How does logic help us clarify or solve problems?
Everyday people employ the use of logic to help them clarify or solve problems. Logic may only provide validity or highly probable ideas, but the correct answer, if any, is left for one to decide. The science of thinking and rationalizing, logic is like a double-edge sword. When logic is utilized it may become an efficient tool, capable of discovering correct ideas and understandings. Yet, it can also become an unsolvable maze, causing more confusion than clarity. There are certain methods of logic to determine possible solutions for a problem and to verify them. Induction and deduction are arguments that may give a solution, which is not considered absolutely true but rather having correct reasoning. For logic can only determine “the distinction between correct and incorrect reasoning” (Copi, p.5) of a problem. Well these methods can be useful; it still can make a problem more confusing such as with the case of paradoxes. It is up to one to make the leap of faith to decide if the conclusions of the methods are acceptable in practice or not.
The argument of induction is based upon the idea of having a set of given general information called the premise. From the premise, one then can formulate a conclusion that supercedes the information, from the problem. A simple example of this is:
There was one apple missing from the basket that was in the house.
John was seen leaving the house with an apple.
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Therefore John must have taken the apple.
The conclusion made from this argument seems right, but an inductive argument can only produce a probable answer and therefore is not absolutely true. So when induction is used, there is still a chance that the conclusion might be wrong. Hence any inductive conclusion must be thought as highly probable but having a chance that it might be wrong. It is up to one to judge for themselves if they have solved the problem or not.
“In induction our reasoning takes us beyond what we already know, it widens our knowledge.” (Dilman, p.29) Induction is used in scientific problems for the reason that with given knowledge on can “provide conclusions whose content exceeds that of their premises.” (Salmon, p.87) Although one must still face the fact that the conclusions of an inductive argument may be wrong though the premise might be true. Even with the uncertainty of inductive reasoning, being right or wrong, “most of our everyday reasoning is inductive.” (Olen, p.318)
To give an accurate conclusion for induction, one must be aware that the premises are all true but also that there is enough information for one to actually make a concluding statement. For example a scientist finds that crow #1 is black, crow #2 is black, and crow #3 is black. He then concludes that all crows are black. The final statement is considered to be incorrect because there is a lack of information provided to concluded an “all” statement but that lead to another question. How much information is needed to make a correct solution? The obvious answer would be to find out what color all the crows are, but in practice that would be impossible. It is up to one to decide how many crows should be tested, the more tested, the higher the probability that it is true. This type of question often occurs in scientific studies, where scientists test an experiment over and over before coming to a conclusion. The lack of information in inductive reasoning is the reason why this type of logic only provides probable answers.
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People live in a world of probability. Induction is used so often that some philosophers question the justification of it. David Hume first introduced the so-called problem of induction. Hume argued that to justify it, the problem “resorts to induction in order to justify induction,” (Olen, p.323) and therefore “provides no justification at all.” (Olen, p.323) This logical reasoning of Hume and other philosophers on the problem creates disagreement with other philosopher’s views upon induction. Thus confusion arises on the truth of the solution, for logic can only give valid or probable ideas.
Deduction is a logical argument that is created through specific information given. Using the information one can produce a correct general conclusion. The purpose of deductive reasoning is to determine if a problem is valid or invalid. When the conclusion is said to follow from the premises, a sound deduction, “it is impossible for the premises to be true without the conclusion also being true.” (Black, p.28) An example is:
All cars are red
Hondas are cars
Therefore Hondas are red
The conclusion of Hondas being red logically follows from the two given general information which makes it a sound deduction. Although this example’s conclusion has correct reasoning and is valid, it is obviously not true and therefore one must conclude that the solution is wrong. Since the premise of the problem is false a wrong conclusion will be produced because the conclusion logically follows a false premise, it becomes wrong. For logic to help one to clarify or provide validity, the information that one has must be true in order to have correct reasoning.
The information, premise, plays a vital role in deduction. Take for instance:
All dogs have two eyes
John has two eyes
Therefore John is a dog
It is apparent that this example is wrong. One has to make sure that the information given makes sense, is not too vague and provides enough information to make a true and valid conclusion.
With the method of deduction, the problem it creates is not in the process itself. The problem is in the specific information given for the question. Information such as “all dogs are born with four legs” and “all ravens are black” comes from inductive reasoning, both having a chance of being wrong. When they are used in deductive reasoning, the statement is considered true but it still can be wrong. Therefore even if the conclusion is soundly deducted, the premise can be false, making the conclusion wrong. One must remember that when dealing with deduction, the main concern is with the premise, whether or not it is true. Without having true information the conclusion will always be wrong.
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Logic is useful in many ways but in some cases it proves to be the confusion. The confusion of logic is greatly amplified in the idea of a paradox. Some philosophers looked at this idea; one philosopher was Bertrand Russell. He proposed some paradox such as: If a barber only shaves all the people who don’t shave themselves, does he shave himself? If one were to logical rationalize an acceptable solution, the answer that one can get is impossible. When the barber shaves himself, it contradicts the statement that “he only shaves all the people who don’t shave themselves” and vice versa when he does not shave himself. In practice, the barber must get shaved or else he does not shave at all but using logic it is impossible and thus making the problem confusing. Russell concluded that for a paradox there is two sets of reasoning, “all values of the said function are true” (Russell, p.75) or “when the collection forms part or whole of the range of significance of some prepositional function.” (Russell, p.75) In other words:
Sets that do contain themselves
Sets that do not contain themselves
The second statement of Russell’s “cannot be properly defined without reaching another contradiction.” (Cirrito, p.13) This confusion can only teach one to be more precise with the language used of else a paradox might occur.
Logic plays a very important role in clarifying or solving problems. Most of the time it creates clarity and acceptable ideas but sometimes it can be the cause of all the confusion. The argument of induction is a logical method to provide one with acceptable answers. Although the process can be correctly reasoned out, one must still realize that the conclusion might be wrong. Induction can only produce highly probable conclusions and therefore never absolutely true. Logical deduction is a process of determining validity of a problem. When there is a sound deduction it is absolutely impossible for the premise to be true unless the conclusion is true also. To have correct deduction one must ensure that he or she has enough true evidence to make a concluding statement. People should not always rely upon the use of logic to solve problems, such problems as paradoxes hinder the idea of logic. The final decision on the right solution, if any, of a problem depends on the person trying to solve the question. Logic is just a tool for someone to use.
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Cited Works
Jeffrey Olen, “Persons and their World”
Wesley C. Salmon, “Logic”
Ilham Dilman, “Induction and Deduction”
Irving M. Copi, “Introduction to Logic”
Max Black, “Critical Thinking”
Bertrand Russell, “Logic and Knowledge”
Fabio Cirrito, “International Baccalaureate Mathematics Higher Level (Core)”
