Maybe?
That's a good one.
To me that exists in the mind before hits the paper. It's like language but more accurate.
I'd disagree. To suggest that something must first exist in the mind would suggest that it must be created or invented before it can exist. Examples would be Henry Ford envisioning the automotive assembly line before creating it or Ben Franklin envisioned bi-focals before actually building a pair.
But mathematics isn't invented, it's discovered.
For a long time, people didn't understand why objects fell to the ground when dropped, it was just what happened. It took centuries of research, study and discovery for us to understand, not just why the apple falls, but why that force affects every physical object in the universe. Gravity's affect exists whether we understand it or not.
Let's say I wanted to draw a triangle. I take a ruler and measure out two 3" lines that meet at a 90 degree angle. I can take my ruler and figure out that the third line will be a little over 4", but I might not understand "why" it's that long or that a formula could have helped me know that length without a ruler.
Additionally, if I draw a line in the dirt without a ruler, an exact measurement of that line exists regardless of whether or not I measure it.
Also, if you're not familiar with the show, check out . The guy interviews a bunch of intellectuals trying to answer that exact question.
These are not my words but I think it would add to the conversation. I found it on quora. I'll watch the video and respond from my own experience.
Numbers are an arithmetical esteem, communicated by a word, sign, or figure, symbolizing to a specific value and utilized as a part of tallying and making computations, and for demonstrating requests in an arrangement. They're not "real", they're un-materialistic conceptual elements theoretically existent in our metaphysical creative ability. Mathematics is an array of algorithmic equations used to harness the fictional idea that is ‘numbers’.
Arithmetic is natural because it’s an experimentally unavoidable practice, however isn't “real” in light of the fact that it's built upon an ontological premise.
Real: “actually existing as a thing or occurring in fact; not imagined or supposed.” - Oxford English Dictionary
Reality as a concept is dependent and requires the presence of an alternative term so as to establish its own meaning, validity, purpose and reason. You can't have words like "real" and not have words like "unreal", the pair depend on one another to make sense and exist. So if abstract entities aren't ‘unreal’, then what is? Wouldn’t the contrariety between imagination and reality be conflated?
Math is fictive reason.
Real: “actually existing as a thing or occurring in fact; not imagined or supposed.” - Oxford English Dictionary
Reality as a concept is dependent and requires the presence of an alternative term so as to establish its own meaning, validity, purpose and reason. You can't have words like "real" and not have words like "unreal", the pair depend on one another to make sense and exist. So if abstract entities aren't ‘unreal’, then what is? Wouldn’t the contrariety between imagination and reality be conflated?
If I have 2 objects in a box and then put another 2 objects in a box, I'd have a total of 4 objects. It doesn't matter what those objects are, their size, color, weight or smell. It doesn't matter if I imagine the total to be 5, 3 or 107. The fact is that when 2 objects are added to another 2 objects, what occurs is a total of 4 objects. That's a fact.
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