Logical Fallacies

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Logical Fallacies

Postby Marilyn » Wed Jun 14, 2006 2:25 pm

Logical Fallacies

Readers often ask about critical thinking and how to reason better. One of the best ways is to learn about logic, which is both fun and useful. Following are examples of the most common logical fallacies. You can use them as exercises to find the flaws in your own thinking.

Simple errors arising from ambiguity.

The same word may be used in different senses (called equivocation): “Marriage is a subject of great gravity, so getting married will make us gain weight.” Or a sentence construction may produce a double meaning (amphiboly): “We’re having some friends for dinner.” Or a word may be emphasized inappropriately (accent): Contrast “I just love my dog!” with “I just love my dog!” Or words that are similar in form may not be similar in sense (figure of speech): “Does he have cold feet?” Who asked: Your husband’s mother or his doctor?!

Confusing the parts with the whole.

We may mistakenly assume that what is true of the parts must be true of the whole (composition): “A chimpanzee is an intelligent animal and even grasps certain numerical concepts, such as the difference between one and two. So a dozen chimpanzees probably would be able to divide a dozen bananas among themselves equally.” Not too likely, right?! But what about this? “Every member of a congressional committee is bright and understands fiscal policy. So the committee likely would be able to successfully restructure the country’s fiscal policy.” It’s the same fallacy.
And sometimes we assume that what is true of the whole must be true of the parts (division): “A group of musicians is wildly popular. Therefore, if they break up, each will be wildly popular.” Of course, that’s incorrect. But how about this? “A corporation consisting of several subsidiaries produces goods of high quality and is profitable. Therefore, each subsidiary can be expected to produce goods of high quality and be profitable.” Again, it’s the same fallacy.

Considering the form of an argument.

We’ve all heard of “if-then” arguments: If this is so, then that must be so. One source of error is assuming “this” defines the only way in which “that” can occur (affirming the consequent): “If a person has full-blown AIDS, then his or her T-cell count will be low.” True. But the following is false: “A person has a low T-cell count. Thus, he or she has AIDS.” Other conditions cause low T-cell counts. A twin error occurs in the opposite manner (denying the antecedent): “A person does not have AIDS. Thus, he or she does not have a low T-cell count.” False, and for the same reason: Other conditions cause low T-cell counts.

Learning about deductive reasoning.

Have you ever heard this? “Every man is mortal; Socrates is a man; therefore, Socrates is mortal.” It’s a famous “syllogism,” a form of deductive reasoning that consists of a major premise, a minor premise, a “middle,”and a conclusion. (The “middle” appears in both premises, linking them.)
An error occurs when the middle contains a term used in two different senses (four terms): “Wool coats shrink if they get wet. Sheep have wool coats. Thus, sheep get smaller when they stand in the rain.” Obvious, right? But what about this? “Many people pay no taxes. The working class is composed of many people. Thus, the working class pays no taxes.” Obviously wrong!
Or the middle term may be used inappropriately to link the two premises (undistributed middle): “Truffles often are found by dogs trained to locate them by scent. Illegal drugs often are found by dogs trained to locate them by scent. Thus, truffles are often illegal drugs.” Oops! This is wrong, just as wrong as the following. “Executives often are ambitious and want to make a lot of money. Criminals often are ambitious and want to make a lot of money. Thus, successful executives are criminals.”
One error occurs when the conclusion is broader than the major premise allows (illicit major): “Politicians are actually reasonable people and not biased nitwits. All politicians are human beings. Therefore, no human beings are unreasonable or biased nitwits.” Another error occurs when the conclusion is broader than the minor premise allows (illicit minor): “Politicians love power. All politicians are human beings. Therefore, all human beings love power.”

Considering the fabric of an argument.

Capital punishment is the source of many an argument, both good and bad. Following are some bad ones, all containing an irrelevant conclusion (ignoratio elenchi). In this one, the opponent is attacked instead of the premise of the debate (argumentum ad hominem): “Capital punishment is wrong because people who favor it tend to be less religious.” And in this one, the opponent is attacked by means of a countercharge (tu quoque): “Capital punishment is right because those who oppose it are more likely to be criminals themselves.”
Abortion is also the source of many bad arguments. The following contain irrelevant conclusions, too. This form uses an appeal to pity (argumentum ad misericordium): “Abortion is wrong; what have these innocent babies ever done to deserve such a cruel fate?” And this form uses an appeal to popular passion (argumentum ad populum): “Pro-choice is right; if your daughter became pregnant as the result of a rape, should she be forced to bear the child?” This form relies on an authority (argumentum ad verecundiam): “Abortion is wrong because my religion says so.”
One last form of irrelevant conclusion is used by just about everyone, so let’s look at an example that is hard to criticize. This form maintains that because a premise is not known to be untrue, it may indeed be true (argumentum ad ignorantium): “No one has ever disproved the existence of the Tooth Fairy. Therefore, it won’t hurt to put your grandfather’s previous set of false teeth under your pillow every night. After all, she may be easy to fool.”

Circular Arguments

Scientists and creationists are always at odds, of course. The following fallacy is called “vicious circle.” In it, the conclusion also appears as an assumption (circulus in probando): “The story of divine creation as related in Genesis must be true because God would not deceive us.” Another fallacious argument is called “begging the question.” The conclusion appears as an assumption, but in a different form (petitio principii): “Miracles cannot occur because they would defy the laws of nature.” (All those talk show hosts who say, “And that begs the question...” when they mean, “And that prompts the question...” are simply wrong.)

Errors of Principles

Evolution has long been the target of illogical arguments that use presumption (secundum quid). One is called “direct accident,” in which the truth of an abstract principle is applied to a specific circumstance: “The theory of evolution maintains that man evolved from apes. Thus, the apes in our wildlife preserves will someday be found reading the newspaper.” Wrong, right?! So is the one called “converse accident,” which is the reverse: “Because the apes in our wildlife preserves will never be found reading the newspaper, man did not evolve from apes.”

Contradiction, Diversion, and Superstition

In one fallacy, the argument declares that an assumption is false if a contradiction can be drawn from it (reductio ad absurdum): “Intelligent people have open minds. Politicians are supposed to be intelligent. But anyone who says that recreational drugs should not be legalized has a closed mind. Therefore, politicians are not intelligent people.” In another fallacy, the argument takes the form of a question phrased so that a direct reply (instead of a denial) supports the implications of the question (plurimum interrogationum): “How many family members have you put at risk with the handgun you bought for self-defense?” Yet another fallacy (“after this, therefore because of it”) is the source of much of the world’s superstition, a legacy from early times (post hoc, ergo propter hoc). Can you imagine the audience reaction if a speaker were to be struck by lightning while denouncing creationism from an outdoor podium? It would make news all over the world!

That just doesn’t follow!

And in the notorious fallacy of non sequitur, the conclusion doesn’t follow from the argument, as in this example: “Because fish have gills and birds have wings, because dinosaurs are extinct and snakes are not, because the duckbilled platypus and the spiny anteater have characteristics of both reptiles and mammals, because animals need the waste products of plant respiration to survive and plants need the waste products of animal respiration, because plenty of plants need insects for fertilization but earthworms don’t even need another earthworm, because dolphins are intelligent and whales can sing, because crustaceans look so much like big bugs and primates look so much like humans, and because nearly every meat on the planet doesn’t taste all that much different from chicken, the theory of evolution is correct.” That just doesn't follow!
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Postby Shade » Wed Jun 14, 2006 3:38 pm

Hi Marilyn, good to see you posting...This is very intresting, I often find people reason in these ways that are wrong, I think I've been known to do it too
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Re: Logical Fallacies

Postby stardust » Wed Jun 14, 2006 4:27 pm

Marilyn wrote:
Contradiction, Diversion, and Superstition

In one fallacy, the argument declares that an assumption is false if a contradiction can be drawn from it (reductio ad absurdum): “Intelligent people have open minds. Politicians are supposed to be intelligent. But anyone who says that recreational drugs should not be legalized has a closed mind. Therefore, politicians are not intelligent people.”


What's confusing about this is that reductio ad absurdum is a valid method of proving validity. The method is to show that if the conclusion is negated, and this negation can then be shown to be absurd (i.e., does not follow from the premises), it's reverse, the original conclusion, must be true. It's used all the time in deductive proofs, as you know.

It seems that your example mainly illustrates the concept of equivocation. Both the word "intelligent" and the phrase "open mind" are not exact concepts. They are subject to degrees, and hence, to interpretation. So, they will always be subject to contradiction because of this inability to precisely define them. It's not that reductio ad absurdum in itself is a fallacy; it's more that many arguments are fallacies due to the fact that their wording cannot be precisely defined. In other words, deductive proofs are valid with symbols and logical operators, but when you plug words into those symbols, you might end up with a fallacy untless you severely restrict the wording, and perhaps add qualifiers (new premises), to eliminate the confusion caused by the wording as opposed to the preciseness of symbols that you proved, using RAA, were valid in that argument form. Otherwise you accept the fact that most arguments are invalid in word form, as opposed to symbols, and then judge them on the basis of strength rather than validity. It seems the latter is the approach you are illustrating with this: just because an argument is invalid doesn't mean that it is not strong; or, just because an argument is proven valid using RAA in symbolic form doesn't mean that it will hold up in verbal form, and even though it does not hold up does not prove that it is invalid in symbolic form. The problem is with the language, not with the argument form.

Am I going down the wrong path on this? For example, you could also say intelligent people have closed minds (sometimes), or that everybody behaves irrationally (sometimes), or that males tend to act irrationally from teenage years to about age 25, and then they begin to act more rationally. Each of these use terms that can be equivocated. Therefore, the error in finding a contradiction is not due to RAA but due to equivocation in finding that contradiction.

I guess what bothers me about the example you gave regarding politicians is that if an argument has an exception, indeed it is invalid. Yet if an assumption is not clearly worded, then it will be true in the sense that it was intended, but not in the sense that the reader is who is responding to it (or, in your example, who is finding a contradiction to it). The reader is not creating a fallacy from RAA but a fallacy from equivocation. So, if he says the assumption is false because of RAA, he is wrong. It's only false because of equivocation. In other words, it is not disproved because he has not found a true contradiction, only an equivocation of terms.

Another way of looking at this is that the statement "intelligent people have open minds" does not say whether it is "some" or "all" intelligent people. So, I guess from that standpoint, if the original intention was "some", then finding a contradiction would not prove the original assumption to be false if the missing word were "some" and not "all". The assumption is not very clear. It's hard to say precisely what was meant by hte phrase, "Intelligent people have open minds." If I change the intended meaniing such that it is misrepresented and then attack the misrepresentation, isn't that a straw man fallacy?

There's another concept in logic that applies here as well, and that is, arguments are supposed to be interpreted in a way that is fair and charitable to the author of the argument. So, if the statement that intelligent people are open minded is to be interpreted as an element of an argument, it is to be interpreted not in a way that would make it false but in a way that would make it true. Otherwise, you are not being fair and charitable. So, when you consider whether intelligent people are open minded, you interpret the ambiguity in the best llight. If it is still untrue, then it may be incorrect or improperly worded, and you take the liberty of rewording it according to what you eliminate ambiguity and make it correct.

To be open minded about this RAA/equivocation question, it may be that Marilyn did not intend to say that RAA is one type of fallacy but that a contradiction does not prove an assumption untrue due to such a high likelihood of ambiguity. For even how she used the RAA example introduces some ambiguity, and perhaps that was her point to begin with: you have to keep an open mind.
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Postby stardust » Sat Jun 17, 2006 10:10 pm

I'm thinking of a different example today which perhaps is another way of saying what marilyn was pointing out but which is more obvious to me.

let's say an experiment is designed to test people's powers of observation and recall. they are told they will be asked to recall certain details of a particular house on a street after they have pass down that street. they won't be told which house it is until they pass down the street. when they get to the end of the block, they will be told which house it is, and then they will list everything they recall about that particular house. all observations will be compared against a list of observations of the house compiled by a group of experts known for their powers of observation.

say one million people pass down that street over the course of a week, and one of those people is a retarded 5 year old kid. each lists his or her observations, and many of them are very observant. some attain close to 100% recall compared to this master list. the 5 yr old kid remembers only one thing about that house: there was a speckle of red paint on one window.

a million people passed down that street. none of them observed a speckle of paint on that house except a retarded kid. even the experts didn't have that on the answer key.

the exception is the 5 yr old kid's observation. it turns out his observation was accurate. there was a speckle of paint on that window. does that mean all those people who took the test cannot possibly be geniuses? or the people who gathered the list of observations for the test cannot possibly be good scientists? the answer is no. the exception--that a retarded kid has made a unique observation--does not overturn the assumption--that there were many experts involved in this study.
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logic and consciousness

Postby LAURENCETOP » Sun Jun 18, 2006 3:38 pm

Dear Marilyn, I would like to send you some emails so we can have a one-on-one conversation about the content of them. Is this possible?

Laurence Topliffe

The emails will not be nonsense or harmful but quite interesting and will contain an argument that I believe you will not be able to refute and I will offer proof. Have you ever heard it said that Man is using only 5 or 10% of its mental potential? You may say this isn't true but I will send you proof that it's true and how to develop 100%, which essentially is our normal state. :D
Just a decent guy who likes to spread useful good knowledge and have intelligent conversations about important subjects such as peace and health and realizing our full human potential
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Postby Vosh » Mon Jun 19, 2006 2:05 am

Dear M,

Welcome to the internet. ;)
"A new scientific idea does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die and a new generation grows up that is familiar with it." -Max Planck
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Postby niles » Mon Jul 10, 2006 4:03 pm

As stardust noted above, reductio ad absurdum is not a logical fallacy. It is a valid method of logical proof, as I recall from the many high school and college mathematics courses in which it was taught. It is true that an assumption is false if a contradiction can be logically drawn from it.

The article seems to imply that the contradiction drawn in a reductio ad absurdum argument is the fallacy. The contradiction is not the fallacy. Instead the contradiction is an intermediate result that allows us to conclude that our initial assumption is false.

The example in the article does not actually illustrate reductio ad absurdum; it is instead one step away from a valid conclusion via reductio ad absurdum. It draws a contradiction and stops there instead of going on to conclude that the initial assumption is false.

Specifically, in the example given in the article, we start with the assumption that intelligent people have open minds and use that assumption to derive a contradiction: that politicians are not intelligent people, but politicians are supposed to be intelligent people. (More precisely, the arguments presented in the article lead to the conclusion that politicians opposed to legalizing recreational drugs are not intelligent, but people would generally agree that there are plenty of examples of intelligent politicians who oppose legalizing recreational drugs, so we have in fact drawn a contradiction from our assumption.)

To complete the reductio ad absurdum argument, we need to conclude that our initial assumption was false. Our initial assumption was that that intelligent people have open minds. We therefore conclude via reductio ad absurdum that we can negate our initial assumption. We conclude that not all intelligent people have open minds. There is no fallacy in this conclusion, nor in the reductio ad absurdum argument used to derive it.

In mathematics, for example, reductio ad absurdum provides an elegant way of proving that the square root of two is irrational. Assume that sqrt(2) is rational. Then there exist integers p and q, such that p/q = sqrt(2). Let us require that the fraction p/q is expressed in "lowest terms" so that p and q are not both even; if they were, we could divide each by two until we came upon p and q not both even. By squaring each side we have p*p = 2*q*q. Therefore p*p is even, and p must be even since even numbers have even squares, and odd numbers have odd squares. So p = 2*r where r is some other integer. Therefore we have 2*2*r*r = 2*q*q, or 2*r*r = q*q. This implies that q is even by the same argument. We have thus reached a contradiction, namely that p and q are both even, in contradiction of our requirement that p/q be in lowest terms. Therefore, we have shown that there cannot exist integers p and q such that p/q = sqrt(2).

The incorrect classification of reductio ad absurdum as a logical fallacy detracts from this otherwise fine and thought provoking article. I certainly learned quite a bit from it, and look forward to reading more like it.
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Regarding "Intelligent people have open minds."

Postby Lee » Wed Sep 13, 2006 8:50 am

I do not have an advanced degree in logic or philosophy, so please forgive the following question and explanations if I am missing something basic.

Regarding the statement, "Intelligent people have open minds," I see both assumption and equivocation. Assuming the statement is true, is this a statement of causation, correlation, or equation? As causation, the meaning could be, "Being intelligent causes people to have open minds." As correlation, this meaning could be, "Though intelligence and open mindedness are separate and distinct qualities, people that are intelligent are also open minded." As equation, the meaning could be, "At least part of the definition of intelligence is being open minded."

Regarding causation, the scientific method would demand more than observations and anecdotes to prove it to be true (i.e. not an assumption). The statement provided by Marilyn is an observation, therefore the logical analysis of the statement would never be sufficient. A Causation hypothesis must be proved by experimentation.

Regarding correlation, a test would also have to be devised to prove the correlation between intelligence and open-mindedness. From what I understand, the IQ test is the standard measure for intelligence. What is the standard measure for open mindedness? (aside: And is there a point where a person can be open-minded to a fault, thus making them play the role of the unintelligent?)

Regarding equation, there would have to be agreement that the definition of intelligence includes open-mindedness. In scientific terms, this is called establishing the classification system. Scientists do this so that equivocation can be minimized and communication becomes clear. Going back to the standard for measuring intelligence, the IQ test, are there really questions/problem statements in the IQ test that are designed to test open-mindedness?

Therefore, it seems to me that once it is established whether the statement is one of causation, correlation, or equation, then the proof of whether the assumption is true is always established by a complete followthrough of the scientific method. A scientific law (i.e. "the truth") can never be established by stopping short at a single observational statement or anecdote.

Remembering my geometry, logic seems to me to be a method of determining an answer to a question that is provided with initial conditions, the method using universal (natural) connections that have been proven by scientific method and described by agreed-to classification systems (conventions). (aside: By the way, this logical method also works in solving physics problems, though, in my experience, most physics instructors are ignorant of the approach, and thus have difficulty teaching physics students how to solve physics problems.)

Maybe I'm saying the same thing as all of you, but from a different perspective.
Einstein once thought he was wrong; then he discovered he was wrong.
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Two coins were flipped and at least one is a tail.

Postby Elmo » Tue May 08, 2007 3:27 pm

1.Two coins were flipped and at least one is a tail.

2. Marilyn thinks that the complement to that sentence is "Two coins were flipped and there were no tails."

3. Eldon says that the complement is "Two coins were flipped and at least one is a head."

4. Marilyn seems not willing to discuss Eldon's argument.
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Postby emilynghiem » Sun Sep 16, 2007 11:20 am

http://eagar.mit.edu/EagarPresentations ... logic.html

Here is another helpful link to various degrees and types of logical fallacies, including arguments based on generalizations and emotions.

In general, whenever I find contradictions in someone's logic or perception or rationale behind it, there is some degree of "projection" going on (1) either perceived bias from the past, a certain interpretation assigned to why something happened or what someone's motive is (2) unresolved thinking, behavior, or communication patterns repeating from past relations or generations that is seeking correction (3) a mutual separation from people with opposing views, so again the purpose is to seek correction.

For example, the arguments and defenses I run across most in trying to discuss the idea that "there is one God or universal truth" and how or to what degree people could "reconcile" the "relative" views or expressions of absolute truth seem to be a mix of (a) bifurcation, arguing either/or when the answer could be all of the above or none of the above as interpreted, which leaves the door open to change the interpretations to something univerally consistent (b) discrediting or attack the source of the perspective or its opposition, which tends to be a mutual trap, where parties either accept or reject each other (c) false analogy/faulty thesis, or defining a religion or God or whatever is opposed to be something "negative" or "false" and therefore proving it is wrong or does not exist, instead of seeking a universal, beneficial interpretation and defining the true God or religion to be THAT instead.

All these tend to come from "projections" of past perceptions, when in fact if there is one universal truth it must come from future interpretations where all these conflicts are resolved, and cannot be based on such past teachings that are clearly contradictory!

I find that when people choose to align their views or focus on values or meanings that are mutually respected and agreed to be positive and good, then the rest of the reconciliation can follow from there. But if people put up emotional defenses or mutual attacks, there is no end to the conflict that can result. I prefer correction, reconciliation and healing but there often needs to be mutual forgiveness and acceptance FIRST before the communication can take place in order to arrive at a reasonable conclusion that satisfies all standards by different parties on what is truth and what is God, and what is our purpose on the planet.

So the irony is that in order to receive a fuller perspective of these answers, one may need to let go of past perceptions or emotions that otherwise get in the way of that process. As long as people have faith that they can discern truth from falseness, I have found that that is enough to continue the path toward finding one truth, and there all the other answers can be found about the nature of God, religion and life.
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Re: Logical Fallacies

Postby larryhuey » Thu Oct 25, 2007 5:28 pm

[quote="Marilyn"]Logical Fallacies

Readers often ask about critical thinking and how to reason better. One of the best ways is to learn about logic, which is both fun and useful. Following are examples of the most common logical fallacies. You can use them as exercises to find the flaws in your own thinking.

In the article, Marilyn very informatively discusses some great tools to use to examine your own thinking. Logic, as defined by wikipedia, is the study of the principles and criteria of valid inference and demonstration. We should use logic to critique our own thoughts and ideas as suggested in Marilyn's post, and also, to review the arguments of others. When discussing an issue with someone, it is often much easier to respect the logic someone used to get to their conclusions, than it is to initially accept their conclusions. An intelligent conversationalist, no matter his opinion on the subject, will invariably listen to your arguments if your logic is sound.

Logic, however, is not the end of our training. Logic is but the second part of the classical trivium; that being, Grammer, Logic, Rhetoric.

Rhetoric takes the skills we learned in logic and manifests itself as the art of persuasion, a skill in itself. As we learn to think, critique and form substantive arguments, logic is of little value, if we have not the skills to persuade.
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Re: Logical Fallacies

Postby Bodhisattva » Wed Jan 09, 2008 6:05 pm

stardust wrote:
Marilyn wrote:
Contradiction, Diversion, and Superstition

In one fallacy, the argument declares that an assumption is false if a contradiction can be drawn from it (reductio ad absurdum): “Intelligent people have open minds. Politicians are supposed to be intelligent. But anyone who says that recreational drugs should not be legalized has a closed mind. Therefore, politicians are not intelligent people.”


What's confusing about this is that reductio ad absurdum is a valid method of proving validity. The method is to show that if the conclusion is negated, and this negation can then be shown to be absurd (i.e., does not follow from the premises), it's reverse, the original conclusion, must be true. It's used all the time in deductive proofs, as you know.



No. Marilyn is not saying that using a reductio ad absurdum to disprove an argument is wrong. It is clear that if an argument results in a contradiction in terms, it is wrong. However, a deductive argument uses many terms. For instance, in Marilyn's example:

Term 1: Intelligent prople have open minds

Term 2: Politicians are supposed to be intelligent

Term 3: Politicians believe recreational drugs should be illegal

Term 4: Anyone who believes recreational drugs should be illegal has a closed mind.

The reductio ad absurdum proves that some part of the argument is false. Assuming it proves term 2 false (concluding that politicians are not intelligent) is the fallacy. It could very well be that term 1 is false, or term 3 is, or term 4 is. Using the reductio ad absurdum proves an argument wrong, not one term in it. But then again... didn't she already mention this under "confusing parts with the whole?"
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Neutrality

Postby Sparx » Fri Jan 11, 2008 9:32 am

I am new here. My name is Mark (Sparx). I apologize in advance
if I have not read any of this forum but I have a job. I will be gone
this weekend on a Nice Guy Project.

There are 11 (at least) types of logic. I am a Mathematician.
There is a secret society of Mathematicians who dable in
axiomatic logic, philosophy, etc:

http://www.gallup.unm.edu/~smarandache/ ... ormats.htm

In the Philosophy section look at:

Neutrality and Many-Valued Logics, by A. Schumann, F. Smarandache

They outline 11 types of logic. It is appropriate for this site
which deals in logical fallacies. Which logical construct
do you refer to. Perhaps some (if not all) of this has been
discussed her. The paper provides a good mathematical
overview and is not Layman.


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Re: Two coins were flipped and at least one is a tail.

Postby Bodhisattva » Wed Jan 16, 2008 7:42 pm

Elmo wrote:1.Two coins were flipped and at least one is a tail.

2. Marilyn thinks that the complement to that sentence is "Two coins were flipped and there were no tails."

3. Eldon says that the complement is "Two coins were flipped and at least one is a head."

4. Marilyn seems not willing to discuss Eldon's argument.


Marilyn may not be willing to discuss, but I am.

If I'm not mistaken, the compliment of a statement is the reversal of the yes and no results in an algorithm. So make a a chart of the algorithm. The statement is "2 coins were flipped and at least one is a tail" if this is true you could have gotten:

HT
TT
TH

The rule for this set is "2 coins were flipped and at least one is a tail"

If you reverse the yes and no (the statement is false), you only could have gotten 2 heads. The rule for this set is "Two coins were flipped and there were no tails."
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The beginning of logic!

Postby cacao » Tue Mar 25, 2008 6:09 pm

Logic it self doesnt exist unless there is someone willing to use it and has the capacity to use it! The easy way to start studing logic is using the mind. First you have to build a concept where the logic can be used in a purpuse. Than with in that purpuse, use the logic to define the sequence of exact priorities. This by it self implies allready a fuzzy concept if thats the right way to call it.

Intermezzo- obviously there has to be a way of formulating the information-clusture.

This is a statement of truth with in the concept jet it can be formulated with out using the concept if you have a formal language such as math language. What I mean is a form of logic that doesnt interact in any way explicitly with the concept, but makes sence and can be formulated to make sence alone fused in to the concept with some type of variabl. The fuzzy is some where in between, but the variable changes! This may be also a way of understanding fluid intelligence.
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