Logic basics
“Logic is the anatomy of thought." (John Locke)
Logic is one of the fields of Philosophy, developed by the Greek Aristotle (384-322 BC), one of the most influential thinkers in the entire history of Western philosophy. It can be considered as an introductory discipline for any philosophical study and basically predicts that it is possible to come to consistent conclusions from preliminary notions on a specific subject.
It is not necessary, for the objectives of this work, to undertake an in-depth study of logic, full of formulas and filled with a complex language, since we will use very simple and objective arguments. However, for those unfamiliar with this subject, we will present some fundamental concepts, so that they can understand how we can use this powerful tool to guide our reasoning and develop logical arguments with valid conclusions, contained in the next chapters.
Logical argument
The first step to understand how logic works is to know what an argument is. Argument is a set of statements, also known as "propositions" or "premises", which are related to each other, and lead to a conclusion. It is a logical reasoning, where every premise, like every conclusion, may be only true or false.
Example:
Premisse 1: "All metals are conductors of electricity (TRUE)
Premisse 2: "Copper is a metal" (TRUE)
Conclusion: "Copper conducts electricity" (TRUE)
Valid or consistent argument
For an argument to be considered valid or consistent, it is necessary that the conclusion presented by it is really a consequence of what was stated in the premises, that is, the inference between the premises must inevitably lead to the conclusion.
Analyzing the above argument, we see that there is a "logical inference" between its premises, that is, from the interaction between the two premises, we can come to an irrefutable conclusion. Therefore, the argument can be considered "valid" or "consistent".
Now, if all metals conduct electricity, and copper is a metal, then we can conclude unequivocally, that is, without any possibility of error, that the copper conducts electricity. A valid argument that has been derived from true assumptions is called a "consistent argument." Such arguments necessarily lead to true conclusions.
Refutation of an argument
It is not possible to refute a logical argument only by presenting a "belief" or a personal opinion that it is false. To refute an argument by logic it is necessary to demonstrate that:
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At least one of the premises of the argument is not true, or
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There is no logical inference between the premises that leads to its conclusion
For example, using the argument presented above, we could only refute it and prove that its conclusion would not be true, in other words, that copper would not be a conductor of electricity, by presenting at least one of the following three situations:
1. Demonstration of 1st premise falsehood: We would have to demonstrate that not all metals are conductors of electricity. Therefore, even copper being a metal, it could not conduct electricity.
2. Demonstration of 2nd premise falsehood: We would have to demonstrate that copper is not a metal and, therefore, if all metals conduct electricity, copper would not co
conduct it.
3. Demonstration that the premises do not lead to the conclusion: We would have to show that even if all metals conduct electricity (premise 1) and that copper is a metal (premise 2), we could not conclude that copper conducts electricity, which is obviously impossible, that is, the inference between the two premises is clear and they lead us to the unequivocal conclusion that copper conducts electricity.
Since at least one of the above three situations does not occur, it is impossible to refute the argument and question its conclusion. In the same way, one cannot refute an argument simply because it goes against a dogma or something that is written in a "holy book." Such an argument could not be regarded as a logical refutation, merely the presentation of a personal opinion.
"Fallacy" or Invalid Argument
An argument is called a fallacy when, although its premises may be true, there is no logical inference between them to support the conclusion.
Premise 1: “All Brazilians speak Portuguese”
Premise 2: “José speaks Portuguese"
Conclusion: “José is Brazilian”
Even assuming that the two premises above are true, the argument is invalid or, in other words, we can call it a fallacy, because premise 2 (José speaks Portuguese) does not allow to conclude that José is Brazilian, once "not all who speak Portuguese are Brazilian." José could be, for example, from Portugal, or have another nationality.
There are several kinds of fallacies. One of the most used by those who fail to present a logical refutation to an argument is what we call "Argumentum Ad Ignorantiam," or "Appeal to Ignorance." This fallacy consists in refuting a statement just because no one has proven it to be true, or in defending it, just because no one has proven it to be false.
Premise 1: "No one has ever proved the existence of God"
Conclusion: “God does not exist”
Or else:
Premise 1: “No one could prove that God does not exist”
Conclusion: “God exists
The proponents of this fallacy put themselves in a very comfortable situation, because they shift the burden of proof to those who disagree with them, and in the absence of such proof they assume that their argument is true.
If we could go back in time to distant ages, when people believed that the Eearth was flat, the advocates of such theory could falsely assert that "since no one had been able to prove that the Earth was round, then it was certainly flat." So we can see that the fallacious arguments are not consistent, so they do not produce true conclusions.
Principle of Non-Contradiction
One of the principles of logic, the "Principle of non-contradiction," states that a premise cannot be false and true simultaneously, that is, a thing cannot "be" and "not be" at the same time, because the truth of one of them automatically cancels the other one. Contradiction consists of a logical incompatibility between two or more statements.
Example:
Premise 1: No mammals lay eggs
Premise 2: The platypus is a mammal, but it lays eggs
The two premises above are completely incompatible because, if the first one is true (no mammal lays eggs), the second one (the platypus is a mammal, but it lays eggs) must be false. On the other hand, if the second premise is true, the first premise will be false. In this way it is impossible for the two premises to be true at the same time, since one contradicts the other.
Using Logic to invalidate dogmas
In our work we will often use logic to identify the contradictions in religious dogmas, as exemplified in the argument below:
Premise 1: The forgiveness of God is infinite.
Premise 2: God does not forgive after death.
In the above argument, we find a clear contradiction between the premises: “Infinite” is something which has no end, so the infinity of a quality completely excludes the possibility of the existence of a contrary quality that would diminish or annul it. The first premise affirms that Divine Forgiveness is infinite, but the second one presents a situation (after death) in which Divine forgiveness "ceases to exist", that is, it has a limit, it is finite. But something cannot be "finite" and "infinite" at the same time.
Therefore, we can say that logic is the best tool to help us find out the truth, or come as close to the truth as possible, because through it we can demonstrate the consistency or not of an argument, in an absolutely impartial way, free from any kind of dogmas and "Absolute truths".