1.4 true or false + notes (Phil 120)
Inductive arguments (1.3)
-
Some arguments are true, and some are false.
F
valid argument, true premise, true conclusion
SOUND
T or False: attempt #1
3/5
T or False: attempt #2
4/5
Cogency
An argument is cogent if it is inductively strong and has premises that are all true. This means that the internal reasoning of the argument is such that the conclusion follows from the premises with probability, and that all the premises are true. If these two criteria are met, then the conclusion of the argument will probably be true (although it still could be false). To evaluate an argument for cogency, you should first determine whether the argument is strong and then inquire whether the premises are all true. But if the argument fails to meet either of these criteria, then the argument will be uncogent. You should note that you cannot draw an inference about the truth values of an argument's premises or conclusion if the argument is uncogent. Cogent inductive arguments must also meet the "total evidence requirement," which states that the premises of a cogent argument must not ignore a piece of information that would lead to a different conclusion.
Strong argument, false premise, prob true conclusion
uncogent
Weak argument, false premise, prob true conclusion
uncogent
Weak argument, true premise, prob true conclusion
uncogent
weak argument, false premise, prob false conclusion
uncogent
weak argument, true premise, prob FALSE conclusion
uncogent
invalid argument, false premise, false conclusion
unsound
invalid argument, false premise, true conclusion
unsound
invalid argument, true premise, false conclusion
unsound
invalid argument, true premise, true conclusion
unsound
valid argument, false premise, prob false conclusion
unsound
valid argument, false premise, true conclusion
unsound
sound argument =
valid argument + all premises true
An immediate consequence of these definitions is that there is no middle ground between valid and invalid. There are no arguments that are "almost" valid and "almost" invalid.
-
Because a valid argument is one such that it is impossible for the premises to be true and the conclusion false, and because a sound argument does in fact have true premises, it follows that every sound argument, by definition, will have a true conclusion as well. A sound argument, therefore, is what is meant by a good, or successful, deductive argument in the fullest sense of the term.
-
deductive arguments (1.3)
-
Soundness
An argument is sound if it is deductively valid and has premises that are all true. This means that the internal reasoning of the argument is such that the conclusion follows from the premises with necessity and that the premises are all true. If these two criteria are met, the argument's conclusion is guaranteed to be true. To evaluate an argument for soundness, you should first determine whether the argument is valid and then inquire whether the premises are all true. But if the argument fails to meet either of these criteria, then the argument is unsound. You should note that you cannot draw an inference about the truth values of an argument's premises or conclusion if the argument is unsound.
in valid deductive argument
a deductive argument in which it is possible for the conclusion to be false given that the premises are true. In these arguments the conclusion does not follow with strict necessity from the premises, even though it is claimed to.
unsound argument
a deductive argument that is invalid, has one or more false premises, or both.
valid deductive argument
an argument in which it is impossible for the conclusion to be false given that the premises are true. In these arguments the conclusion follows with strict necessity from the premises.
Weak Inductive argument
an argument in which the conclusion does not follow probably from the premises, even though it is claimed to.
Strong Inductive argument
an inductive argument in which it is improbable that the conclusion be false given that the premises are true. In such arguments, the conclusion does in fact follow probably from the premises.
uncogent
an inductive argument that is weak, has one or more false premises, fails to meet the total evidence requirement, or any combination of these.
Strong argument, true premise, prob true conclusion
cogent
An uncogent inductive argument must have premises that are all false.
f
If an argument is deductively invalid, then the argument's conclusion must be false.
f
Some deductive arguments are neither sound nor unsound.
f
Some statements are valid, and some are invalid.
f
to test an inductive argument for cogency, the first step is to inquire whether the premises are all true.
f
Strong argument, true premise, prob FALSE conclusion
none exists
valid argument, true premise, false conclusion
none exists
cogent argument =
strong argument + all true premises
An uncogent inductive argument does not have to be weak.
t
If a deductive argument has true premises and a true conclusion, then the argument still could be unsound.
t
In a strong inductive argument with true premises, the conclusion may be false.
t
The conclusion of an uncogent inductive argument could be true.
t
To test a deductive argument for validity, you should begin by assuming that the premises are all true.
t
Strong argument, false premise, prob false conclusion
uncogent
A deductive argument is either sound or unsound, with no middle ground.
T
A sound deductive argument must be valid.
T
If no contradiction results from assuming that an argument's premises are true at the same time that its conclusion is false, then the argument is deductively invalid.
T
It is proper to speak of arguments that rely on statistical reasoning as being either strong or weak, rather than being valid or invalid.
T
Some valid deductive arguments have false premises
T
9. True/False Review and Chapter Summary
Use your knowledge of the definitions of validity, soundness, strength, and cogency to determine which of the following statements are true. Check all that apply.
Cogent
an inductive argument that is strong and has all true premises. Also, the premises must be true in the sense of meeting the total evidence requirement. If any one of these conditions is missing, the argument is uncogent.
If an inductive argument is weak, then the argument's premises are false.
f
If every statement in a deductive argument is false, then it must be an invalid argument
f
If the premises and conclusion in an inductive argument are all true, then you know that the argument's reasoning must be inductively strong.
f
In a strong inductive argument with true premises, the conclusion may be false.
f
Some deductive arguments are more valid than others.
f
If an argument is deductively valid, then it must also be sound.
F
If an argument is deductively valid, then the argument's conclusion must actually be true.
F
If an inductive argument is cogent, then the argument cannot be strong
F
If an inductive argument is strong, then it must also be cogent.
F
If the premises and conclusion in a deductive argument are all false, then you know that the argument's reasoning must be invalid.
F
If you do not know the truth values of a deductive argument's premises, then the argument must be unsound.
F
In a strong argument, the conclusion is probably false if the premises are false.
F
The first step in testing a deductive argument for soundness is to inquire whether the premises are all true.
F
Validity
In a deductive argument, the conclusion is claimed to follow from the premises with necessity. The concept of validity is used to evaluate whether the conclusion actually does follow from the premises with necessity. To evaluate an argument for validity, you should first assume that the argument's premises are all true, even if they are actually false. If the conclusion must therefore necessarily be true, given the truth of the premises, then the argument is a valid argument. If the conclusion still could be false under the assumption that the premises are all true, then the argument is invalid. Validity does not admit of varying degrees. Every deductive argument is either completely valid or completely invalid. Therefore, it does not make sense to say that some arguments are more or less valid than others. The actual truth values of an argument's premises and conclusion are inadequate when determining the argument's validity except in a single case: If the argument has premises that are actually true and a conclusion that is actually false, then the argument is invalid. This is because if a conclusion necessarily follows from the premises, then it will be impossible for the premises to be true and the conclusion to be false. Any argument in which it is impossible for the premises to be true and the conclusion to be false simultaneously is a valid argument. This means that you can have a valid argument with false premises and even a false conclusion. But what matters for validity is whether the conclusion would have to be true if you assume that the premises are true, regardless of the actual truth values of the argument's premises and conclusion.
Strength
In an inductive argument, the conclusion is claimed to follow from the premises with probability. The concept of strength is used to evaluate whether the conclusion actually does follow from the premises with probability. To evaluate an argument for strength, you should first assume that the argument's premises are all true, even if they are actually false. If the conclusion is likely to be true also, given the truth of the premises, then the argument is a strong argument. Even if the premises are assumed to be true, the conclusion of a strong inductive argument still could be false, but it is unlikely to be false given the truth of the premises. Unlike deductive validity, inductive strength admits of varying degrees. It does not make sense to call one deductive argument more valid than another, but one inductive argument can be stronger or weaker than another. The actual truth values of an argument's premises and conclusion are irrelevant to the argument's strength. What matters for strength is that the conclusion should be likely to be true when you assume that the premises are true. This means, for example, that you could have a strong argument with false premises and a false conclusion, as long as the conclusion is probably true if you assume that the premises are true. You should note that even a strong inductive argument could have a conclusion that is actually false, even if the premises are true; but if the argument is strong and the premises are true, the conclusion is unlikely to be false.
Section 1.4 Summary:
The concepts of validity and soundness are used to evaluate deductive arguments, and the concepts of strength and cogency are used to evaluate inductive arguments. What follows is an explanation of how these concepts should be applied and an explanation of some of their important nuances.
sound argument
a deductive argument that is valid and has all true premises. Both conditions must be met for an argument to be sound; if either is missing the argument is unsound.
You cannot tell the strength of an inductive argument solely from the truth values of the argument's premises and conclusion.
t
