You may remember that yesterday, I said how logic was basically the math of formalized ideas, so I thought I might draw a few comparisons between the logic as the math of ideas and the math of numbers.
Now instead of talking about the mind-numbingly easy parts of math like arithmetic and stuff, I’ll just jump into the fun stuff.
So in math, you have functions, which basically take a number of variables as input, crunch the numbers, and spit out the output (that was quite possibly the coolest description of a mathematical thing that I’ve ever made :D). Now, in logic, we have almost the same things. You have things like ‘Statement P AND Statement Q NOT Statement R’ which is a bit like the equation in the function. You then have the truth table, which basically substitutes the values of all the statements (either true or false) and then outputs the values (which are also true or false).
Now, in ‘number math’, you can also express the output of the functions in a graph. And while you can’t strictly ‘graph’ logical statements, there are certain subparts in logic that you can ‘graph’. Take, for example, sets, which is basically logic with a bit of math thrown in. Now, when you draw venn diagrams, they are essentially to show exactly how certain groups are structured and how their different elements intersect. You can also add the number of elements there are in a set to the diagram, but at the end of the day,the venn diagram basically shows the structure of all the sets. The intersections between these sets can be viewed as logical statements, for example, the intersection between two sets P and Q can be written as ‘P and Q’, and the part of P that is not a part of Q can be written as ‘P not Q’.
There is a large part of logic that is just simply structured thinking and reasoning, but that too is just a more abstract form of this. It’s hard to capture the logical processes that go on in a brain with ‘mathematical’ or logical notation, but at the end of the day, most of our decisions are made using cost-benefit comparisons, which are a whole bunch of logical statements (for example, this AND this will happen but this will NOT happen’.
So it’s interesting to see how fundamental mathematical concepts can be applied to our ideas, and how we can even think of our own thought processes like this.
Well, that’s about it 🙂
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