INTRODUCTION Show Validity: To test whether or not an argument is valid, you should first imagine that the premises are true—whether or not they actually are—and then ask yourself, without appealing to any other knowledge you have, could you still imagine the conclusion being false? If you can, the argument is invalid. If you can't, then the argument is valid. Note that validity is a matter of the form or structure of an argument, as opposed to the content. If an argument is valid, then any other argument with the same logical structure will also be valid, regardless of its content. Also, keep in mind that an argument can be valid even if its premises are not actually true. An argument that has true premises (regardless of whether it is valid or invalid) is said to be factually correct. An argument that is both valid and factually correct is sound . Some hints on determining validity: Clearly, this argument is not factually correct, for the premises are false. But it may be of a valid argument form. To check this, we must imagine a possible world in which all the premises are true. So consider premise 1. We can represent what it is saying by drawing two circles. One circle represents a collection of all the dogs in the possible world, and the other circle represents all the cats. Since the premise says that ALL dogs are cats, we know that every member in the circle of cats must also be a member in the circle of dogs. So we must put the dog circle INSIDE the cat circle. Keep in mind that there are no premises telling you that all CATS are DOGS. Thus, there should be some leftover area of the cat circle that falls outside of the dog circle, to show that there may be some cats that are not dogs. Now, look at the second premise. If all cats are lizards, then the whole CAT circle (with the DOG circle still inside it) must be placed within the circle of all the lizards in the world. At this point, we should have an accurate representation of the premises. Do they guarantee the conclusion? That is to ask: is it possible in that world for the conclusion to be false? Since you will notice that there is no area of the dog circle outside the lizard circle, you should see that if these premises were true, the conclusion must also be true. The argument is therefore valid. "if…then" premises: Below are some arguments. For each argument try to determine whether or not it is valid (you may want to take note of whether or not you think the argument is sound as well). It is worth taking the time to symbolize each argument (for instance, using 'P's and 'Q's to stand for statements. Pay attention to which symbolized arguments are valid and which are invalid. Doing so will help you recognize valid and invalid arguments with greater ease. I have included answers with some comments following the exercises. EXERCISES: A. B. C. D. E. F. G. H. I. J. K. L. M. N. O. P. Q. (Note: the word 'OR' is a logical term much like 'if…then', 'therefore' and 'it is not the case that…' Like these other terms, 'OR' is part of the structure or form of the argument, rather than the content.) R. ANSWERS: A. B. C.
D. E. F. G. H. I. J. K. L. M. N. O. P. Q. R. When the premises of a deductive argument are true the conclusion is false?FALSE: A valid argument must have a true conclusion only if all of the premises are true. So it is possible for a valid argument to have a false conclusion as long as at least one premise is false.
Can the conclusion of a deductive argument be false?A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid.
Can a conclusion be true if the premises are false?False premises can lead to either a true or a false conclusion even in a valid argument. In these examples, luck rather than logic led to the true conclusion.
Can a valid deductive argument have false premises and a false conclusion?A valid argument can have false premises; and it can have a false conclusion. But if a valid argument has all true premises, then it must have a true conclusion.
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