# Fundamentals of Logic

## 142 posts in this topic

A conclusion is a statement which is (or has been) asserted as following from other statements (premises). It is thus impossible for an invalid argument to demonstrate a true conclusion. One could only say that the statement of the conclusion, considered by itself, and not as the conclusion of a particular argument, might be true.
Not only that, but to even say a conclusion might be true or might be false would require reference to some other knowledge. If a question were to consider a conclusion simply by itself, then (by definition) it would be an arbitrary claim.

And this is the reason why you are are mistaken. Inferences from premises to conclusion don't occur in a vacuum, unrelated to other knowledge that one possesses. Who has ever asserted that a conclusion should be considered by itself? No one but you. And yes, it would be arbitary to do so.

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I'll ask this question one last time to see who else agrees or disagrees with the following:
If an argument is invalid, the argument is properly dismissed.

When the argument is dismissed, one has two options in regards to the conclusion:

1 - reconnect the conclusion to reality by providing a different argument

2 - absent a different argument, dismiss the conclusion because it remains unsupported - ie it is arbitrary

3 - Look at the premises offered and the stated conclusion and look at reality to see if they correspond.

My basic focus is on what is true or false about reality, not what may or may not be a valid argument.

I am glad we agree on the method by which one would determine whether one should (1) reconnect the conclusion to reality or (2) dismiss it.

Are you suggesting that method actually provides another alternative besides the ones I have identified - ie an alternative other than supporting the conclusion differently or dismissing the conclusion? If so, I would be very eager to have you identify that other alternative.

I'm saying more. In addition to reality-checking the conclusion, one should also reality-check the premises. In so doing, one may discover facts that support the conclusion.

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We Objectivists are not skeptics who doubt all conclusions. We also hold that all ideas, even false ideas, have their ultimate origin in sense perception. Therefore, totally lacking any facts that contradict a given conclusion, it is very reasonable to assume that the conclusion is true.
"We Objectivists" do not believe that man is infallible. We hold that a man can be wrong about his inferences. That the claims which constitute his premises are (hopefully) ultimately based upon sense perception does not guarantee the validity of those inferences. Thus, by itself, the "lack of any facts that contradict" a given conclusion is not grounds to assume a conclusion is true.

Assuming a conclusion is true because it hasn't been contradicted is a logical fallacy. It is the argument ad ignorantium. It is the claim that X is true because you have not disproved X.

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I'm saying more. In addition to reality-checking the conclusion, one should also reality-check the premises. In so doing, one may discover facts that support the conclusion.
Please identify how you logically conclude that saying one can "reconnect the conclusion to reality by providing a different argument" includes ONLY "reality-checking the conclusion" and somehow excludes "reality-checking the premises".

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We Objectivists are not skeptics who doubt all conclusions. We also hold that all ideas, even false ideas, have their ultimate origin in sense perception. Therefore, totally lacking any facts that contradict a given conclusion, it is very reasonable to assume that the conclusion is true.
"We Objectivists" do not believe that man is infallible. We hold that a man can be wrong about his inferences.

True, but that is no reason to arbitrarily assume that he is wrong without evidence.

That the claims which constitute his premises are (hopefully) ultimately based upon sense perception does not guarantee the validity of those inferences. Thus, by itself, the "lack of any facts that contradict" a given conclusion is not grounds to assume a conclusion is true.

I'm not saying that it is. What may be grounds for assuming a conclusion is probably true, particularly when proposed by a member here on THE FORUM, is that most people mostly say reasonable things most of the time -- particularly here.

Assuming a conclusion is true because it hasn't been contradicted is a logical fallacy. It is the argument ad ignorantium. It is the claim that X is true because you have not disproved X.

That was not my argument. I did offer, originally and above, evidence for giving the conclusion some weight based on the above-mentioned evidence.

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I'm saying more. In addition to reality-checking the conclusion, one should also reality-check the premises. In so doing, one may discover facts that support the conclusion.
Please identify how you logically conclude that saying one can "reconnect the conclusion to reality by providing a different argument" includes ONLY "reality-checking the conclusion" and somehow excludes "reality-checking the premises".

If that is what you meant to say, fine.

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That the claims which constitute his premises are (hopefully) ultimately based upon sense perception does not guarantee the validity of those inferences. Thus, by itself, the "lack of any facts that contradict" a given conclusion is not grounds to assume a conclusion is true.
I'm not saying that it is.
That is what I got from this assertion:
Therefore, totally lacking any facts that contradict a given conclusion, it is very reasonable to assume that the conclusion is true.
We Objectivists are not skeptics who doubt all conclusions. We also hold that all ideas, even false ideas, have their ultimate origin in sense perception. Therefore, totally lacking any facts that contradict a given conclusion, it is very reasonable to assume that the conclusion is true.
"We Objectivists" do not believe that man is infallible. We hold that a man can be wrong about his inferences.
True, but that is no reason to arbitrarily assume that he is wrong without evidence.
Excellent. I am glad we agree that one should neither assume the falsehood or truth of a claim without evidence.
What may be grounds for assuming a conclusion is probably true, particularly when proposed by a member here on THE FORUM, is that most people mostly say reasonable things most of the time -- particularly here.
This is verecundiam.

A claim is not to be assumed true (to whatever degree) DESPITE the fact of a logical fallacy or false premise for that claim, simply because of the 'authority' of the person making the claim. Doing so is exactly what identifies such an appeal as fallacious rather than legitimate.

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A conclusion is a statement which is (or has been) asserted as following from other statements (premises).

No, a conclusion is -- or ought to be -- a statement about reality. In many cases, a 100% true and certain conclusion follows directly from sense perception without any preceding statements or premises at all.

Also, premises are -- or ought to be -- statements about reality as well. As such, they can and should be evaluated in terms of their correspondence to reality and not just by the way they may have been used in an argument.

I'm a little late getting back here, but I agree that all statements ought to be about reality. But as regards the conclusion of a syllogistic argument I would say the following:

If I present the argument:

A is B;

C is D;

Therefore A is A,

my premises do not conclude in "A is A"; that is, "A is A" is not the conclusion of the premises. The premises, as they stand, do not lead to any conclusion. We can conclude nothing from them. This is true whether or not the bare statement, by itself, or in other contexts, represents truth. When we say that a conclusion "does not follow" we are using "conclusion" to refer to the formal place of a statement in respect to other statements. But, since it does not follow, we in fact have no meaningful conclusion. Which means, of course, that a true statement (even one which is easy to comprehend) can be a meaningless conclusion of bad or wrong premises.

In

All A's are in B;

All B is in C;

Therefore, all A's are in C,

we have both kinds of conclusions: 1) the formal position of a statement in relation to other statements and 2) a statement which actually is a conclusion of the other statements.

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We Objectivists are not skeptics who doubt all conclusions. We also hold that all ideas, even false ideas, have their ultimate origin in sense perception. Therefore, totally lacking any facts that contradict a given conclusion, it is very reasonable to assume that the conclusion is true.
"We Objectivists" do not believe that man is infallible. We hold that a man can be wrong about his inferences. That the claims which constitute his premises are (hopefully) ultimately based upon sense perception does not guarantee the validity of those inferences. Thus, by itself, the "lack of any facts that contradict" a given conclusion is not grounds to assume a conclusion is true.

Assuming a conclusion is true because it hasn't been contradicted is a logical fallacy. It is the argument ad ignorantium. It is the claim that X is true because you have not disproved X.

That is not the argument from ignorance.

Appeal to Ignorance

The fallacy of appeal to ignorance comes in two forms: (1) Not knowing that a certain statement is true is taken to be a proof that it is false. (2) Not knowing that a statement is false is taken to be a proof that it is true.

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A conclusion is a statement which is (or has been) asserted as following from other statements (premises).

No, a conclusion is -- or ought to be -- a statement about reality. In many cases, a 100% true and certain conclusion follows directly from sense perception without any preceding statements or premises at all.

Also, premises are -- or ought to be -- statements about reality as well. As such, they can and should be evaluated in terms of their correspondence to reality and not just by the way they may have been used in an argument.

I'm a little late getting back here, but I agree that all statements ought to be about reality. But as regards the conclusion of a syllogistic argument I would say the following:

If I present the argument:

A is B;

C is D;

Therefore A is A,

my premises do not conclude in "A is A"; that is, "A is A" is not the conclusion of the premises. The premises, as they stand, do not lead to any conclusion. We can conclude nothing from them. This is true whether or not the bare statement, by itself, or in other contexts, represents truth.

First of all, these expressions are not the form typically used in logic examples, unless they are mathematical expressions. As such, there are many conclusions that can be drawn from each. From A is B, we can conclude that B is A; that A/2 + A/2 = B; etc. And the same for the other expressions. So there are literally thousands of mathematical conclusions.

When we say that a conclusion "does not follow" we are using "conclusion" to refer to the formal place of a statement in respect to other statements. But, since it does not follow, we in fact have no meaningful conclusion. Which means, of course, that a true statement (even one which is easy to comprehend) can be a meaningless conclusion of bad or wrong premises.

That is one way to view the meaning of conclusion. Another might be that it is the identification of the relationship that elements in two propositions have in common with another element. When an invalid inference is made, we have a factually true and meaningful proposition: the conclusion does not follow from the premises, i.e., the elements are not in the required relationship. This all requires factual identifications by a consciousness.

In

All A's are in B;

All B is in C;

Therefore, all A's are in C,

we have both kinds of conclusions: 1) the formal position of a statement in relation to other statements and 2) a statement which actually is a conclusion of the other statements.

But it is not the relationship between statements that yields the conclusion. It is the factual relationships among the elements in the propositions in the premises that yields the conclusion.

The above is why

All dogs are bones;

All bones are cats;

Therefore all dogs are cats

is meaningless nonsense.

Yet

All men are mortal;

Socrates is a man;

Therefore Socrates is mortal

is meaningful.

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What may be grounds for assuming a conclusion is probably true, particularly when proposed by a member here on THE FORUM, is that most people mostly say reasonable things most of the time -- particularly here.

This is verecundiam.

No, it is an observable fact. Most of the members of THE FORUM are sharp people who are right about things much more than they are wrong.

Giving weight to that observable fact is no more an appeal to authority than the observation that Ayn Rand was right about all the basic issues of philosophy she wrote about and, that if she said something about an fundamental or abstract issue, she was probably right.

A claim is not to be assumed true (to whatever degree) DESPITE the fact of a logical fallacy or false premise for that claim, simply because of the 'authority' of the person making the claim. Doing so is exactly what identifies such an appeal as fallacious rather than legitimate.

But one cannot just claim there is a logical fallacy or false premise without evidence and then demand that someone disprove it. The proper presumption, based on evidence, is that people around here know what they are talking about, yet anyone who has evidence to the contrary can present that evidence in a manner appropriate to the context.

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A claim is not to be assumed true (to whatever degree) DESPITE the fact of a logical fallacy or false premise for that claim, simply because of the 'authority' of the person making the claim. Doing so is exactly what identifies such an appeal as fallacious rather than legitimate.
But one cannot just claim there is a logical fallacy or false premise without evidence and then demand that someone disprove it.
WHERE has that been the context of ANY discussion here?

Most of the statements here have been made in the context of 'finding a logical fallacy or false premise' in an argument. And if you want to trace back the context of this particular thread of the discussion, it was an individual who makes a claim but can't identify for anyone his reasons for his support. And in that case, one certainly doesn't 'assume' their conclusion is true absent any evidence except that they are members of the forum. That TOO is verecundiam.

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And if you want to trace back the context of this particular thread of the discussion, it was an individual who makes a claim but can't identify for anyone his reasons for his support. And in that case, one certainly doesn't 'assume' their conclusion is true absent any evidence except that they are members of the forum. That TOO is verecundiam.

If you want to include the reason for the example, it was to show why it may not be helpful to stop at discrediting someone's reasons for supporting an argument, and why you shouldn't dismiss the conclusion just because they can't support it. Take for example a misguided but implicitly rational conservative who accepts altruism explicitly but selfishness implicitly. He is an advocate of Capitalism and believes in a government limited to protecting the rights of its citizens. His reasons he would give for advocating Capitalism would likely be invalid. However showing him that his argument was bad and stopping there would only serve to turn him away from Capitalism (which is, in fact, the best system).

Now say you're not an Objectivist, you don't know that Capitalism is right, but you are honest and rational. So, you don't know that the conclusion is true. Do you see why it's important not to dismiss the conclusion when the argument is bad, and that by dismissing it you might actually be dismissing good values to your life? It's true you should not accept the conclusion as valid, but neither should you discard it as arbitrary. In fact, until the conclusion has been proven false (which is different than a fallacious argument), the debate should remain open.

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Take for example a misguided but implicitly rational conservative who accepts altruism explicitly but selfishness implicitly.

Capitalism and altruism cannot co-exist in the same individual because they are philosophic opposites. Its either/or. Finally, conservatives are not advocates for Capitalism. So the confused individual you describe, if he exists, is nothing other than an altruist.

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Capitalism and altruism cannot co-exist in the same individual because they are philosophic opposites. Its either/or. Finally, conservatives are not advocates for Capitalism. So the confused individual you describe, if he exists, is nothing other than an altruist.

It's certainly possible for someone to be conflicted and hold contradictory ideas, including being implictly selfish while explicitly holding altruistic ideals. It happens all the time. If it was either-or, then everyone who was not an Objectivist would be a destroyer.

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Take for example a misguided but implicitly rational conservative who accepts altruism explicitly but selfishness implicitly.

Capitalism and altruism cannot co-exist in the same individual because they are philosophic opposites. Its either/or. Finally, conservatives are not advocates for Capitalism. So the confused individual you describe, if he exists, is nothing other than an altruist.

This argument is fallacious: non-sequitor. Ethical and political systems are not properties of individuals. Individuals may advocate systems that are incompatible.

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Take for example a misguided but implicitly rational conservative who accepts altruism explicitly but selfishness implicitly.

Capitalism and altruism cannot co-exist in the same individual because they are philosophic opposites. Its either/or. Finally, conservatives are not advocates for Capitalism. So the confused individual you describe, if he exists, is nothing other than an altruist.

Extending your argument, faith and reason also cannot coexist within the same individual.

That's why historically all successful Scientists like Newton were atheists and not religious...

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And if you want to trace back the context of this particular thread of the discussion, it was an individual who makes a claim but can't identify for anyone his reasons for his support. And in that case, one certainly doesn't 'assume' their conclusion is true absent any evidence except that they are members of the forum. That TOO is verecundiam.

If you want to include the reason for the example, it was to show why it may not be helpful to stop at discrediting someone's reasons for supporting an argument, and why you shouldn't dismiss the conclusion just because they can't support it. Take for example a misguided but implicitly rational conservative who accepts altruism explicitly but selfishness implicitly. He is an advocate of Capitalism and believes in a government limited to protecting the rights of its citizens. His reasons he would give for advocating Capitalism would likely be invalid. However showing him that his argument was bad and stopping there would only serve to turn him away from Capitalism (which is, in fact, the best system).

Now say you're not an Objectivist, you don't know that Capitalism is right, but you are honest and rational. So, you don't know that the conclusion is true. Do you see why it's important not to dismiss the conclusion when the argument is bad, and that by dismissing it you might actually be dismissing good values to your life? It's true you should not accept the conclusion as valid, but neither should you discard it as arbitrary. In fact, until the conclusion has been proven false (which is different than a fallacious argument), the debate should remain open.

Why is it assumed that showing a supporter of Capitalism (or _any_ idea) that his argument is bad will cause him to turn away from Capitalism?

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Take for example a misguided but implicitly rational conservative who accepts altruism explicitly but selfishness implicitly.

Capitalism and altruism cannot co-exist in the same individual because they are philosophic opposites. Its either/or. Finally, conservatives are not advocates for Capitalism. So the confused individual you describe, if he exists, is nothing other than an altruist.

This argument is fallacious: non-sequitor. Ethical and political systems are not properties of individuals. Individuals may advocate systems that are incompatible.

This is getting off topic. I have no further comments on this issue, but I will provide a quote from Ayn Rand that may point you in the right direction and may help clear up some of the confusion that is now running rampant in this thread.

From "Conservatism: An Obituary", by Ayn Rand

Yet capitalism is what the "conservatives" dare not advocate or defend. They are paralyzed by the profound conflict between capitalism and the moral code which dominates our culture: the morality of altruism...Capitalism and altruism are incompatible; they are philosophical opposites; they cannot co-exist in the same man or in the same society.

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A conclusion is a statement which is (or has been) asserted as following from other statements (premises).

No, a conclusion is -- or ought to be -- a statement about reality. In many cases, a 100% true and certain conclusion follows directly from sense perception without any preceding statements or premises at all.

Also, premises are -- or ought to be -- statements about reality as well. As such, they can and should be evaluated in terms of their correspondence to reality and not just by the way they may have been used in an argument.

I'm a little late getting back here, but I agree that all statements ought to be about reality. But as regards the conclusion of a syllogistic argument I would say the following:

If I present the argument:

A is B;

C is D;

Therefore A is A,

my premises do not conclude in "A is A"; that is, "A is A" is not the conclusion of the premises. The premises, as they stand, do not lead to any conclusion. We can conclude nothing from them. This is true whether or not the bare statement, by itself, or in other contexts, represents truth.

First of all, these expressions are not the form typically used in logic examples, unless they are mathematical expressions. As such, there are many conclusions that can be drawn from each. From A is B, we can conclude that B is A; that A/2 + A/2 = B; etc. And the same for the other expressions. So there are literally thousands of mathematical conclusions.

When we say that a conclusion "does not follow" we are using "conclusion" to refer to the formal place of a statement in respect to other statements. But, since it does not follow, we in fact have no meaningful conclusion. Which means, of course, that a true statement (even one which is easy to comprehend) can be a meaningless conclusion of bad or wrong premises.

That is one way to view the meaning of conclusion. Another might be that it is the identification of the relationship that elements in two propositions have in common with another element. When an invalid inference is made, we have a factually true and meaningful proposition: the conclusion does not follow from the premises, i.e., the elements are not in the required relationship. This all requires factual identifications by a consciousness.

In

All A's are in B;

All B is in C;

Therefore, all A's are in C,

we have both kinds of conclusions: 1) the formal position of a statement in relation to other statements and 2) a statement which actually is a conclusion of the other statements.

But it is not the relationship between statements that yields the conclusion. It is the factual relationships among the elements in the propositions in the premises that yields the conclusion.

The above is why

All dogs are bones;

All bones are cats;

Therefore all dogs are cats

is meaningless nonsense.

Yet

All men are mortal;

Socrates is a man;

Therefore Socrates is mortal

is meaningful.

Paul, I see what you're saying, but, in the argument:

Some men are mortal;

Socrates is a man;

Because of this, Socrates is mortal,

"Socrates is mortal" is the formal conclusion; it is meaningful in that it refers to reality and that it is an attempt at deduction from the premises. But, given the premises, it is not the conclusion. The conclusion is "Socrates might be mortal".

While in the argument:

Gods are mortal;

Socrates is a god;

Because of this, Socrates is mortal,

"Socrates is mortal" is the formal conclusion; it is meaningful in that it refers to reality and is a valid deduction from the premises. But, since the premises are total nonsense, the conclusion is nonsense, too (nonsense only in the context of this syllogism). That is, the whole argument is nonsense. This is easier seen in the argument:

Balloons are mortal;

Socrates is a balloon;

Because of this, Socrates is mortal.-----This is nonsense, the whole thing is nonsense. To say that the premises of an argument are nonsense, but that the conclusion makes sense, makes no sense to me.

Premises not tied to reality make no sense to me;

These premises are not tied to reality;

Because of this, the conclusion of these premises makes sense to me.---this does not make sense either.

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Why is it assumed that showing a supporter of Capitalism (or _any_ idea) that his argument is bad will cause him to turn away from Capitalism?

If a person's explicit morality is altruism and you convincingly demonstrate that Capitalism - which they previously supported - is incompatible with that morality, they will have to reject either the morality or the political system. In our culture, they would sooner reject Capitalism. In fact, I think that's the reason so-called conservatives have moved from advocating limited government to supporting many of the same social programs first instituted by the left.

However, for some individuals their case for Capitalism may not actually be based on the presented argument, but on certain rational ideas they formed implicitly - such as life as the standard of morality and reason as man's faculty of knowledge. These ideas of course conflict with their stated ethical system. It's those implicit rational ideas we should be appealing to and expounding on, rather than focussing on debunking invalid arguments.

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From "Conservatism: An Obituary", by Ayn Rand

Yet capitalism is what the "conservatives" dare not advocate or defend. They are paralyzed by the profound conflict between capitalism and the moral code which dominates our culture: the morality of altruism...Capitalism and altruism are incompatible; they are philosophical opposites; they cannot co-exist in the same man or in the same society.

In my judgment, Rick, you have misunderstood this quote. "Philosophic opposites...cannot coexist" means you cannot practice both, one must win over the other. That does not mean that people cannot be inconsistent and hold contradictory ideas, as most people do. It doesn't mean you can't perform an action which is pro-man one minute, and anti-man the next, which is commonplace (buying groceries vs. going to Church). To say that people cannot accept ideas that contradict each other puts you in the position of claiming that everyone is 100% integrated and consistent. Or dead.

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Why is it assumed that showing a supporter of Capitalism (or _any_ idea) that his argument is bad will cause him to turn away from Capitalism?

If a person's explicit morality is altruism and you convincingly demonstrate that Capitalism - which they previously supported - is incompatible with that morality, they will have to reject either the morality or the political system. In our culture, they would sooner reject Capitalism. In fact, I think that's the reason so-called conservatives have moved from advocating limited government to supporting many of the same social programs first instituted by the left.

However, for some individuals their case for Capitalism may not actually be based on the presented argument, but on certain rational ideas they formed implicitly - such as life as the standard of morality and reason as man's faculty of knowledge. These ideas of course conflict with their stated ethical system. It's those implicit rational ideas we should be appealing to and expounding on, rather than focussing on debunking invalid arguments.

This last paragraph might apply to a situation where Joe, say, is the only Objectivist in Don's life, but does it apply to The Forum? And as to motivation, are you saying that the main motive of every poster should be the rational growth of every poster he responds to?

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This last paragraph might apply to a situation where Joe, say, is the only Objectivist in Don's life, but does it apply to The Forum? And as to motivation, are you saying that the main motive of every poster should be the rational growth of every poster he responds to?

No, of course not, the main motive should be sharing your values.

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...it was to show why it may not be helpful to stop at discrediting someone's reasons for supporting an argument...
Then it was a good thing that was never the suggestion and is in fact the opposite of explicitly made statements. However, for reasons of time, interest, or even knowledge (you too may not know that X is true or false) etc, it is certainly quite a legitimate thing to do. It is not your responsibility to think for another person. You are identifying that he needs to check his premises (that is what both a false premise and invalid logic shows one must do). Or, in this specific example, you are showing he needs to identify his premises and their connection to his conclusion - or he must dismiss them.

I am sorry if it is your position that is not 'helpful'.

Now say you're not an Objectivist, you don't know that Capitalism is right, but you are honest and rational. So, you don't know that the conclusion is true. Do you see why it's important not to dismiss the conclusion when the argument is bad, and that by dismissing it you might actually be dismissing good values to your life?
As I have already stated, I do not accept things on faith (nor do I encourage others to accept things on faith). I do this precisely BECAUSE I am honest and rational.

As has been stated multiple times, the requirements of reason are that a person either needs to connect the conclusion to reality - or - dismiss it. Doing something else takes the person out of the realm of reason. The argument from ignorance which you provide (don't dismiss the conclusion because X might be good - you haven't proven its not) for doing something other than those two things does not somehow make it rational.

Do not accept ANYTHING on faith - not even Ayn Rand.