction is logic of certainties. Upon reflection, I realized that this modern definition (and it is only modern, because Aristotle, the very authority you cite, did not define it this way) is actually proof of modern philosophers' laziness and conceptual fuzziness. Originally we inherited the Classic definitions of the two words, which everyone has been trying to convince you of here:

Deduction, given true premises, will necessarily give a true conclusion, but it does not provide you with any new knowledge, nor can you verify the said premises by another process of deduction.

Induction has room for error, though it can still provide neecessarily true conclusions (if you take context into account), and is the only way of validating deductive premises, and for arriving at any new knowledge.

Aristotle, however, didn't develop inductive logic as much as the deductive syllogism, so since the modern philosophers weren't babyfed by him with all of the answers, they decided to proclaim that the Inductive logic had no answers to begin with. In other words, due to impotence they decided to switch the definition of Induction as something that *by design and conception* can never be certain, and that we should not demand precise and definite answers from philosophers who have none. However, if one assumes some arbitrary rules and applies them in dogmatic and acontextual ways, he can produce some semblance of a syllogism, and this modern professors call Deductive logic.

So, if I were you, I wouldn't go around saying I know everything about logic, after taking a course entitled "Introduction to Logic", and moreover taking a course that is based on modern philosophy and modern theories of logic and linguistics. That's why I said you were shortchanged; I hope the money you paid for the course at least gave you a checkmark for General Education requirements, because it bought little else.