The word ‘logic‘ is not easy to define, because it has slightly different meanings in various applications ranging from philosophy, to mathematics to computer science. In philosophy, logic determines the principles of correct reasoning. It’s a systematic method of evaluating arguments and reasoning, aiming to distinguish good (valid and sound) reasoning from bad (invalid or unsound) reasoning.
The essential difference between informal logic and formal logic is that informal logic uses natural language, whereas formal logic (also known as symbolic logic) is more complex and uses mathematical symbols to overcome the frequent ambiguity or imprecision of natural language. Reason is the application of logic to actual premises, with a view to drawing valid or sound conclusions. Logic is the rules to be followed, independently of particular premises, or in other words using abstract premises designated by letters such as P and Q.
So what is an argument? In everyday life, we use the word ‘argument’ to mean a verbal dispute or disagreement (which is actually a clash between two or more arguments put forward by different people). This is not the way this word is usually used in philosophical logic, where arguments are those statements a person makes in the attempt to convince someone of something, or present reasons for accepting a given conclusion. In this sense, an argument consist of statements or propositions, called its premises, from which a conclusion is claimed to follow (in the case of a deductive argument) or be inferred (in the case of an inductive argument). Deductive conclusions usually begin with a word like ‘therefore’, ‘thus’, ‘so’ or ‘it follows that’.
A good argument is one that has two virtues: good form and all true premises. Arguments can be either deductive, inductive or abductive. A deductive argument with valid form and true premises is said to be sound. An inductive argument based on strong evidence is said to be cogent. The term ‘good argument’ covers all three of these types of arguments.
Deductive arguments
A valid argument is a deductive argument where the conclusion necessarily follows from the premises, because of the logical structure of the argument. That is, if the premises are true, then the conclusion must also be true. Conversely, an invalid argument is one where the conclusion does not logically follow from the premises. However, the validity or invalidity of arguments must be clearly distinguished from the truth or falsity of its premises. It is possible for the conclusion of a valid argument to be true, even though one or more of its premises are false. For example, consider the following argument:
Premise 1: Napoleon was German
Premise 2: All Germans are Europeans
Conclusion: Therefore, Napoleon was European
The conclusion that Napoleon was European is true, even though Premise 1 is false. This argument is valid because of its logical structure, not because its premises and conclusion are all true (which they are not). Even if the premises and conclusion were all true, it wouldn’t necessarily mean that the argument was valid. If an argument has true premises and its form is valid, then its conclusion must be true.
Deductive logic is essentially about consistency. The rules of logic are not arbitrary, like the rules for a game of chess. They exist to avoid internal contradictions within an argument. For example, if we have an argument with the following premises:
Premise 1: Napoleon was either German or French
Premise 2: Napoleon was not German
The conclusion cannot logically be “Therefore, Napoleon was German” because that would directly contradict Premise 2. So the logical conclusion can only be: “Therefore, Napoleon was French”, not because we know that it happens to be true, but because it is the only possible conclusion if both the premises are true. This is admittedly a simple and self-evident example, but similar reasoning applies to more complex arguments where the rules of logic are not so self-evident. In summary, the rules of logic exist because breaking the rules would entail internal contradictions within the argument.
Inductive arguments
An inductive argument is one where the premises seek to supply strong evidence for (not absolute proof of) the truth of the conclusion. While the conclusion of a sound deductive argument is supposed to be certain, the conclusion of a cogent inductive argument is supposed to be probable, based upon the evidence given. Here’s a classic example of an inductive argument:
- Premise: Every time you’ve eaten peanuts, you’ve had an allergic reaction.
- Conclusion: You are likely allergic to peanuts.
In this example, the specific observations are instances of eating peanuts and having allergic reactions. From these observations, you generalize that you are probably allergic to peanuts. The conclusion is not certain, but if the premise is true (i.e., every time you’ve eaten peanuts, you’ve had an allergic reaction), then the conclusion is likely to be true as well.
Whilst an inductive argument based on strong evidence can be cogent, there is some dispute amongst philosophers as to the reliability of induction as a scientific method. For example, by the problem of induction, no number of confirming observations can verify a universal generalization, such as ‘All swans are white’, yet it is logically possible to falsify it by observing a single black swan.
Abductive arguments
Abduction may be described as an “inference to the best explanation”, and whilst not as reliable as deduction or induction, it can still be a useful form of reasoning. For example, a typical abductive reasoning process used by doctors in diagnosis might be: “this set of symptoms could be caused by illnesses X, Y or Z. If I ask some more questions or conduct some tests I can rule out X and Y, so it must be Z.
Incidentally, the doctor is the one who is doing the abduction here, not the patient. By accepting the doctor’s diagnosis, the patient is using inductive reasoning that the doctor has a sufficiently high probability of being right that it is rational to accept the diagnosis. This is actually an acceptable form of the Argument from Authority (only the deductive form is fallacious).
References:
Hodges, W. (1977) Logic – an introduction to elementary logic (2nd ed. 2001) Penguin, London.
Lemmon, E.J. (1987) Beginning Logic. Hackett Publishing Company, Indianapolis.
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From ChatGPT-4: Logic is a branch of philosophy that deals with principles of reasoning and inference. It’s a system or set of principles that guides us in making valid arguments and distinguishing good reasoning from bad reasoning.
Logic can be symbolic or mathematical, where symbols are used to represent abstract ideas and relationships, and the reasoning process is carried out according to specific rules. This is often seen in areas like computer science, mathematics, and linguistics.
There are several types of logic, including:
Deductive Logic: This is reasoning from the general to the specific. For example, if we know that all men are mortal and Socrates is a man, we can deduce that Socrates is mortal.
Inductive Logic: This is reasoning from the specific to the general. For example, if we observe that the sun has risen every day for thousands of years, we might conclude that the sun will rise tomorrow.
Abductive Logic: This is reasoning from the best available explanation. For example, if the road is wet, the most reasonable explanation might be that it has rained recently.
Modal Logic: This deals with possibility and necessity. For example, it could be possible that it will rain tomorrow, but it’s not necessarily the case.
Logic forms the foundation of scientific methods, mathematical proofs, and many other areas where clear and precise thinking is required.
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Here’s another article on this topic. https://www.fs.blog/2018/05/deductive-inductive-reasoning/
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In reply to Tim Harding’s post of December 13, 2015 at 12:02 pm:-
Yes, now I understand. This gentleman is a professor of Astrophysics. Thanks for clarifying this as I was quite puzzled by his not agreeing to this.
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Do you agree or disagree with the following and why:-
As logic does not apply to things but only to thoughts, statements, propositions and theories etc. about things, so there can be no logical or illogical planets, galaxies or worlds etc. but only logical or illogical propositions etc. about planets,galaxies or worlds etc.
Similarly when some people claim that quantum physics has shown that the world is Illogical, they are making a mistake as only quantum theory can be logical or illogical and not the world.
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I agree with this view. Logic is part of social reality rather than physical reality. The relevant test is whether logic would exist in a world without human beings or other animals capable of applying logic. I say logic would not exist in those circumstances. The deterministic laws of cause and effect would still apply, but they are different to logic.
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Thank you Tim Harding for your prompt answer. This is what I also said in a discussion with a University professor but he did not agree with me.
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It could turn on a different definition of ‘logic’ – some physicists seem to equate logic with determinism – probably because they have not studied philosophy and refuse to do so.
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You’re welcome. If by ‘self-evident’ you mean the avoidance of contradictions, then I would agree.
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I thought of the same example when posing the question and was really struck by how simple, tautological and “self-evident” (at least they seem so now) those three laws of Aristotle’s are.
I can’t thank you enough for your responses and time. You’ve really clarified things for me.
Dka
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I think I used self-evident because of certain forms like A > B, B >C, A > C which seemed a bit different then others but I guess it’s still deductive.
Do you think that new knowledge can come from deduction? I heard someone say this and the only thing I can think of is that while deduction may be tautological or something akin you do need this seemingly obvious, innate process to draw conclusions out of premises. (Not that logic doesn’t becomes difficult at higher levels.)
And do the laws or rules of logic go back to Aristotle? In reading it appears his three basic laws–identity, contradiction, excluded middle–are logic’s backbone, at least at base levels.
Thanks so much.
D
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Yes, I do think that new knowledge can come from deduction. For instance, if you didn’t know that A>C, but you knew that B>C and A>B, then you could deduce that A>C and that would be new knowledge from your perspective. Yes, the basic rules of deductive logic go back to Aristotle. He discovered 13 logical fallacies.
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Would you say that all reasoning is essentially tautological or self-evident in nature regardless of it’s complexity?
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No, I wouldn’t go that far. I suspect you mean deductive reasoning, but there is also inductive and abductive reasoning, which are not tautological at all. The term ‘self-evident’ is a response of the reader, rather than a logical term.
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Would it be correct to say deductive logic is a natural cognitive process which we also call inference or reasoning. At a simple level, don’t we all do it properly. And when done properly aren’t the conclusions redundant because they already reside within the premises So what exactly is this process, how can it be described, why do we naturally do it.?
As to formal logic, could it be said that it’s a set of rules applied to arguments to insure they’re valid and that these rules are based off our natural deductive process that we properly perform at a basic level?
Thanks,
D
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Formal logic simply uses symbols instead of words. Deductive logic doesn’t really rely on mental processes – it is just the avoidance of contradictions. Perhaps an example might help. See:
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Under the heading of Deductive Reasoning on April, 7 you give a riddle about a white and black haired boy and girl. In figuring that out, what process did I go through? What process does say Sherlock Holmes perform to find the culprit? And does this relate to deductive logic.
Seems you’re telling me that logic isn’t about figuring anything out but just a set of rules to see if an argument is valid. But isn’t the validity of all deduction–at least syllogisms like you posted above– tautology? i think this is why I’ve been saying that deductive logic doesn’t do anything.
Thanks.
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It’s a long time since I read any Sherlock Holmes detective stories, but my recollection is that he used deduction and abduction (see my article above), as today’s detectives still do.
You may be right saying that deduction doesn’t add anything – except clarity. Its usefulness is more in avoiding errors of reasoning.
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I’ve been having trouble describing deduction. Induction is easy to describe: it’s concluding based on observation. But deduction isn’t so easy. it seems to me that it really does nothing at all, that it’s self-evident. All men are mortal and Socrates is a man. Of course we conclude, then, that Socrates is mortal because we’ve already established men are mortal. I suppose it’s important for navigating the world and validating arguments/claims but it just seems very hard to describe.
Thanks.
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Deductive logic works not because the premises are true, but because of the structure of the argument e.g ‘If all As are Bs, then if this is an A it must be a B.’ If this A was not a B, then that would contradict the first premise that all As are Bs. Thus deductive logic is about internal consistency, or the avoidance of contradictions.
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