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Logic: Truth vs. Validity

Updated on May 25, 2012

Logic: Truth vs. Validity

Logic and reason alone cannot determine the truth of an argument. However, they can provide the basis for determining the validity of an argument. This leads us to the battle between truth and validity. An argument can be valid but not truthful, if its phrasing is technically correct but the point it is ultimately making is false. An argument can also be truthful but not valid, as it can raise a true point and yet not be properly phrased so as to be logically valid. Why, then, should we bother with logic if it cannot present us with the truth? The answer is this: if we are making an argument and our point is true, but we don’t have the knowledge of logic to form a valid and sound argument for it, then our argument could fall apart simply because it is not validly phrased or supported. Thus we need both logic and a true point in order to form a perfect argument.

An argument can be valid, but not truthful. Let’s take the issue of religion, for example. A theist, or believer, could pose a perfectly valid argument, by the rules of logic, and have it be completely false. For example, the argument that there is no proof that God does not exist. They could postulate that if there is no proof that something does not exist, then there is a possibility that it exists. There is no proof that God does not exist, therefore it is possible that he exists. This would be a perfectly valid argument under the ‘if p then q; p, therefore q’ basis of reasoning. However, their argument fails to realize that there is no proof that God does exist. Thus it falls under the ad ignoratium fallacy of argument. Their argument could be deemed completely valid and logical, but is completely fallacious and fallible.

The opposing side, that of the atheist, could postulate very similarly. If there is no proof that something exists, then it does not exist. There is no proof that God exists, therefore it logically follows that he must not exist. This could be deemed just as valid and sound an argument as the previous one, depending on your point of view. However, neither of them truly derives the truth of the matter, and both are fallacious arguments on the basis that neither of them have any proof either way.

However, if one were to argue the point of evolution, one could back it up with true facts. Their argument could be as follows: If there is fossil evidence that points to the evolution of the human species over time, then it is possible and likely that the human race evolved. There is fossil evidence that points to human evolution, therefore the human race must have evolved. This would be just as valid as the religion arguments, but it also can be supported by truth. We do actually have evidence from fossils that humans have evolved over the course of millions of years. This is an example of an argument that is both valid and true.

An argument can also be true but not valid. If someone were to say, “If he cooks, then I will stay. He didn’t cook, so I didn’t stay,” then their argument would be invalid, although it could reasonably appear to an amateur logician to be true. It would seem that a logical point is being made, but they have presented it in such a way that invalidates it using the rules of logic of ‘if p, then q; p, therefore q.’ In this manner, it is presented as ‘if p, then q; -p, therefore -q.’ One with little knowledge of logic would think that this argument presents a valid form of logic, with the consequence necessarily following from the premises. However, one who is trained in the valid forms of logic would know better.

This still leads us back to the basic question: Why do we even bother with logic if it cannot ultimately lead us to the truth of the matter? Well, we bother with it because logic helps us present arguments that are both true and valid. If one does not know the valid forms of a logical argument from the invalid ones, then one could form a completely invalid argument, even though the ultimate point they are trying to make is true, as in the above example. Therefore it is necessary to have at least a basic knowledge of logic and valid forms of logical arguments before one can present a valid logical argument. Valid logical arguments are essential to everyday life. Our decisions about various issues in life most often stem from valid logical arguments for wanting or not wanting certain outcomes of an event or decision. Furthermore, we find it very hard to convince others of a certain fact if we cannot immediately provide proof for it, or provide a valid and true logical argument for the existence of this fact. For example, some people still believe the earth is flat. If one were to try to convince them otherwise, they would have to provide them with factual evidence, and with valid logical arguments to support the fact that the earth is, in fact, a sphere. Some evidence could be pictures of the earth from space, or the faintly visible curvature that one sees over the ocean when one gazes into the horizon. The convincer’s logical argument could be as follows: “If I can provide you with evidence of the spherical shape of the earth, then you must believe me. I can provide you with evidence, therefore you must believe me.” One could also argue: “If we have pictures that show the spherical shape of the earth, then we can prove that the earth is round. We have pictures from space that show the spherical shape of the earth, therefore we can indeed prove that the earth is round.”

Thus, logic may not provide us with the ultimate truth of a matter, but it can provide us with the means of forming a valid logical argument. This is important because in order to form a perfectly sound argument, the argument must be both valid and true. If one has no knowledge of the valid forms of logical arguments, then it is impossible for them to form one. It is entirely possible for an argument to be valid, and not true. It is also entirely possible for an argument to be true, and not valid. One who has no knowledge of valid argument forms could potentially form an argument of the latter type, which has true premises and a true conclusion but not necessarily a valid form. Therefore, we bother with logic so that we may make good arguments that are both valid and true.

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