The Basic Metaphor of Infinity

It can be questioned what the link between mathematical concepts and natural human perception is. So, the Basic Metaphor of Infinity and many other concepts were introduced by G. Lakoff to explain the gap.

The Basic Metaphor of Infinity can be understood only if we start from the beginning of a child who is accustomed to natural numbers, and it is found that the concept of an infinite linear sequence of one thing after another is based on the human ability to speak.

For human development, being familiar with natural numbers is essential. It can be observed among kids how they learn numbers without even knowing what they are used for, and they just mimic the words in a queue. And this is how they start learning, which keeps on going from numbers to formulas, and they discover the quantitative aspects of numbers like the commutative law, a+b=b+a, and so on.

Humans have the power to identify infinity. Infinity is the ability to recognize a situation where some kind of symbols or words stand in a queue in space or in such a way in the time that every item is followed by the other item and has no end to it.

Aristotle said that an ongoing process or motion which does not have any end is known as potential infinity. He made a distinction between potential infinity and actual infinity. Actual infinity is an infinity that forms an idea as a realized thing. In mathematics, potential infinity is found all the time, but, interestingly, infinity in modern mathematics is a case of actual infinity.

It can be found that the concept of the actual infinity of mathematics is metaphorical in nature. There is a common procedure that produces the fundamental metaphorical result without any end. This metaphorical concept is known as the Basic Metaphor of Infinity. Through this metaphor, we can understand that processes that can go on indefinitely are conceptualized to have an end and a final result. The Basic Metaphor of Infinity is used to give a metaphorical completion to the ongoing process.

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