ELI5: Explain Like I'm 5


Okay, so imagine you have a basket with some apples in it. Now, imagine you have another basket with some oranges in it. You can count how many apples are in the first basket, and how many oranges are in the second basket, right?

Now, let's say you want to compare the two baskets. You might say, "I have more apples than oranges," or "I have the same number of apples and oranges." This is a way of saying something about how the two baskets relate to each other in terms of their contents.

Neo-logicism is kind of like this. It's a way of comparing different kinds of mathematical things (like numbers, sets, and functions) to see how they relate to each other. But instead of using words like "more" or "less," we use logical symbols and rules to show how different mathematical objects can be combined or compared.

For example, one rule of neo-logicism is that any two sets with the same number of things in them can be put into a one-to-one correspondence (which means you can match up each thing in one set with exactly one thing in the other set). This is a way of saying that two sets with the same size are "equal" in a certain sense.

Another rule is that you can define a new mathematical object (like a number or a function) in terms of simpler objects using logical rules. For example, you can define the number 2 as the set of all sets with exactly 2 elements, and then use logical rules to show how to add or subtract these "2-sets" to get other numbers.

So, neo-logicism is a way of using logical rules to define and compare different mathematical objects. It's kind of like counting apples and oranges, but with more abstract concepts and symbols.
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