A lesson in logic.
An argument is any combination of sentences that intend to prove a point. With some analysis those seemingly ordinary sentences can be broken up into what logicians call premises and a conclusion (true arguments will often have many premises, but only ONE conclusion). A premise is a sentence that is intended to give support (give evidence); a conclusion is the sentence that is supposed to be supported [by the premises]. For example:
If Dimitra is sexy then the boys will like her
the boys don't like her
therefore, Dimitra must not be sexy.
In the example "if D is sexy then the boys will like her," and "the boys don't like her" are both the premises: they "give evidence" to support the conclusion. So what does it seem like those premises are trying to give evidence of? They were giving evidence that "D must not be sexy" and this is the conclusion. (it is often helpful when reading, and when listening to people talk to ask yourself, "what is their point?" "what are they trying to convince me of?" The answers to these questions will lead you to the conclusion.
Arguments come in two types. Well, for our purposes two types is sufficient. The first being Valid, and the second being Invalid. The validity of an argument (whether it's valid or invalid), and here is where things get a little tricky (but all the more interesting), does not depend at all on whether or not what is being said is true. An argument such as
all men have purple skin
Hillary Clinton is a man
therefore, Hillary Clinton has purple skin
is completely Valid even though everything it says is untrue. The reason the argument is Valid is because of its FORM (its form is valid). Again, it is the structure of the argument (not the content) that makes or breaks an argument with regard to validity. So how are we to know what this form is? A simple way to answer this question is to ask yourself this question when you are faced with an argument: "Is it possible for the conclusion to be false if the premises are true?" If you are able to answer yes, then the argument is INVALID. If you must answer no, then the argument is VALID. Consider some examples.
all men love their wives
all men love dogs
therefore, wives love dogs.
Ask yourself, is it possible for the conclusion to be false even if the premises are true? Put another way, let us assume that the premises ARE true, would that make the conclusion true? The answer to the first question is Yes, even if all men love their wives and they loves their dogs it DOES NOT mean that their wives love dogs too. In other words the conclusion CAN BE false even if we assume the premises to be true: this argument is INVALID. To answer the second question, No, assuming the premises are true does not make the conclusion true. The FORM is such that the relationship between the premises and the conclusion is not a good relationship. Another example:
all men will die
suzie is a golden retriever
therefore, suzie will not die
In this case it seems pretty common sensical to assume that the premises are true. So ask yourself, is it possible for the conclusion to be false? In other words, if all men are going to die, and if suzie is a dog, is it possible that suzie will die too? The answer is yes. It is possible for the conclusion to be false even with true premises, so we can know for certain that the argument is INVALID. So, perhaps it will be helpful to show how we could make this argument valid.
all men, and only men, will die
suzie is a golden retriever (not a man)
therefore, suzie will not die.
This argument is VALID. One can see that if the premises are true then the conclusion must also be true, for if the only things that die are men (1st premise) and suzie is not one of those things, then we can know for certain that suzie will not die. Take some time, if need be, to see the differences in these two arguments, if you grasp this you have grasped the notion of validity.
Another example:
all turtleneck sweaters cover necks
banana republic makes turtleneck sweaters
therefore, banana republic makes turtleneck sweaters that cover necks.
Is it possible, given that the premises are true, that Banana does not make turtleneck sweaters that cover necks? Your answer should be No. It is not possible for Banana to make turtleneck sweaters that do not cover necks, if the premises are true. You see, in the first premise it says that ALL turtleneck sweaters cover necks, this "all" means every thing that is a turtleneck sweater will cover necks. So if we grant this to be true, then it follows by necessity that if Banana makes turtleneck sweaters, those sweaters MUST cover necks. This argument is VALID. Again, we know it is valid because it is impossible for the conclusion to be false if the premises are true. Here is one that may be more difficult to see:
If Calvin were a protestant then the Augustine was a Romanist
Augustine was not a Romanist
therefore, Calvin was not a protestant.
Ask yourself, if the premises are true, is it possible for the conclusion to be false? Your answer should be No. This argument is VALID, if the premises were true (thank God they are not) then it would be the case that the conclusion had to be true also.
a note on "truth." In logic, when analyzing these formal arguments it is necessary to be able to pretend. Dostoyevsky said, that all men, even intelligent men love to pretend; I know I am one of those. And here in logic we get to use that to our advantage! What we "pretend" in logic is in the realm of possibility. The logician (yourself) must be able to separate himself from the real world and think purely in abstract terms, such that when we see premises like "Hillary Clinton is a man" we don't allow ourselves to be "caught up" with the content, we "pretend" and allow for the logical possibility that indeed Hillary may be a man. "Snow is green" even though we know it's not, we can "pretend" that it is, and so forth. In short, when an argument is asking to be evaluated it is not asking you questions about the REAL world; it is asking you to "make believe" and "pretend." Isn't logic great! The reason this "pretending" is important is because it is crucial when evaluating argument's validity to be able to separate yourself from the content, to leave your mind able to concentrate solely on the FORM: Do these premises, assuming they are true, make it necessary for the conclusion to be true? If you remember only one thing from all this, remember that question.
Review:
We have seen that an argument's validity depends ONLY upon its form not its content.
We have seen examples of Valid arguments and Invalid arguments.
We have seen that an argument can be valid even if everything it says is untrue: It's the FORM stupid!
We have seen that an argument can be invalid even if everything it says is true:
all snow is white
H2O is water
therefore, steam is H2O.
Logic is extremely useful when one is trying to manuever through the morass of newspaper reports, so-called Christian books, television advertisements, what your mom says, etc etc. Logic equips the individual to be able to "see through" the jargon and emotion; it enables those who use it to hone in on truth. Logic is a reflection of the order of the universe. Logic reflects God's grace, in that he hasn't forsaken us to a world chaotic and capricious. I hope this has been somewhat helpful to any of you just beginning, or maybe have not yet studied logic. My hope is to continue this (I will have to re-read this and continue to make modifications) and possibly aid in the growth of truth.
Sola Deo Gloria
Posted by jeremy stock at December 15, 2000 12:27 PM