The task of an argument is to provide statements premises that give evidence for the conclusion. There are two basic kinds of arguments. Deductive argument: involves the claim that the truth of its premises guarantees the truth of its conclusion; the terms valid and invalid are used to characterize deductive arguments. A deductive argument succeeds when, if you accept the evidence as true the premises , you must accept the conclusion. Inductive argument: involves the claim that the truth of its premises provides some grounds for its conclusion or makes the conclusion more probable; the terms valid and invalid cannot be applied.
Valid: an argument is valid if and only if it is necessary that if all of the premises are true, then the conclusion is true; if all the premises are true, then the conclusion must be true; it is impossible that all the premises are true and the conclusion is false. Invalid: an argument that is not valid. We can test for invalidity by assuming that all the premises are true and seeing whether it is still possible for the conclusion to be false.
Of course, the answer is 'no'. If pigs can indeed fly, and if anything that can fly can also swim, then it must be the case that all pigs can swim. Hopefully you will now realize that validity is not about the actual truth or falsity of the premises or the conclusion.
Validity is about the logical connection between the premises and the conclusion. A valid argument is one where the truth of the premises guarantees the truth of the conclusion, but validity does not guarantee that the premises are in fact true. All that validity tells us is that if the premises are true, the conclusion must also be true. This argument is not valid, for it is possible that the premises are true and yet the conclusion is false.
Perhaps Adam loves Beth but does not want Beth to love anyone else. So Adam actually hates Cathy. The mere possibility of such a situation is enough to show that the argument is not valid. Let us call these situations invalidating counterexamples to the argument. Basically, we are defining a valid argument as an argument with no possible invalidating counterexamples. To sharpen your skills in evaluating arguments, it is therefore important that you are able to discover and construct such examples.
Notice that a counterexample need not be real in the sense of being an actual situation. It might turn out that in fact that Adam, Beth and Cathy are members of the same family and they love each other. But the above argument is still invalid since the counterexample constructed is a possible situation, even if it is not actually real.
All that is required of a counterexample is that the situation is a coherent one in which all the premises of the argument are true and the conclusion is false. So we should remember this :.
An argument can be invalid even if the conclusion and the premises are all actually true. To give you another example, here is another invalid argument with a true premise and a true conclusion : "Paris is the capital of France.
So Rome is the capital of Italy. It is not valid because it is possible for Italy to change its capital say to Milan , while Paris remains the capital of France. Another point to remember is that it is possible for a valid argument to have a true conclusion even when all its premises are false. Here is an example :.
All pigs are purple in colour. Anything that is purple is an animal. So all pigs are animals. Before proceeding any further, please make sure you understand why these claims are true and can give examples of such cases.
The concept of validity provides a more precise explication of what it is for a conclusion to follow from the premises. Since this is one of the most important concepts in this course, you should make sure you fully understand the definition.
In giving our definition we are making a distinction between truth and validity. In ordinary usage "valid" is often used interchangeably with "true" similarly with "false" and "not valid". But here validity is restricted to only arguments and not statements, and truth is a property of statements but not arguments.
It is saying essentially that all black things are crows. Not true of course, but not relevant to judging the reasoning. The first premise is false, but this is not relevant to judging the reasoning.
IF these premises are true, we are locked into the conclusion. If we gave these premises to a computer, it would give us back the conclusion. It would simply judge the implications of the alleged information it is given. See the credit score example in the video for Chapter 1. Which one of the following is true about valid arguments? They always have true premises. If the premises are true, then the conclusion will be true.
If we find out that a premise is false, then we change our mind about whether an argument is valid. In 6 when we see that the first premise is false, we know the argument is now invalid. Valid arguments always have true conclusions, even if some of the premises are false. Saying "Only crows are black" means that "If anything is black, it is a crow. All Internet spies for the Chinese government are Chinese. Wen Ho Lee is Chinese. The first premise is not saying that every Chinese person in the world is an Internet spy for the Chinese government.
Question : What if we discover that the conclusion is true? Is the argument now valid? The reasoning is still invalid, but we can get lucky and still have true conclusions. Important -- Invalid arguments can have as a matter of luck true premises and a true conclusion, BUT the key difference is that the premises do not guarantee the conclusion as they do with valid arguments.
All Democrats always tell the truth. President Obama is a democrat. So, President Obama always tells the truth. IF the premises are true, we are locked into the conclusion. We go by what the premises are saying. Question: What if the conclusion of the Obama example is false? What do we know about the premises? IF an argument is valid, but if we know the conclusion is false, then we know at least one premise is false.
Because valid arguments can never have ALL true premises and a false conclusion. Important -- see the section on Logic and Belief Testing in Chapter 1.
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