What are the best arguments against actual infinity?

Infinity has provided a paradise of effective math and theories, and without it theorizing becomes more difficult. Removing infinity from mathematics has failed since Cantor but we still don’t know what mathematics is so mathematical infinity cannot be leveraged to say it actually exists beyond the mind.

Why is actual infinite impossible?

According to Aristotle, actual infinities cannot exist because they are paradoxical. It is impossible to say that you can always “take another step” or “add another member” in a completed set with a beginning and end, unlike a potential infinite.

What is the argument of infinity?

According to the Infinity Argument, an actually infinite regress of past events cannot exist because an actual infinite cannot exist. The Infinity Argument is one of the most common arguments for a beginning of the universe espoused by advocates of the kalām cosmological argument.

Can an actual infinity exist?

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.

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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.

Is Pi an infinite?

Pi is a number that relates a circle’s circumference to its diameter. Pi is an irrational number, which means that it is a real number that cannot be expressed by a simple fraction. That’s because pi is what mathematicians call an “infinite decimal” — after the decimal point, the digits go on forever and ever.

Does infinite have a beginning?

“Infinite” is an adjective that can apply to various objects. For example, the interval [0,1] contains infinitely many points, and it clearly has both a beginning (its left endpoint, 0) and an end (its right endpoint, 1).

Is infinity a contradiction?

20 Hence, the mathematical definition of infinity as a kind of limit implies a limitless limit, which is self-contradictory.

Is infinite regression logical?

It’s a fallacy because it is begging the question that is to say that it is a circular argument. Whether referring to the origins of the universe or any other regressive context, the answer simply moves the question back into infinite regress rather than answering it.

What is wrong with an infinite regress?

There are two ways in which a theory’s resulting in an infinite regress can form an objection to that theory. The regress might reveal a bad feature of the theory—a feature that is not the regress itself, that we have independent reason to think is a reason to reject the theory.

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What did 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 infinity approach?

Infinity is a concept, not a number; therefore, the expression 1/infinity is actually undefined. In mathematics, a limit of a function occurs when x gets larger and larger as it approaches infinity, and 1/x gets smaller and smaller as it approaches zero.

How can infinity exist?

Although the concept of infinity has a mathematical basis, we have yet to perform an experiment that yields an infinite result. Even in maths, the idea that something could have no limit is paradoxical. For example, there is no largest counting number nor is there a biggest odd or even number.

Do numbers end?

The sequence of natural numbers never ends, and is infinite. OK, 1/3 is a finite number (it is not infinite). There’s no reason why the 3s should ever stop: they repeat infinitely. So, when we see a number like “0.999…” (i.e. a decimal number with an infinite series of 9s), there is no end to the number of 9s.

Is infinite regress impossible?

The mere existence of an infinite regress by itself is not a proof for anything. So in addition to connecting the theory to a recursive principle paired with a triggering condition, the argument has to show in which way the resulting regress is vicious.

Can time be defined?

Physicists define time as the progression of events from the past to the present into the future. Basically, if a system is unchanging, it is timeless. Time can be considered to be the fourth dimension of reality, used to describe events in three-dimensional space.

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How many dimensions are there?

The world as we know it has three dimensions of space—length, width and depth—and one dimension of time. But there’s the mind-bending possibility that many more dimensions exist out there. According to string theory, one of the leading physics model of the last half century, the universe operates with 10 dimensions.

Is time an illusion?

According to theoretical physicist Carlo Rovelli, time is an illusion: our naive perception of its flow doesn’t correspond to physical reality. Indeed, as Rovelli argues in The Order of Time, much more is illusory, including Isaac Newton’s picture of a universally ticking clock.