Logic is a little tweeting bird, chirping in a meadow. Logic is a wreath of pretty flowers, that smell bad.
Spock (fictional character), I Mudd
Logic is concerned with the form of an argument. One of the simplest argument forms is as follows:
Paul is taller than Peter.
John is taller than Paul.
Therefore John is taller than Peter.
We do this kind of deduction all of the time in our daily lives. It follows a standard logical form with which we are all familiar (even if we didn’t know that it is a “standard logical form”). The next deduction follows the same logical form:
Paul is better than Peter.
John is better than Paul.
Therefore John is better than Peter.
Here, we have simply replaced the relational operator ‘taller’ for a new one – ‘better’ – in every occurrence of the derivation. We can also replace the nouns in the derivation without changing the form, as long as we replace them consistently throughout. So, replacing Paul, Peter, and John, we get:
X is better than Y.
Z is better than X.
Therefore Z is better than Y.
This gives us the general form, which will be true for any X, Y, and Z. (Stick with me here!) So, if we do the substitution:
Nothing is better than eternal happiness.
A dollar is better than nothing.
Therefore a dollar is better than eternal happiness.
Something has gone wrong here. Of course, it has to do with the way the word “nothing” is being used (in two different ways). The point is that logic is only irrefutable when in a strictly symbolic form – once you start to substitute actual words into the formulae you immediately run the risk of making a mistake.
Logic never adds information – it only reshuffles it. Logic is an internally consistent system with no direct bearing on real life. Logic is not only tricky, it is, in fact, irrelevant in most situations. A logician named Schiller once wrote that:
The central doctrine of the most prevalent logic still consists of a flat denial of relevance.
quoted in The Philosophy of Logics by Susan Haack
To be fair, logic has its place in day to day life. It is an essential aspect of communication. Wittgenstein points out that logic is embedded in human language. If you want to communicate appropriately, you need to make logically coherent statements. However, many of the most important aspects of life cannot be directly communicated. You must give up the idea that logic will somehow answer the most important questions in life.
There’s a flaw in your last syllogism that ought to be obvious. The implied meaning of the word “nothing” changes from the first premise to the second premise. That is why the logic breaks down. It’s not that logic fails, but that there’s an intended deception in the argument.
To clarify, reword the premises in this way:
1. There is nothing in existence that is better than eternal happiness.
2. Owning a dollar is better than owning nothing.
3. Therefore owning a dollar is better than eternal happiness.
It’s quite obvious now that the conclusion (3) does not follow from the two premises (1 and 2).
But anyone with a smattering of common sense could spot that logical fallacy in an instant, which is why that example is used as a humorous joke and not intended as a serious logical proof.
The real breakdown of this article occurs in the initial statement, “Logic is concerned with the form of an argument.” Actually, logic is the art and science of reasoning correctly. The study of logic does involve studying forms of argumentation, however there is much more to logic than merely the form in which an argument is presented. Logic, when handled correctly, does not have “its own set of paradoxes.” The paradoxes occur when people employ logical fallacies, that is, false statements that mimic the form of a logical argument yet are not truly logical.
In the Bible, the Pharisees attempt to use logical fallacies to trap Jesus, but Jesus uses logic to reveal the error in the Pharisees’ argument and to stump them at their own game.
Thus, a proper understanding of logic CAN help you. Just because an argument seems logical doesn’t mean that it is logical.
Hi Tim, and thanks for reading!
Firstly, let me say that I often write posts somewhat tongue-in-cheek with the express purpose of pushing people out of their regular thinking habits. That said, there is an important point to my post, which I will elaborate below, using your comments as a structure:
You: “There’s a flaw in your last syllogism that ought to be obvious. The implied meaning of the word “nothing” changes from the first premise to the second premise. That is why the logic breaks down.”
Me: Yes, that’s stated in the post as: Hint: It has to do with the definition of “nothing”. I’m quite aware of this, and of course your clarification does just that (clarify). However, the bigger picture issue is that language is inherently approximate and therefore these types of false conclusions happen every day. (For more on language being approximate, keep an eye out for some of my posts on Wittgenstein.)
You: “ ‘Logic is concerned with the form of an argument.’ Actually, logic is the art and science of reasoning correctly.”
Me: I’m sorry to disagree with you. I can assure you that logic is based on syllogisms and that those syllogisms which — while guaranteeing correctness and completeness — do not add any information. Thus, “logic will not help you” is correct because without actual information, logic just shuffles the information around, creating usually unsurprising results such as:
If P then Q
P
therefore Q
(modus ponens)
and
If P then Q
not Q
therefore not P
(modus tollens)
For more examples of valid inference rules of logic:
https://en.wikipedia.org/wiki/List_of_rules_of_inference#Rules_of_classical_predicate_calculus
For more on the correctness and completeness of first-order predicate logic, I suggest this book which I had to fully digest and memorize in graduate school:
https://www.amazon.com/Metalogic-Introduction-Metatheory-Standard-First/dp/0520023560/ref=sr_1_7?keywords=meta-logic&qid=1575136608&sr=8-7
What logic does not allow is “stuff” that rational people do every day, such as abductive reasoning (https://en.wikipedia.org/wiki/Abductive_reasoning) and generalizing from a single data point:
Joe ate one of those berries and then died.
I will not eat one of those berries because I will probably die.
This last example is probably one of the reasons homo sapiens survived. But it is not deductively valid; in fact, it is not really even inductively valid. Yet it has survival value. This is what I mean by “logic will not help you.”
You: “Logic, when handled correctly, does not have ‘its own set of paradoxes.’ ”
Me: I’m sorry to disagree with you again. I draw your attention to:
Zeno’s paradoxes: https://en.wikipedia.org/wiki/Zeno%27s_paradoxes
Russell’s paradox: https://en.wikipedia.org/wiki/Russell%27s_paradox
Godel’s incompleteness theorem: https://en.wikipedia.org/wiki/ G%C3%B6del%27s_incompleteness_theorems
Tarski’s undefinability theorem: https://en.wikipedia.org/wiki/Tarski%27s_undefinability_theorem
(I include references to Wikipedia for general information; of course there is more detailed information available on all of these.)
In the end, I agree that logic can be somewhat useful but, as is discussed in my other posts, logic cannot help one to determine answers to the biggest questions in life. (Right now I only have a rotating window of three posts showing on the site, but keep an eye out if you are new to the site.)
Thanks again for your comment and please keep reading!
I’ve updated the original post both here and in the book to add some explanation about the nature of logic. I’ve spent a fair portion of my academic life studying logic and I’m confident of my take on it. However, the reader should look into this him/her-self by looking at the sources in the Reading List.