# Fundamentals of Logic

## 142 posts in this topic

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

So far, it seems I'll only be able to address my response to the three questions to B.Royce.

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(As to the issue of 'certainty', since you didn't specify the degree to which the 'belief' was accepted, neither did I. In other words, I was simply following your example of non-qualification.)
Addendum: Note, however, I consistently used the term 'think' rather than the term 'know' in my statements - as in 'I think the conclusion is true' - rather than 'I know the conclusion is true'. The latter expresses certainty. The former does not specifically identify a degree.

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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

So far, it seems I'll only be able to address my response to the three questions to B.Royce.

I am also in agreement.

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What I am saying in addition is: if neither of you can present arguments to support that conclusion (or refute it), then neither of you have a basis for continuing to consider the conclusion. In that case, the conclusion must therefore be dismissed. Otherwise you are accepting the conclusion arbitrarily.

Does that sound rational to you?

Just because one cannot always identify an explicit basis for a conclusion doesn't justify considering it's acceptance arbitrary.
I see. Your position is that an assertion for which one cannot provide support is not arbitrary.
A hundred life experiences that you are not aware of may lead you to a correct conclusion
'I am not "aware" of why, but it is right' is an explicitly arbitrary assertion. It is the opposite of rational.

At this point there is no logical basis on which we can have a rational discussion.

It is not arbitrary, because it is based on experience he does not consciously identify. He just can't put into words why he thinks something is wrong with the position he disagrees with.

You can't seem to grasp that you may win the argument with this person, but that doesn't mean you are right. It only means his argument is deficient for his conclusion, not that he has no basis for that conclusion. As has been pointed out to you, children reach correct conclusions by induction, not logical deduction. This is not to dispute the importance of logic in reaching correct conclusions; it is to say that explicit logic is not the only way to reach correct conclusions. You look to reality for that.

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A hundred life experiences that you are not aware of may lead you to a correct conclusion
'I am not "aware" of why, but it is right' is an explicitly arbitrary assertion. It is the opposite of rational.

At this point there is no logical basis on which we can have a rational discussion.

Brian, again, you are failing to make another distinction: between cognitive arbitrary, and arbitrary in a conversation. An excellent example has been given of a little kid who has not verbalized their internals, but which doesn't mean everything they express or believe is arbitrary! Merely just because they cannot pass the muster of your philosophical scrutiny! One may dismiss some of their conclusions as arbitrary based on private experience ("no person could reach this conclusion rationally"); but also may validly accept some other conclusions, based on inductive experience with the rationality of this person, etc ("they never can verbalize their reasoning process, but at every step their premises and conclusions accorded with facts").

To claim that only explicitness of an expression is the only and last arbiter of anything you will consider, is preposterous.

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If someone makes a claim and his argument (his stated reasoning) is invalid - and he cannot provide another argument for his claim - then the claim is arbitrary. --------------

Denying the antecedent

http://forums.4aynrandfans.com/index.php?s...ost&p=64977']If the premises are true and the argument is valid, the conclusion is true.

The argument is not valid,

Therefore the conclusion is not true.

Can anyone differentiate Brian's statement from Denying the Antecedent?

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I "don't know how" I came to this conclusion, but I think it is true" is "based in observation". I "don't know how" I came to this conclusion, but I think it is true" is not "a sheer assertion with no attempt to validate or connect it to reality."

For clarity's sake, do you understand what I mean when I say "implicit belief"? It is to say, an unstated belief, and specifically in this discussion a belief that was formed automatically and one you are not consciously aware of. However, once that belief comes under conscious introspection, you are faced with a choice to accept it or to reject it. If you accept it, this is a conscious and explicit choice. At that point it is no longer implicit. So I am not talking about beliefs that people choose to accept even though they have no evidence for them, I am talking about beliefs people accept by default without being aware of it.

Unless the individual is just making noise or scribbles and not actually asserting a conclusion, this claim makes no sense. It especially makes no sense in the context where you keep talking about people's 'beliefs' which they cannot support. A belief is an idea one accepts as true. A belief one doesn't know why they accept is arbitrary.

This relates back to implicit vs. explicit beliefs.

(As to the issue of 'certainty', since you didn't specify the degree to which the 'belief' was accepted, neither did I. In other words, I was simply following your example of non-qualification.)

I think the topic of certainty might overcomplicate the issue, so I'll drop it.

don't do mind reading, so I have to go by what comes out of peoples' 'mouths' (especially in the context of forums or the like). If you are indeed using a different standard than that, then we have no basis for rational discussion.

Exactly. You cannot know someone's implicit beliefs, so you cannot say whether they are arbitrary or not.

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If someone makes a claim and his argument (his stated reasoning) is invalid - and he cannot provide another argument for his claim - then the claim is arbitrary. --------------

Denying the antecedent

http://forums.4aynrandfans.com/index.php?s...ost&p=64977']If the premises are true and the argument is valid, the conclusion is true.

The argument is not valid,

Therefore the conclusion is not true.

Can anyone differentiate Brian's statement from Denying the Antecedent?

The only difference is that in Brian's statement that you quote, he uses the word "arbitrary" where it should be "false". Again to quote Dr. Peikoff on the arbitrary:

"Arbitrary" means a claim put forth in the absence of evidence of any sort, perceptual or conceptual; its basis is neither direct observation nor any kind of theoretical argument. [An arbitrary idea is] a sheer assertion with no attempt to validate it or connect it to reality.

The false, on the other hand is "an attempt to...connect to reality", it's just a failed attempt. An arbitrary claim should be dismissed, whereas a false claim can actually be corrected and lead to new knowledge.

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For those who have grasped my arguments about the 'arbitrary' etc, I have now posted my rebuttal to the 'three questions' issue HERE.

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If someone makes a claim and his argument (his stated reasoning) is invalid - and he cannot provide another argument for his claim - then the claim is arbitrary. --------------

Denying the antecedent

http://forums.4aynrandfans.com/index.php?s...ost&p=64977']If the premises are true and the argument is valid, the conclusion is true.

The argument is not valid,

Therefore the conclusion is not true.

Can anyone differentiate Brian's statement from Denying the Antecedent?

The only difference is that in Brian's statement that you quote, he uses the word "arbitrary" where it should be "false". Again to quote Dr. Peikoff on the arbitrary:

"Arbitrary" means a claim put forth in the absence of evidence of any sort, perceptual or conceptual; its basis is neither direct observation nor any kind of theoretical argument. [An arbitrary idea is] a sheer assertion with no attempt to validate it or connect it to reality.

The false, on the other hand is "an attempt to...connect to reality", it's just a failed attempt. An arbitrary claim should be dismissed, whereas a false claim can actually be corrected and lead to new knowledge.

Fallacies pertain to the structure of the argument, not to the specific words. So I'll take your answer to mean that there is no logical difference.

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

So it is a matter of semantics?

Quote provided is taken from the wikipedia site provided.

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

(Bold is mine.)

A category error is semantic in the sense that it applies to language. It is about the way we apply certain adjectives to certain nouns. It is not, however, merely semantic. It has an ontological -- i.e., reality -- basis as well.

In reality, certain adjectives (characteristics) cannot apply to certain nouns (entities). It is a category error to speak of a "hungry equation."

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

This is confusing categories again.

"True" and "false" are categories pertaining to the correspondence of an idea with reality.

"Arbitrary" and "non-arbitrary" are categories pertaining to the amount of evidence supporting a conclusion.

"Valid" and "invalid" are categories pertaining to whether a process produces the intended result.

"Valid" and "invalid" are properly applied to the concept "argument." A valid argument, given true premises, always results in a true conclusion. An invalid argument may or may not. The argument may result in a conclusion that corresponds to reality, but the argument itself is valid or invalid, not corresponding or non-corresponding.

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I agree that an invalid argument proves nothing about the conclusion one way or the other - ie it proves neither the conclusion's truth nor it's falsehood. An invalid argument is properly rejected. It is dismissed. As such, it cannot say anything about a conclusion at all.

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

One cannot assume that a conclusion is unsupported simply because an argument offered on its behalf may be invalid or even that some premises offered in support may be false. The entire context , including facts known to me but not stated or known by others, is what matters.

The conclusion might be demonstrably true despite any invalid arguments made on its behalf. If ten facts are presented in support of a conclusion and one of them is false, the conclusion might be well-supported by the other nine facts.

Sad to say, invalid arguments are made for true conclusions all the time. For instance, I am not going to stop advocating capitalism or consider it arbitrary because of all the libertarians who make factually wrong or logically invalid arguments on behalf of capitalism. Instead, if I care to, I will simply present truer facts or a more valid argument.

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Premises and conclusions, because they are about reality can possibly fail to correspond with, or contradict, something else in reality. Arguments, because they are a method of consciousness, do not themselves correspond with or contradict reality.
Not true. The argument - the relation between the premises' and conclusion - can either correspond or contradict one fact of reality - Identity - AisA.

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The entire context , including facts known to me but not stated or known by others, is what matters.
I can't read your mind. I can only go by your arguments. If your argument is found to be invalid, then - in the context of my knowledge - your conclusion is unsupported until you present another argument (or until I provide one). What thoughts you might or might not have which you think may or may not support the argument cannot be identified by me as supporting your argument until they are actually communicated. Until that time, I can only consider what has been communicated. But at that time I can and do consider any new argument.
The conclusion might be demonstrably true despite any invalid arguments made on its behalf.
This is not in dispute. My only point is that they do have to be demonstrated - ie the argument actually has to be made.
Sad to say, invalid arguments are made for true conclusions all the time.
Again, that fact is not at all in dispute

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This is confusing categories again.
While I disagree with your categorization, I believe you mistook the meaning of my statement because it should not be a violation of even your categories. The intent was simply to identify that the terms valid and invalid are being applied to 'argument' - and that such application is not done on the basis of whim.

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I agree that an invalid argument proves nothing about the conclusion one way or the other - ie it proves neither the conclusion's truth nor it's falsehood. An invalid argument is properly rejected. It is dismissed. As such, it cannot say anything about a conclusion at all.

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

One cannot assume that a conclusion is unsupported simply because an argument offered on its behalf may be invalid or even that some premises offered in support may be false. The entire context , including facts known to me but not stated or known by others, is what matters.

The conclusion might be demonstrably true despite any invalid arguments made on its behalf. If ten facts are presented in support of a conclusion and one of them is false, the conclusion might be well-supported by the other nine facts.

Sad to say, invalid arguments are made for true conclusions all the time. For instance, I am not going to stop advocating capitalism or consider it arbitrary because of all the libertarians who make factually wrong or logically invalid arguments on behalf of capitalism. Instead, if I care to, I will simply present truer facts or a more valid argument.

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.

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

Sad to say, invalid arguments are made for true conclusions all the time. For instance, I am not going to stop advocating capitalism or consider it arbitrary because of all the libertarians who make factually wrong or logically invalid arguments on behalf of capitalism. Instead, if I care to, I will simply present truer facts or a more valid argument.

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.

No one has maintained that an invalid argument demonstrates a true conclusion. What has been stated is that invalid arguments have been given for conclusions that are, in fact, true.

Example: The sky is blue. Why? Because god made it that way. Are you going to deny that the sky is blue because an invalid argument was made to support it? You would simply say that the argument is invalid. The truth of the conclusion can be demonstrated by direct observation, no matter whether the argument is valid or not. No one (except possibly Brian who has explicitly stated he judges truth based only upon the argument) drops the entire context of his knowledge when judging the truth of a conclusion.

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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

I've been away and I'm a little late in catching up, but here's my answer:

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.

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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.

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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.

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You miss the point. In that instance, whatever the conclusion might be is immaterial. If the person states he 'doesn't know how' he came to his conclusion, that is an explicit admission that his conclusion is arbitrary. He is explicitly stating "I can't support my conclusion". It is exactly his lack of support which makes his conclusion arbitrary

If someone made an argument based on some factual claim (his premises), I don't see how this can be arbitrary.

His premises may be false or his argument may be invalid, but he did not present his conclusion without evidence or argument, which is the definition of "arbitrary."

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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.

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If for some reason they are not able to identify an abstraction formed on "auto-pilot" by their own automized processes, but that abstraction was correctly formed...
You presume that which is trying to be proven - ie that their conclusion is correct.

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.

If one does have facts that contradict the conclusion, that's where the focus should be and not on the argument alone.

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You miss the point. In that instance, whatever the conclusion might be is immaterial. If the person states he 'doesn't know how' he came to his conclusion, that is an explicit admission that his conclusion is arbitrary. He is explicitly stating "I can't support my conclusion". It is exactly his lack of support which makes his conclusion arbitrary
If someone made an argument based on some factual claim (his premises), I don't see how this can be arbitrary.
In the example you quote, not only does the person not present any argument (ie he presents no premises), but he also explicitly states he himself doesn't even know what his premises are for that conclusion.

As such, when you claim "his argument may be invalid, but he did not present his conclusion without evidence or argument" I have no idea what example you might be referencing. I can only say it is not the one given here.