What does Aristotle mean when he says that an infinity is potential rather than actual?
If a statute potentially-is, that means that there will be an actual statute. The infinite does not potentially exist in this sense — there will be no actual infinite. Rather, to say `there is the infinite’, according to Aristotle, means that one thing after another will be coming into being.
What is the difference between potential and actual infinity?
Potential infinity refers to a procedure that gets closer and closer to, but never quite reaches, an infinite end. For instance, the sequence of numbers 1, 2, 3, 4, … Completed infinity, or actual infinity, is an infinity that one actually reaches; the process is already done.
What does philosophy say about infinity?
… It is always possible to think of a larger number: for the number of times a magnitude can be bisected is infinite. Hence the infinite is potential, never actual; the number of parts that can be taken always surpasses any assigned number.
Is time infinite in philosophy?
Temporal finitism is the doctrine that time is finite in the past. The philosophy of Aristotle, expressed in such works as his Physics, held that although space was finite, with only void existing beyond the outermost sphere of the heavens, time was infinite.
Do actual infinities exist?
The actual infinite involves never-ending sets or “things” within a space that has a beginning and end; it is a series that is technically “completed” but consists of an infinite number of members. According to Aristotle, actual infinities cannot exist because they are paradoxical.
Does infinity exist in real life?
In the context of a number system, in which “infinity” would mean something one can treat like a number. In this context, infinity does not exist.
Why is infinity so important?
Infinity is denoted by the symbol ∞. The concept of infinity is extremely important in a variety of contexts, most notably calculus and set theory.
Infinity in terms of Cardinality.
|Natural numbers||Even numbers|
|⋮ \vdots ⋮||⋮ \vdots ⋮|
Is infinity a metaphysical concept?
Infinity in Physical Science. From a metaphysical perspective, the theories of mathematical physics seem to be ontologically committed to objects and their properties. If any of those objects or properties are infinite, then physics is committed to there being infinity within the physical world.