Ethical Realism

October 10, 2012

What is Logic?

Filed under: philosophy — JW Gray @ 6:10 am
Tags: , , , ,

Logic is a domain of philosophy concerned with rational criteria that applies to argumentation. Logic includes a study of argumentation within natural language, consistent reasoning, valid argumentation, and errors in reasoning. It is divided into two main domains: Formal and informal logic.

Formal logic

Formal logic is the traditional domain of logic in western philosophy. It is a domain that covers logical form, consistency, valid argumentation, and logical systems.

Logical form

Logical form allows us to symbolize statements by stripping statements of their content. For example, consider the statement “if it will rain today, then the roads will become slippery.” The logical form of this statement would be presented in propositional logic as “if A, then B.” In that case “A” stands for “it will rain today” and “B” stands for “the roads will be slippery.” Logical connectives are kept, such as “if,” “and,” “or,” and “not.”

Logicians don’t usually write statements as “if A, then B.” Instead, they usually use a symbol for logical connectives, such as “→.” We can state “if A, then B” as “A → B.”


Two statements are consistent if it’s possible for them both to be true at the same time. For example, the statement “if it will rain today, then the roads will be slippery” is consistent with the statement “it will not rain today.” Logic provides us with a way to determine when statements are consistent, which is important to us because all true statements about the world are consistent. (Two true statements can never form a contradiction. For example, “Aliens live on another planet” and “aliens don’t live on another planet” form a contradiction, so one of the statements is false.)

We know that two statements are consistent as long as they can all be true at the same time, and contradictory when they can’t. Whenever two propositions contradict, one proposition can be symbolized as “A” and the other can be symbolized as “not-A.” For example, “it will rain today” contradicts “it will not rain today.”

Some statements are also self-contradictory, such as “one person exists and no people exist.” Many self-contradictions can be symbolized as “A and not-A.” These statements are always false.

Tautological statements are always true, such as “either the Moon revolves around the Earth or the Moon doesn’t revolve around the Earth.” Many tautologies can be symbolized as “A or not-A.”

Valid argumentation

A valid argument has an argument form that could never have true premises and a false conclusion at the same time. For example, “If it will rain today, then the roads will be slippery. It will rain today. Therefore, the roads will be slippery” is valid because it has the argument form “If A, then B. A. Therefore, B.” All arguments with this form are valid.

Logic gives us the tools to determine when an argument is logically valid. If a deductive argument is not logically valid, then it does not provide us with a good reason to agree with the conclusion. If the premises are true, then the conclusion could still be false.

An example of an invalid argument is “At least one person exists. If at least one person exists, then at least one mammal exists. Therefore, no mammals exist.” Although the premises are true, the conclusion is false. This argument does not do what arguments are supposed to do—provide us with a good reason to think the conclusion is true.

Logical systems

Logical systems have (1) a formal language that allows us to symbolize statements of natural language, (2) axioms, and (3) rules of inference.

  1. A formal language is a way we can present the form of our statements involving logical connectives.
  2. Axioms are rules, such as the rule that states that contradictions can’t exist.
  3. Rules of inference are rules that state what premises can be used to validly infer various conclusions. For example, a rule known as “modus ponens” states that we can use “A” and “if A, then B” as premises to validly infer that “B.”

Logical systems are needed in order for us to best determine when statements are consistent or when arguments are valid.

Informal logic

Informal logic is domain that covers the application of rational argumentation within natural language—how people actually talk. What we call “critical thinking” is often said to involve informal logic, and critical thinking classes generally focus on informal logic. Informal logic mainly focuses on rational argumentation, the distinction between inductive and deductive reasoning, argument identification, premise and conclusion identification, hidden assumption identification, and error identification.

Rational argumentation

Arguments are a series of two or more statements including premises (supporting statements) and conclusions (statements that are supposed to be justified by the premises). For example, “All human beings that had lived in the distant past had died. Therefore, all human beings are probably mortal.”

The idea of rational argumentation is that it is supposed to give us a good reason to believe the conclusion is true. If an argument is good enough, then we should believe the conclusion is true. If an argument is rationally persuasive enough, then it would be irrational to think the conclusion is false. For example, consider the argument “All objects that were dropped near the surface of the Earth fell. Therefore, all objects that are dropped near the surface of the Earth will probably fall.” This argument gives us a good reason to believe the the conclusion to be true, and it would seem to be irrational to think it’s false.

The distinction between deductive and inductive reasoning

Deductive arguments are meant to be valid. If the premises are true, then the conclusion is supposed to be inevitable. Inductive arguments are not meant to be valid. If the premises of an inductive argument are true, then the conclusion is supposed to be likely true. If an inductive argument is strong and the premises are true, then it is unlikely for the conclusion to be false.

An example of a valid deductive argument was given above when valid arguments were discussed. Let’s assume that “if it will rain today, then the roads will be wet” and that “it will rain today.” In that case we have no choice but to agree that “the roads will be wet.”

An example of a strong inductive argument was given in the argument involving dropping objects. It is unlikely that dropped objects will not fall in the future assuming that they always fell in the past.

Argument identification

Knowing what arguments are and why people use them helps us know when people give arguments in everyday conversation. It can also be helpful to know the difference between arguments and other similar things. For example, arguments are not mere assertions. A person who gives a mere assertion is telling you what she believes to be true, but a person who gives an argument tells you why she believes we should agree that a conclusion is true.

Premise and conclusion identification

Knowing what premises and conclusions are helps us know how to know which are which in everyday conversation. For example, a person can say “the death penalty is wrong because it kills people.” In this case the premise is “the death penalty kills people” and the conclusion is “the death penalty is wrong.”

Hidden assumption identification

Knowing that an argument is meant to be rationally persuasive can help us realize when hidden assumptions are required by an argument. For example, the argument that “the death penalty is wrong because it kills people” requires the hidden assumption that “it’s always wrong to kill people.” Without that assumption the argument will not be rationally persuasive. If it’s not always wrong to kill people, then perhaps the death penalty is not wrong after all.

Error identification

Knowing about several errors of reasoning (i.e. fallacies) can help us know when people have errors of reasoning in arguments they present in everyday conversation. For example, the argument “my friend Joe never died, so no person will die in the future” contains an error. The problem with this argument is the unjustified assumption that we can know what will happen to everyone in the future based on what happened to a single person given a limited amount of time. This type of error is known as the “hasty generalization” fallacy.

What’s the difference between logic and epistemology?

Epistemology is the philosophical study of knowledge, justification, and rationality. It asks questions, such as the following:

  1. What is knowledge?
  2. Is knowledge possible?
  3. What are the ways we can rationally justify our beliefs?
  4. When it is irrational for a person to have a belief?
  5. When should a person agree that a belief is true?

These issues are highly related to logic, and many philosophers have equated “logic” with “epistemology.” For example, the Stoic philosophers included epistemology in their domain of “logic.”

I believe that logic should now be considered to be part of the domain of epistemology. However, for educational purposes it is considered to be a separate subject and it’s not taught in epistemology classes.

Logic classes deal with argument form and certain rational criteria that applies to argumentation, but epistemology classes generally deal with somewhat abstract questions, as were listed above. Perhaps one of the most important issues that logic deals with much less than epistemology is justification—logic tends not to tell us when premises are justified and how well justified they are, but epistemology attempts to tell us when premises are justified, and when a premise is justified enough to rationally require us to believe it’s true.

Why do logic and epistemology classes teach different things? Perhaps because philosophers who have an interest in epistemology have historically not cared as much about logic and vice versa.

But why would philosophers who care about epistemology not care as much about logic? Perhaps because logic tends to be concerned with issues that can be answered with a much higher degree of certainty. We know what arguments are. We know that good arguments must apply certain rational criteria. We can determine when arguments are valid or invalid. We can determine that many arguments have hidden premises or various errors. However, we can’t determine the nature of knowledge, justification, and rationality with that degree of certainty. It is more controversial when a belief is justified and at what point a belief is justified enough to rationally require us to believe it’s true.

What is the essence of logic?

I don’t think that logic has an essence. It’s a domain concerned with certain rational criteria involved with argumentation, but not all criteria. Epistemology also covers related issues. What we consider to be logic or epistemology mainly has to do with a history of philosophers (and mathematicians) who label themselves as “logicians” or “epistemologists” and teach classes in the corresponding domains. These terms are used merely because they are convenient to us.

However, I think we can say that logic is a domain of epistemology that has a restricted focus, and that focus is mainly restricted to issues that we think we can answer with a much higher degree of certainty than usual. Logic and mathematics are now often taken to be part of the same domain, and both generally offer us with a degree of certainty higher than the natural sciences. Whenever scientific findings conflict logic, we are much more likely to think that our scientific findings are false than that our understanding of logic is false.

The same can not be said of epistemology once logic is removed from it. There are examples of epistemological issues that do seem to involve a great deal of certainty. I think we should be confident that we should believe that “1+1=2” and that it’s irrational to believe that “1+1=3.” Epistemology tells us what we should believe in that sense. However, there is also a great deal of uncertainty that is usually involved with epistemology. The big questions in epistemology are still very controversial.

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  1. I think there are more perspicuous reasons logic and epistemology are usually regarded as separate areas of research. The first has to do with the difference between valid inference and rational belief revision, which gets a good treatment in Harman’s article ‘Logic and Reasoning’, Synthese (1984). The other has to do with closure of knowledge under logical consequence, which has been contested by, e.g. Nozick. These articles suggest in different ways that the subject matter of logic is only obliquely connected to the core concerns of epistemology.

    Comment by Colin Caret — October 14, 2012 @ 7:11 pm | Reply

    • Could you elaborate on that a bit? I’m not quite sure exactly what you are saying. How exactly is logic only obliqely connected? The informal fallacies actually are concerned with how justified premises are. There’s also probability involved. I think I’ve also said a lot to suggest it’s somewhat clear how they are connected.

      I don’t think logic is only concerned with “logical consequence” or “valid inference.” That only concerns deduction, but logic also has a lot to say about inductive reasoning. Perhaps those philosophers are only talking about “formal logic.”

      Comment by JW Gray — October 14, 2012 @ 7:41 pm | Reply

      • Hi, sorry yes you are right, I was being too hasty and identifying logic with deductive logic. So my point has more to do with the connection between deductive logic and epistemology. But if we expand logic to include all of inductive, abductive, and informal ‘critical’ reasoning, perhaps also processes of belief revision, then there is a strong connection between this wide range of phenomena and epistemology.

        To elaborate on my claim from before, the main issue Harman argues for is that it is not always rational to update our beliefs by deductive inference, and Nozick argues that our state of knowledge is not always closed under deductive inference. Again, these are restricted to deductive logic. Here is a particularly interesting example: you might think there is at least one obvious connection between deductive logic and epistemology, something like an epistemic obligation not to believe anything logically inconsistent. Harman argues that even this isn’t true. The reason, he claims, is that any rational agent ought to believe that at least one of his/her beliefs is false; if this belief is true then one of the agent’s other beliefs is false; if the rest of the agent’s beliefs are true then this belief is false; so, necessarily, a rational agent ought to have beliefs which are inconsistent.

        Comment by Colin Caret — October 14, 2012 @ 9:48 pm

      • Thank you for the clarification. I agree with the conclusions of the philosophers you mention. I personally think it can be rational to have inconsistent beliefs if we have two beliefs that are highly justified and no way to resolve which is false. Deduction is only part of the picture and should not replace epistemology or anything like that.

        Comment by JW Gray — October 14, 2012 @ 10:18 pm

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  6. ever read “the laws of form” by g spenncer brown?

    Comment by jon.e.whiteford — October 22, 2012 @ 1:26 am | Reply

  7. What is logic? I can give you a very simple answer. Never believe anything that cannot be proven. This is a permanent shield that will defend you from any mythology, ideology, sociology, political idea, or accepted theory presented as fact. You don’t need a greek philosopher or an exotic religion. You just need your brain, freethought, and an iron resolve to never believe anything that cannot be proven. That which remains, that can’t be answered, be honest, and say, I don’t know.” It’s easy. The search ends for that which is not there, and you can separate yourself from the war and hatred. But the bad news is your are still going to die, and there is no afterlife. That is real logic. Are you ready?


    Comment by NeoWolfe — October 30, 2012 @ 2:51 am | Reply

    • NeoWolf, I have the impression that you have never taken a logic class. Both logic and philosophy have a lot to offer as far as thinking rationally is concerned. Using our brain is not sufficient to think rationally. We make mistakes in our thinking all the time. However, logic and philosophy education go a long way in correcting those mistakes.

      Comment by JW Gray — October 30, 2012 @ 3:57 am | Reply

      • Well, Mr. Gray, I can think quite rationally. And you are correct that I have never wasted a single dollar on logic classes. And neither has the world you hope to win for freethought. Especially difficult since you have not found it yourself. You have said yourself, that atheist heroes like Richard Dawkins envision a possibility of a spark behind the universe. Granted, none of them, Dawkins, de Grasse, etc have ever expressed a belief in the idea, they do not demonstate the huberous to discount it. These are the great freethinkers of our generation.
        So, you think you see the universe in a clearer light. Good luck with that and your logic classes.
        I see the universe from the point of view of the liberated brainwashed, and I think you would like to see the rest of us liberated, as would I. Your arrogance and huberous is why all your expended cartridges end up in your foot. If you want to succeed get the hell out of the way. Atheism is religion because it presumes facts not in evidence. People arising out of the brainwash want no part of a new religion. They want real logic, which is based upon current scientific understanding which leaves one conclusion only, based on logic : “I don’t know”. Now, if you want to prove to us the universe is an accident, present the evidence. Is that too much to ask? If you are not ready, maybe you should stop calling freethinkers “TROLLS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!”


        Comment by NeoWolfe — November 6, 2012 @ 1:41 am

      • I hope you can think quite rationally. Everyone has a limited understanding of logic. However, their understanding is limited and they make mistakes. That is why fallacies are so common and effective. People are manipulated by the media precisely because they are not entirely rational. We suffer from biases. Logic can help us fight against manipulation and make less mistakes in our thinking.

        Without the existences of logic classes you wouldn’t be typing on a computer right now. Computers use formal logical systems that were originally invented by philosophers. Mathematicians also require logic and have helped develop logic. Higher level mathematics could not exist without the logic that philosophers created.

        Comment by JW Gray — November 6, 2012 @ 3:43 am

  8. I have a link above about what you need from formal logic. It explains at least some reasons about why it is important in detail. To dismiss everything I say there out of hand is not a good idea. If you want to know why logic as philosophers discuss it is important, then you should try to find out for yourself.

    Comment by JW Gray — November 8, 2012 @ 5:28 am | Reply

  9. […] What is logic? James Gray | Ethical Realism […]

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