Logic

Basics:

The subject of logic is the study of reasoning. More specifically, it is the study of the form of reasoning, i.e., the relations between premises (alleged facts) and conclusions (inference made from the premise(s)). Premises and conclusions are types of statements (sentences that declare something, i.e., a sentence that you may determine to be true or false). When you combine one or more premises with one conclusion, you have an argument (a discourse that attempts to prove something).

• It is raining.
• The blobfish is the national fish of New Zealand.
• I am mad.

• Are you mad?
• Go suck an egg.
• Ouch!

These sentences are, respectively, interrogative (a question used to request information (or make a point in the rhetorical case)), imperative (a command used to tell someone to do something), and exclamatory (a statement that conveys emotions). These types of sentences have different purposes than a declarative sentence. Remember, if you can't evaluate the sentence as true/false, it is not a statement. Do not confuse interrogative sentences with their answers. You may answer True or False to the question Are you mad?, but the sentence itself Are you mad? is neither true nor false. As for exclamatory sentences, sometimes the distinction from declarative sentences is not clear. I have a cookie! can be evaluated as true/false, but the ! indicates that the emotional factor is the focus rather than the statement. Otherwise, one could have simply stated, I have a cookie.

Only declarative sentences will be used in our study of logic.

• The ground outside is wet. It must have rained.
• You stole my lunch, so I'm mad.
• All cars are vehicles, and all vehicles have engines, therefore all cars have engines.

These aren't necessarily "good" arguments (for example, the ground could be wet because of fog/dew, someone hosed the ground, underground water pipes broke, somebody else (or nobody) stole the lunch, there could exist vehicles that have no engine and run on hopes and dreams, etc.), but they are arguments. They use some premise(s) in order to support the conclusion. Logic is not concerned with the contents of the premises, i.e., whether the facts used are accurate or not. Though valuable in its own right, we will not focus on evaluating truth values of statements. Instead, logic is concerned with the form/structure of the argument made. Given the premise(s), does the conclusion make sense? Assuming the premise(s) is/are true, is it reasonable to make this conclusion?

One benefit of focusing on form over content is that it helps to weed out the bad arguments from the not-so-bad arguments. For example, imagine someone trying to prove that God doesn't exist, or We don't exist, or We really exist in a virtual reality/The Matrix/Plato's Cave. In my experience, these discussions usually devolve into a chaotic soup of emotional nonsense. However, people usually arrived at these broad claims through a series of smaller claims and arguments. You can put some order to this chaos by systematically breaking down the parts to these broad claims.

One may reason that primitive humans, trying to cope with forces way beyond their understanding, invented God, and therefore God doesn't exist. Or one may reason that humans are dependent on precedents/ancestors for their existence, and tracing this dependency all the way down to the first being, that first being needed a precedent, an uncaused cause, the precursor to all life, and therefore all of us impermanent life prove the existence of an uncaused cause, i.e., God. In either case, you can evaluate each argument down the line, and weed out those that have flaws in their logic. As for disputing the truth values of each premise, these will be debated till the end of time.