013. Not The Rapper

tldr: it is fun to be logical

I have talked a bit before about how I like Philosophy and took a Symbolic Logic course last semester (Blog 05. The Duality of a Double Major). Upon further conversations however, I very quickly realized that not many people know what a logic class entails– and thus, a blog idea was formed. In some parts of this blog I will shorten Symbolic Logic to SL for simplicity. This won’t be every nook and cranny of the class, but rather just an outline of what we covered.

Simply put, Symbolic Logic tries to represent everyday human language and meaning in terms of symbols. The point of the class is to take the logic of our language and our understanding of the world, and have a way of representing it on paper. If/when we symbolize our thinking, we can (logically) manipulate the symbols to prove arguments are valid.

Here is an example:
– All cats are animals.
– Garfield is a cat.
– Therefore, Garfield is an animal.
We should know logically, this argument is valid (meaning that if the premises are true, the conclusion must be as well). Proving that it is valid however, requires a process– one that is learned in a class like SL. But why is this a philosophy class? [I am glad you asked, Paige] If I propose an ethics argument, if said argument is illogical, then why even bother debating it? For instance:
– All acts of killing are wrong.
– Abortion is an act of killing.
– Therefore, abortion is wrong.
I EXTREMELY disagree with this argument, but it is undeniably a *valid* one. If the premises are true, then the conclusion has to be as well. I, like many others, fundamentally disagree with the premises, and that is where a debate can happen. On the other hand, such a debate would have been frivolous if the argument was *invalid* to begin with.

The first part of the class was essentially definitions and classifications (for instance, the new definition of valid that may be different from how we usually understand it. Which is valid. Wait.). The second part is where it started to get interesting in my opinion. Here we started learning Propositional Logic (sometimes called Sentential Logic). This is where we learned how to start writing sentences in terms of symbols, with symbols standing for ‘and’, ‘or’, ‘not’, ‘if…then’, and ‘if and only if’. From there we learned how these symbols (“operators”) affected truth. For instance
– ‘I like math AND I like philosophy’.
is only true if I like BOTH of them. I will do one more example:
– ‘I like math OR I like philosophy’.
is only false if I DON’T like BOTH of them. This was the building blocks to start doing proofs.

If you have done some proofs, it is the same idea. We try to derive a given conclusion from the premises following certain LOGICAL steps [from a given list]. For instance, one logical step is double negation:
– ‘I am not not gay’ can be turned into ‘I am gay’.
What makes these proofs difficult is knowing what steps are useful for getting from the premises to the conclusion, but it mostly takes practice.

Finally, the third part of the class was about Predicate Logic. This type builds on Propositional Logic with a few added symbols: ‘there exists something x‘, ‘for all x‘. Note: the x‘s are variables, just like algebra. Using these new symbols, we could now represent new sentences such as:
– ‘There exists something that is mental, and there exists something physical, but there does not exist something that is both mental and physical.’
Further, with these new symbols comes new logical steps we can perform. For instance:
– ‘All dogs have fleas’ can be turned into ‘There does not exist a dog that does not have fleas’.

That was it. Some SL classes emphasize the mathematical side more (such as set notation). My professor made it more language based. He taught why certain statements and logical steps make sense. And they should make sense! We are fundamentally logical people. All we are trying to do is symbolize our thinking.

I love this course. It (similar to other math classes like Linear Algebra) forces you to see things from a new light and critically think about every step you perform. Also! This class starts from complete scratch! At this point in one’s education, is very rare that a class requires *no* prior knowledge. From here, logic can go into a few different areas. You could look into the philosophy of language or mathematical logic– but what I am most interested in is Metalogic. Simply put: symbolic logic focused on the logic of OUR world- human language and understanding of it; metalogic is logic that can be applied to ALL worlds- regardless of language and our ability to understand it. Can’t wait til I learn more about it- and I hope you have a better understanding of what I mean by logic. I do not mean the rapper.


Published by Paige Bright

Hi- my name is Paige Alexandria Bright. I am a rising junior at MIT interested in mathematics and philosophy. I have been writing this blog since the beginning of COVID. Lets see where this goes.

3 thoughts on “013. Not The Rapper

  1. oh lmao. did you know the philosophy department offers several logic classes which technically count for the hass requirement but are basically math classes content-wise because the math department only offers like two logic classes

    Liked by 1 person

    1. I did! A big part of why I want to double major in philosophy– a lot of my HASSES will be in the subject anyways so why not just take a the few extra classes to major in it. Although I wish there were more math logic classes.


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