It was difficult to compose this question. My understanding of logic is limited to simple abstractions and experiences that most people have with it. "2+2 = 4" because it is empirically true that if I take two pencils, and gather two more pencils, the description of that is 4. As an argumentative example, if someone stated that they baked a pie, it is logical to assume that they tried to bake said pie, as it would be absurd to assume that they accidentally baked anything.

This was to illustrate the extent of my understanding of logic, which, by my account, is very primitive.

What are the subjects in logic one must understand?

I read some guide a few months back and it was some 30 pages long with lists of books and subsets of subjects in logic, which seems absurd to me.

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    I would first make a distinction between different types of reasoning. There is deductive reasoning, inductive reasoning, abductive reasoning, etc. I think it is misleading for novices to call everything rational logic. Deductive reasoning is usually what people here call logic. In the streets the most frequently used reasoning is inductive. Many people don't recognize there are distinct TYPES of logic: mathematical, Aristotelian, modal, fuzzy, etc. This is why you should not just use the term LOGIC. You should be specific which one you refer to. – Logikal May 3 '18 at 18:17
  • You used empirical evidence (inductive reasoning) to justify something a priori (“2+2=4”) and you tried to use deductive reasoning to justify an empirical a posteriori claim. You have this exactly backwards. Math is deductive, it isn’t true for empirical reasons and that’s not how we prove math. Similarly, you can’t use deductive reasoning (someone baked a pie so they must have tried to) to justify empirical statements. It is likely that they tried, but you can’t know that they did, unlike in deductive reasoning cases. Look up the problem of induction. – Not_Here Jun 2 '18 at 22:48
  • I’m assuming the guide you are talking about was Peter Smith’s Teach Yourself Logic? That guide is for the field called mathematical logic, which is related to theoretical computer science and the foundations of mathematics. Informal logic/beginning formal logic is of course much more simple. That guide is intended for people who want to understand a very complicated field. – Not_Here Jun 2 '18 at 22:54
  • I would recommend C.A. Whittaker 'Aristotle's De Interpretatione'. It is not a first book on the topic, but once you've grasped the general idea this book will keep you on the straight and narrow. It covers all you need for philosophy.unless you want to become a dialethist. . . . – user20253 Jul 3 '18 at 10:29
  • "2+2 = 4" because it is empirically true" - it's not that simple. You should actually learn language (human thought expressions) in order to understand why is "2+2=4" even meaningful, let alone true. – rus9384 Aug 31 '18 at 19:09

I think there are two aspects to logic which are more important above all others. The first is to understand what makes a valid logical argument. At the moment, mathematics' Proof Theory is probably the most extreme version of that, but you don't need to go that far. The key to this is being able to say "If I start with a set of statements that represent things that mean something true (semantic truth), then here is a set of operations I can do on those statements, regardless of what they truly mean, which result in the production of additional true statements (syntactic manipulation).

To give an example, proof theory will dig into your "2+2 = 4" because it is empirically true that if I take two pencils, and gather two more pencils, the description of that is 4, and argue that "2+2=4" is true regardless of the empirical side. In particular, we typically do not define 4 to be the result of adding 2 + 2. It is usually defined to be the number following the number following the number following the number following the number zero (Peano arithmetic people would write that as Su(Su(Su(Su(0)))) where Su is the "successor function"). Two would be defined as the number following the number zero (written Su(Su(0))). It can then show that 2+2=4 using the rules of Peano arithmetic, which are all manipulations of symbols (such as 0 + a =a and a + Su(b) = Su(a) + b). We also use logic to show that this addition operator has consistent properties like the ones we are used to (such as a + b = b + a).

Note that that entire section was devoted to manipulation of the abstract symbols, without mention of the meaning behind those symbols. That's one half of the story. The other half of the story is being able to determine valid abstract symbols to represent the real life events that you are talking about. Mathematics has Model Theory, which is very good at handling this once you've already abstracted things to mathematical symbols, but philosophy opens the door for many opinion about what abstract symbols and what rules are "valid."

In your example, we can say "If I take two pencils, and gather two more pencils, then the number of pencils I have is well described using 2 + 2 = 4." How do I prove that? I have to convince you that pencils can be represented by numbers, and thus the laws of addition apply to them.

Eventually, I'd recommend everyone read about Tarksi's Semantic Theory of Truth. It's a rather quirky little beast, which you may not agree with, but which is very good for demonstrating the nature of this process of converting meaning into symbols so that an argument can be made.

Finally, I'd pick a few famous systems of logic. A logical proof is only valid if the person admitting the argument believes that kind of logic is true. For example, an argument involving infinity would be rejected by a finitist. I would argue the most influential logic in the Western world is propositional logic, so no matter what you do, it would be worth your time to be familiar with its rules and patterns. Beyond that, it's up to you. Myself, I find First Order Logic to be useful, despite its flaws, but the systems you research are really up to you.

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