Is a distinction between actual and potential infinity philosophically significant?

The only difference between the sequence and the set is that the sequence is ordered. So it would seem that there isn’t an especially meaningful distinction between “potential” and “actual” infinities. But there is a meaningful distinction between the size of A itself and the size of the individual elements of A.

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.

Did Aristotle believe the universe was infinite?

He didn’t. He placed the earth at the center of a finite universe. For Aristotle, the universe is decidedly not infinite; he argued that there were potential infinities, but not actual infinities.

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.

Why is infinity important?

infinitely small,” it can also describe an object that is smaller than any number. It is important to take special note that infinity is not a number; rather, it exists only as an abstract concept.
Infinity in terms of Cardinality.

Natural numbers Even numbers
⋮ \vdots ⋮ ⋮ \vdots ⋮

Is infinity real or imaginary?

No. Imaginary numbers are well defined and do not include a number called infinity.

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.

What does Aristotle say about infinity?

Aristotle postulated that an actual infinity was impossible, because if it were possible, then something would have attained infinite magnitude, and would be “bigger than the heavens.” However, he said, mathematics relating to infinity was not deprived of its applicability by this impossibility, because mathematicians …

What is philosophical theory of eternity?

According to Tatevatsi the notion of eternity of the world stems from the eternal and immutable nature of the God: «As the God Self is everlasting, staying and eternal, likewise the world, the result of His glorious Business, will be staying and everlasting.

Why did Aristotle think zero was impossible?

The first notion of an abstract zero, that is a number zero, in the history of human thought appeared in Aristotle’s philosophy in the 4th c. BC, when the Babilonians elaborated a zero as a lack of units of some order. The Philosopher could not accepted it since it would lead him to contradiction.

Who believed that all things can be divided infinitely?

The origin of the idea in the Western tradition can be traced to the 5th century BCE starting with the Ancient Greek pre-Socratic philosopher Democritus and his teacher Leucippus, who theorized matter’s divisibility beyond what can be perceived by the senses until ultimately ending at an indivisible atom.

Why is Zeno’s paradox wrong?

It might seem counterintuitive, but pure mathematics alone cannot provide a satisfactory solution to the paradox. The reason is simple: the paradox isn’t simply about dividing a finite thing up into an infinite number of parts, but rather about the inherently physical concept of a rate.

What is the first paradox?

The first known paradoxes were given by the ancient Greek School of philosophy at Elea. Parmenides (c. 515-c. 450 B.C.E.) had held that motion is an illusion and that existence is one indivisible whole.

What is the snail paradox?

Achilles paradox, in logic, an argument attributed to the 5th-century-bce Greek philosopher Zeno, and one of his four paradoxes described by Aristotle in the treatise Physics. The paradox concerns a race between the fleet-footed Achilles and a slow-moving tortoise.

What is the tortoise paradox?

In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead. — as recounted by Aristotle, Physics VI:9, 239b15. In the paradox of Achilles and the tortoise, Achilles is in a footrace with the tortoise.

What is the Arrow paradox?

From Wikipedia: “In the arrow paradox […], Zeno states that for motion to occur, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one (duration-less) instant of time, the arrow is neither moving to where it is, nor to where it is not.

What is Achilles paradox?

Meaning that Achilles could never overtake. Taken to an extreme, this bizarre paradox suggests that all movement is impossible, but it did lead to the realization that something finite can be divided an infinite number of times.

What are the paradoxes of Zeno?

paradoxes of Zeno, statements made by the Greek philosopher Zeno of Elea, a 5th-century-bce disciple of Parmenides, a fellow Eleatic, designed to show that any assertion opposite to the monistic teaching of Parmenides leads to contradiction and absurdity.

What is the halfway paradox?

In its simplest form, Zeno’s Paradox says that two objects can never touch. The idea is that if one object (say a ball) is stationary and the other is set in motion approaching it that the moving ball must pass the halfway point before reaching the stationary ball.

Is infinity a paradox?

The paradox arises from one of the most mind-bending concepts in math: infinity. Infinity feels like a number, yet it doesn’t behave like one. You can add or subtract any finite number to infinity and the result is still the same infinity you started with. But that doesn’t mean all infinities are created equal.