An abstraction in mathematics is a simple, small idea that we use to describe and understand a large variety of objects. For example the concept of an algebraic group is an abstraction that can be applied to numbers, functions, matrices, etc. We can understand all these objects using the same concept.
Are all words this way? Take the word "orange". Are all oranges the same? They all have variations in taste, texture, color, etc. They are all physically separate objects. But we use the same idea to understand and describe them. Maybe this is more clearly seen with the word "fruit".
This applies to verbs too - think of the verb "to run". Usain Bolt runs in a very different way from normal people, but we use the same concept to understand what they do.
These abstractions "leak", i.e. cause confusion when the underlying reality doesn't match up. Is a tomato a fruit? If I trained as an Olympic sprinter would I have to abandon misconceptions about how to move my body, misconceptions caused by a lifetime of using the word "run"?
An abstraction in mathematics is a simple, small idea that we use to describe and understand a large variety of objects. For example the concept of an algebraic group is an abstraction that can be applied to numbers, functions, matrices, etc. We can understand all these objects using the same concept.
Are all words this way? Take the word "orange". Are all oranges the same? They all have variations in taste, texture, color, etc. They are all physically separate objects. But we use the same idea to understand and describe them. Maybe this is more clearly seen with the word "fruit".
This applies to verbs too - think of the verb "to run". Usain Bolt runs in a very different way from normal people, but we use the same concept to understand what they do.
These abstractions "leak", i.e. cause confusion when the underlying reality doesn't match up. Is a tomato a fruit? If I trained as an Olympic sprinter would I have to abandon misconceptions about how to move my body, misconceptions caused by a lifetime of using the word "run"?
Is every word an abstraction?