Logic
Logic is supposedly the science that evaluates arguments.
There are college classes in logic. We use the word all the time. We often call each other illogical, when we disagree. Or we denigrate others’ ideas by showing that the logical implications of their idea would lead to absurdity. “By that logic, such and such would be reasonable…” But are there limitations to logic?
Most of us have probably not studied logic. But we still talk about it like we have.
Logic can be divided into the inductive (where the stronger the argument the more likely the conclusion is true with no guarantees) or deductive, (where a valid argument guarantees the truth of the conclusion, based on the structure [or form, sometimes considered formal logic] of the argument rather than content).
Inductive arguments seem pretty useful. We can use a bunch of facts or data to create a stronger argument. As long as the facts or data support what we are concluding, the argument can be strong. But there are no guarantees in inductive arguments. How useful does that make it?
When we are not focusing on the form of an argument (which we will get to in a minute), we can look at the content and to see if an argument makes sense. Luckily, some medieval scholars catalogued groups of informal fallacies, like fallacies of relevance, presumption, and ambiguity. Despite the fact that arguments using these faulty types of reasoning can seem convincing, they are nevertheless examples of faulty reasoning. These informal fallacies are fantastic at spotting spurious arguments made by politicians or anyone really. But do they help us construct convincing arguments? Maybe that depends on who we are trying to convince and what we are trying to convince them of. People use fallacies all the time to convince other people, and it often works. Maybe the limitation is our ability to spot them?
But what about the form of arguments?
There are different systems of deductive (or formal) logic devised by philosophers. Aristotle had his categorical syllogisms. They took the form of:
All A are B.
All B are C.
Therefore, all A are C.
Or:
All P are Q.
No R are Q.
Therefore, no R are P.
We are dealing strictly with categories and categorical statements here. Each letter stands in for a category. We can make a universal statement (All P are Q, or No R are Q). We can also make particular statements (Some A are B, Some P are not Q). It has rules for making valid deductions. Makes pretty good sense for what it is.
An example
All A are F. All apples are fruits.
All F are P All fruits are plants.
Therefore all A are P. Therefore all apples are plants.
You get the idea.
This is getting boring. Is there a point?
Then there is the propositional calculus, often credited to the 3rd century Stoic philosopher, Chrysippus. It uses letters to stand in for propositions and five symbols to indicate operations:
⊃ conditional, where A ⊃ B means if A, then B
∨ disjunction, where A v B means A or B
•conjunction, where A • B means A and B
~ negation, where ~A means not A
≣ biconditional, where A ≣ B means B if and only if A
We can construct arguments in a variety of forms, and this system also has rules for making valid deductions, called rules of inference. For example, this is a hypothetical syllogism (a valid form):
A ⊃ B
B ⊃ C
—————
A ⊃ C
That translates as if A, then B. If B, then C. Therefore, if A, then C. Basically, if you have A, then you also have C. Doesn’t really matter what the letters stand in for. The form of the argument gets us a valid deduction. But it may lead to absurdity.
If Apples are fruits, then Bulldogs are smelly.
If Bulldogs are smelly, then Crocuses are my favorite flower.
Therefore, if Apples are fruits, then Crocuses are my favorite flower.
That’s a valid deduction. Doesn’t sound like a great argument, that if Apples are fruits (which we know them to be), then Crocuses are my favorite flower (which maybe true). So much for a guarantee! But it doesn’t do much for us in terms of convincing anyone of anything.
This is getting boring. Is there a point?
There is also the quantificational logic, which tries to combine the universality and particularity of categorical statements with the propositional calculus. It gets rather complicated, especially to type, since it uses some additional symbols as quantifiers that are hard to create with a keyboard. We’re not going to dive too deep into that because I don’t want to belabor the point (and, I really don’t remember that much about it).
There is a point?
The point is that when we are having discussions about complicated topics like economic policy or a debate about morality, it is rather difficult to frame our arguments with these systems. Our ideas are rather complex, there is a lot to consider, and we would end up with a mess of symbols that we would then need to try to evaluate for validity. Logic is cool, and can be a great exercise in rigorous thinking. But can it actually help us craft real-life valid arguments or evaluate the validity of real-life arguments? I’m skeptical.
My grad school logic professor used to tell a story about a young Ph.D. student who taught undergrad logic courses. Undergrad kids would always ask this Ph.D. student why they had to study logic. He pointed out that logic is the very best preparation for life because it was really hard and really pointless. Point taken. Seems like a logical argument.
So, maybe there is a certain pointlessness to logic (and life, who knows?). Outside of these formal systems it may be hard to actually prove anything in real life. Math is similar. It is a formal system where we can prove that A2 + B2 = C2, and many other things. But in real life it is hard to prove things that really matter to us, like which food is healthier? Which politician will make the economy better? Which action is the moral action in a certain situation? These are tough things to prove.
Can logic help us prove things that matter to us? Can it actually help us convince anyone of anything?
Maybe this is a dead end?