More about Two Logical Virtues The First Logical Virtue: True Reasons
The Second Logical Virtue: Properly Related Evaluation and Validity
What does it take for an argument to be a logically good one? Let's approach this by first looking at arguments that aren't so good.
Example A: Kentucky is north of Indiana, and Indiana is north of Michigan. Thus Kentucky is north of Michigan.
This is a bad argument, but it's not all bad. The problem is with the two reasons. The reasons aren't true! But imagine someone who doesn't know much geography and is not worried about the truth of the two reasons. Such a person would think this argument is just fine. If one place is north of a second place, and the second is north of a third, then the first place just has to be north of the third one. It's perfectly logical, in the sense that the reasons are properly related to the conclusion.
Now let's change the two false reasons into true reasons, so that we have a different argument. This new argument does not have the problem of untrue reasons! It ought to be a better argument.
Example B: Kentucky is south of Indiana, and Indiana is south of Michigan. Thus Kentucky is north of Michigan.
Is it better? Well, yes and no. It now has true reasons, and that is an improvement. But something else is wrong. It doesn't seem to be logical at all! The conclusion has "north" where it should have "south"! The new problem is that the reasons are not properly related to the conclusion. You don't have to know where Kentucky really is to see that.
The main point illustrated by examples A and B is that there are two
logical requirements that a good argument must meet.
The Two Essential Logical Virtues for a Good Argument
1. The reason(s) must be true.
2. The reasons must be properly related to the conclusion.
These two virtues or requirements are independent of one another: either one can be met without the other being met. A really good argument should possess both virtues. So when you try to judge how good an argument is, there are two very different questions you should ask about it: Are the reasons true? Are the reasons properly related to the conclusion?
The third - the practical - virtue needed for a good argument is discussed
in another
section of these web pages.
More about these Two Logical Virtues
Evaluate this argument according to the two virtues; does it have one, both, or neither of them?
Example C: Madagascar is north of the Styx River, because Curacao is north of the Styx River and Curacao is south of Madagascar.
Are the reasons true? Are the reasons properly related to the conclusion? (Hint: Try drawing a little map.)
My guess is that you don't know whether the reasons are true, and you're too lazy to go find out!! But to see whether the reasons are properly related to the conclusion, all you have to do is think for a few seconds -- and maybe draw a quick diagram. It should be clear that they are, that if you start off with those two reasons then they will very logically lead you straight to the conclusion that Madagascar is north of the Styx River.
Example C suggests some interesting points. If you don't already know whether the reason(s) of an argument are true, it may take some research to find out. Even after looking around in encyclopedias and so on, you still may not be sure. It may be hard to find out whether the reasons are really true. But it isn't hard to understand what the reasons-must-be-true requirement means.
On the other hand, the reasons-properly-related-to-conclusion requirement doesn't call for any research -- all you have to do is think carefully about the reasons and conclusion. But probably you aren't very sure about what a "proper" relationship between reasons and conclusion really means. I certainly haven't told you much about it yet! I've just assumed that you can more or less see that in examples A and C the reasons really do lead you straight to the conclusion, and in example B they don't.
These two virtues of a good argument are much like the wheels of a bicycle (or motorcycle). For a bicycle to serve as a good means of transportation, which wheel is it more important to have working: the front or the rear wheel? The answer is that they are equally important. If either wheel doesn't work, you can't go anywhere on the bicycle. But if you want to understand how a bicycle works (or if you are interested in maintaining a motorcycle), it turns out that the rear wheel is a good bit more complicated than the front one. It's harder to understand how it works because the rear wheel is where the gears and sprockets and so forth are located. The two wheels are equally important, but the rear wheel is more complicated and harder to understand.
For a logically good argument, the truth-of-reasons requirement and the properly-related-to-conclusion requirement are equally important; but the properly-related requirement is more complicated and is harder to understand. That's why in this logic part of the course, as in most logic courses, much more attention will be given to the properly-related requirement. Not because it is more important, but because it is more complicated and harder to understand.
The main purpose of an argument is to prove that its conclusion is true. If you know -- or think you know -- that one or more of an argument's reasons are just plain false, then the argument will not succeed in proving to you that the conclusion is true, even if the reasons are properly related to the conclusion -- as in example A above. And if you do know -- or think you know -- that the reasons are true, but you can see that they aren't properly related to the conclusion, then the argument will again fail to prove to you that the conclusion is true. Example B above is like this.
Once more: a logically good argument should meet both requirements -- should
have both these logical virtues! (But we're going to focus mostly on the second
one, because it's harder to understand.)
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THE TRUTH-OF-REASONS VIRTUE (OR, REQUIREMENT)
For an argument to be good, its reason(s) must be true. This requirement is an ideal, and like most ideals it is more often approximated than fully achieved. Occasionally you may already have enough knowledge to judge confidently whether the reasons of an argument are true. Sometimes you will be pretty sure but not completely sure about their truth or falsity. Other times you just won't know. If you are serious about evaluating an argument you may have to expend a good bit of effort trying to find out whether its reasons are true. It may involve library research, or doing experiments, or making observations, and so on. And after making such efforts you may still not know for sure, but only have a somewhat higher level of confidence about whether the reasons are true. Serious investigation of whether reasons are true can involve a lot of time and energy!
Since a good argument -- one that really proves its conclusion -- must meet both requirements, obviously an argument that meets only one of them is a bad argument. It is an argument that fails to prove its conclusion. It doesn't matter which requirement it doesn't meet, because they are equally important. This suggests a possible shortcut for evaluating arguments. If it is easier to test whether an argument meets one of the requirements than the other, then test for that one first. If the argument fails the test then it's bad; it doesn't matter whether it meets the other requirement!
On the other hand, if you are presenting your own argument instead of evaluating someone else's then this shortcut is not available to you. To present a good argument, you have to do your best to insure that both requirements are met!
Is one of the two requirements easier to test for than the other? Most of the time, yes! Usually it is easier to test for the reasons-properly-related-to-conclusion requirement. Provided, of course, that you know how to do it! The reason is that all you need to do to test for this virtue is to think! To test for the reasons-true virtue you also have to think, but in addition you often have to devote time and energy and perhaps money to research, observation, experimentation, and so on. Of course I'm talking about the evaluation of serious arguments, arguments whose conclusions are really of interest to you -- not just little example arguments in logic exercises!
This is about all we'll do with the truth-of-reasons requirement for a while. We will now focus on that second, properly-related-to-conclusion requirement for a long time. Not because it's more important, but because it's harder to understand.
THE REASONS-PROPERLY-RELATED VIRTUE (OR, REQUIREMENT)
What it takes for the reasons of an argument to be properly related to the conclusion is this:
If the reasons are true, then the conclusion either 1) would of necessity have to be true as well, or 2) would very probably be true as well.
Examples:
1) All mice have six legs, and all six-legged things are grey. Therefore, all mice are grey.
2) 97% of students taking ENG 211 are freshmen, and Joe Schmo is taking ENG 211. Therefore, Joe Schmo is a freshman.
Three of the four reasons in these examples are false, and the fourth is suspect (who is "Joe Schmo"?). But obviously, if in 1) the reasons were true, then its conclusion would just have to be true too. And in 2), if the reasons were true, then the conclusion would very likely (97% likely) be true. Thus in both of these examples the reasons-properly-related requirement is met! Even though the true-reasons requirement is not met.
Ideally, of course, we'd like our arguments to meet both requirements. But it is important to realize that an argument can, and often does, meet one of the requirements without meeting the other; and it is important to be able to judge the two requirements separately. If you encounter an argument with pretty obviously false or very suspicious reasons, then it's a bad argument, and you needn't worry much about whether its reasons, if they were true, would lead, with either necessity or probability, to its conclusion. On the other hand, if you encounter an argument for which you can tell, after a little thinking, that its reasons are not properly related to its conclusion, then it's a bad argument, and you needn't worry much about whether its reasons are actually true.
On the third hand, you may encounter an argument for which you don't know whether its reasons are true, but it is pretty clear that the reasons are properly related to its conclusion. Then (if you are really interested in whether the conclusion is actually true) you should be concerned to try to find out whether the reasons are true!
So, there are two ways for the reasons-properly-related requirement to be met:
1) The reasons, if true, would make the conclusion necessarily
(definitely) true also; and
2) The reasons, if true, would make the conclusion very probably
(but not necessarily) true also.
Special logic terminology. An argument of type 1) is called a valid argument. An argument of type 2) is called a strong (but invalid) argument. And an argument in which the reasons, even if true, would not make the conclusion very probably true is also invalid.
It turns out, somewhat surprizingly, that it often easier to determine whether an argument is valid than to determine whether it is strong. This is because validity is an all-or-nothing affair. Every argument whatever is either valid, or invalid; there is no in-between, there are no partially valid arguments, no almost-valid arguments. There are rules and procedures that can usually show whether an argument is valid or invalid. But, by way of contrast, strength in arguments is a matter of degrees. There are very strong (but invalid) arguments, medium-strong (also invalid) aruments, arguments (invalid) of intermediate strength, meduim-weak (invalid) arguments, and very weak (invalid) arguments. And there are very few useful rules or procedures for reliably determining degrees of argumentative strength!
Because validity in arguments is definite, straightforward, precisely
defined, and (usually) can be accurately judged (if you know how to do
it), we will first consider validity. Then later we will turn
to strength.
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Definition. An argument is valid when: if all the reasons were true, then the conclusion would of necessity have to be true also. Otherwise, it is invalid.
Notice that the definition does not require that the reasons in a valid argument must be true! Nor does it require that the conclusion be true! It only requires that there be a certain specified relationship between the reasons and the conclusion. It says nothing about whether reasons or conclusions are actually true. It allows that a valid argument might have any of these combinations of truth and falsehood among its reasons and conclusion:
true reasons, true conclusion false reasons, false conclusion false reasons, true conclusion
Notice that one possible combination is missing: True reasons, false conclusion!!! That's because the definition prohibits that combination. Think about what the definition says and you'll see. Another and equivalent way of defining validity focuses on this prohibition:
An argument is valid when it is impossible that the reasons could be true and the conclusion be false together ("together" means "at the same time, or in the same circumstances, or with reference to the same people or places, etc.")
At this point you might be thinking, "Aha! This means that if an argument does not have true reasons and a false conclusion, then it is valid!" But that would be entirely wrong. Because arguments that are invalid can have any combination of truth and falsehood among their reasons and conclusions!
Here's a table that illustrates the options. You should understand that "reason(s) true" means that all the reasons are true; and by way of contrast, "reason(s) false" means that there is at least one false reason. This is because "not all true" = "at least one false."
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POSSIBILITIES
FOR ARGUMENTS
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VALID
ARGUMENTS
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INVALID
ARGUMENTS
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| Reason(s) |
True
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True
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False
|
False
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True
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True
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False
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False
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| Conclusion |
True
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False
|
True
|
False
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True
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False
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True
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False
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1
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2
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3
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4
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5
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6
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7
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8
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The upshot of this is that you cannot tell whether an argument is valid or invalid by knowing about the actual truth or falsity of its reasons and conclusion -- with one exception. The exception is, if the reasons are actually all true and the conclusion is really false, then the argument is invalid (possibility 6).
So how do you tell whether an argument is valid? In general, by thinking about it in the light of the definition of validity. For more specific and helpful guidelines, pay close attention in class!