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Among the first of the great philosophers to study the philosophy of logic was Aristotle. Aristotle used logic as a way to discover meaning, through his work he developed a system of logic that when followed would lead an individual to the truth. Aristotle’s work is not only significant for being the first of it’s kind, but also for transforming the way in which reasoning was applied.
Aristotle’s logic is structured such that an individual may infer new knowledge by using a syllogism. A syllogism is an argument based on two premises that reaches a logical conclusion. The premise of an argument being the statement upon which the argument is based. The key to using a syllogism to arrive at a conclusion lies in deduction. The best way to illustrate this is with formal logic. Formal logic is one of two types of logic invented by Aristotle. As the name suggests formal logic deals with the proper form of a logical statement. This is where deduction comes into play. A classic example of formal logic can be demonstrated as a mathematical concept as follows: If A is equal to B and B is equal to C, Then A is also equal to C. You are able to reach the conclusion A equals C by using deduction. Another common example to show the logical progression of a form is the expression: if X then Y, X, Then Y. Aristotle describes deduction as, “speech (logos) in which, certain things having been supposed, something different from those supposed results of necessity because of their being so” (as qtd. in “Aristotle Logic 1”) As long as the argument follows the form and you base your deduction on what you know to be true, then the conclusion you are met with must be true because of “necessity”. It is important to note that in formal logic the fact or truth of a statement matters not. Since formal logic deals only with the form of an argument the emphasis is placed on correctness of form. If the form is correctly used than the argument is said to be valid.
Whereas formal logic strictly deals with the form of an argument, substantive logic introduces context. By context I mean the real world premises that are applied to a form. Using the example of formal logic above one could insert the context of numbers, for example: 0 is equal to 1, 1 is equal to 2, then 0 is equal to 2. We know that we are using the correct form of the argument which makes the argument valid, but the issue lies in the truth of the premises. One could say that 0 is equal to 1, but anyone familiar with mathematics knows that this is not true. When a statement uses the correct form but uses premises that are false that statement is said to be unsound. Conversely, when an argument has true premises and uses a valid form it is said to be sound.
The application and the benefit of logic is clear. Logic is a free tool available to all who think critically. If one understands logic then they are able to evaluate statements of logic. This is a huge part of thinking critically and reaching the truth of a statement. Suppose you have discourse with a colleague and can clearly identify that their second premise disproves their first, with logic you are able to immediately see that they are lying. Even more practical than everyday life is the application of logic to the sciences, the ability to discern fact from non-fact lies in the use of logic. A key part to the application of logic in science comes from Aristotle’s first principles.
Science clearly relies upon logic, but in order for that science to work certain things must first be accepted as fact. Aristotle’s first principles seek to allow this to happen. Imagine where science would be if nothing could initially be accepted as fact, there would be no logic because no premise could be accepted as truth. Aristotle establishes the principles based on three criteria, first they must be self-evident, second they are unprovable, and last they are fundamental (“Aristotle Logic 3” ). Aristotle breaks the first principles down into four principles of logic, the principles of identity, the excluded middle, sufficient reasoning, and contradiction. These four principles serve as the foundation of all logic.
The principle of identity deals with how we recognize objects. We accept the identity of certain things based on how we observe them through our senses. A banana is a banana because it is yellow and shaped a certain way and smells a certain way and tastes a certain way. Objects that satisfy certain criteria are identified as that object and the principle of identity states that if any other object meets that criteria then it too is that object. This is important because it is how we decide what something is.
The second principle, the principle of the excluded middle, addresses half-truths. SImply put, there is no half-truth. A statement can only be true or false, if it is any less than true than it is false, and if it is any more than false then it is true. Think of the term ‘almost’, if one were to say they are almost anything then they do not satisfy the requirement of being that thing, therefore they are not, therefore the statement is false.
The third principle of logic, the principle of sufficient reasoning, deals with cause. The principle states that nothing can exist on it’s own. That is to say that everything has to have come from something.
Finally the fourth principle of logic, the principle of contradiction, deals with contradiction. The principle simply states that nothing can be in contradiction with itself. An object cannot have two conflicting identities. An apple cannot be an apple and a banana at the same time. This can be easily applied to an argument that is proved to be false by contradicting claims.
These principles are the foundation of logic because they provide a means to establish premises. Hypothetically let us establish the premise of “A”, first we need A to be identifiable, if A is obscured by ambiguity then A cannot mean the same thing to everyone which in turn prevents us from establishing it, here the principle of identity is used. After we identify A as A, we need to prove that A either is or is not, A cannot almost be A or the opposite, here we use the principle of the excluded middle. Next we establish that A is a thing with the understanding that A has a cause, here we use the principle of sufficient reasoning. Lastly, we establish that A is, and can only be A, here we use the principle of contradiction. Using the four principles of logic we have successfully established a premise that we can use in our argument. Without the ability to establish a premise the soundness of an argument would be unprovable, which would ultimately make logic unreliable.
The greater philosophical question comes from the application of logic. The question of whether or not logic is necessary to arrive at truth. Some would say that logic is indeed required to determine truth, but I would rather question what the nature of truth is. Aristotle establishes truth based on the four principles of logic, but it is in the four principles that I find fault. To arrive at truth one must first establish the identity of an object, my proposition is that truth is merely a reflection of that agreement. If a particular group of people establish the identities of all their world then they are creating a system where every single truth is measured only against what is established. Truth therefore is limited, and does not indicate the real truth of anything, but rather only a fraction of what is true. One can make their own claims of what they feel is the adequate level of truth they desire, but to say that anything is the one and ultimate truth would be impossible. The truth that Aristotle refers to is limited by the confines of our cognition.
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