Contents

## What is wrong with an infinite regress?

The fallacy of Infinite Regress occurs when this habit lulls us into accepting an explanation that turns out to be itterative, that is, **the mechanism involved depends upon itself for its own explanation**.

## Is infinite regression illogical?

**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.

## Is an infinite regress absurd?

As seen in the example given to us by Aristotle, regress arguments can be constructive; that is, they are used as justifications for belief. **For Aristotle, infinite regression presents as something absurd**.

## Why is infinite regress a fallacy?

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.

## Is Infinity a contradiction?

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

## What is infinite regress in the cosmological argument?

An infinite regress is **an infinite series of entities governed by a recursive principle that determines how each entity in the series depends on or is produced by its predecessor**. An infinite regress argument is an argument against a theory based on the fact that this theory leads to an infinite regress.

## What is infinite regress simple?

Definition of infinite regress

: **an endless chain of reasoning leading backward by interpolating a third entity between any two entities** — compare third man.

## Does Infinity exist in math?

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.

## What is the contingency argument for God?

The “Argument from Contingency” **examines how every being must be either necessary or contingent**. Since not every being can be contingent, it follow that there must be a necessary being upon which all things depend. This being is God.

## 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.

## Why does infinity not 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.

## Is the continuum hypothesis true?

Gödel began to think about the continuum problem in the summer of 1930, though it wasn’t until 1937 that he proved the continuum hypothesis is at least consistent. This means that with current mathematical methods, **we cannot prove that the continuum hypothesis is false**.

## What if the continuum hypothesis is false?

If the continuum hypothesis is false, it means that **there is a set of real numbers that is bigger than the set of natural numbers but smaller than the set of real numbers**. In this case, the cardinality of the set of real numbers must be at least א2.

## What is the continuum paradox?

The continuum hypothesis states that **the set of real numbers has minimal possible cardinality which is greater than the cardinality of the set of integers**. That is, every set, S, of real numbers can either be mapped one-to-one into the integers or the real numbers can be mapped one-to-one into S.

## Is infinity an axiom?

In axiomatic set theory and the branches of mathematics and philosophy that use it, **the axiom of infinity is one of the axioms of Zermelo–Fraenkel set theory**. It guarantees the existence of at least one infinite set, namely a set containing the natural numbers.

## Who invented infinity?

infinity, the concept of something that is unlimited, endless, without bound. The common symbol for infinity, ∞, was invented by the English mathematician **John Wallis** in 1655.

## Does the empty set exist?

**An empty set exists**. This formula is a theorem and considered true in every version of set theory.

## Why is the axiom of infinity necessary?

Why do we need the axiom of infinity? **Because we know (and can prove) that the other axioms of ZFC cannot prove that any infinite set exists**. The way this is done is roughly by the following steps: Remember a set of axioms Σ is inconsistent if for any sentence A the axioms lead to a proof of A∧¬A.

## How does axiom of infinity work?

axiom to make them work—the axiom of infinity, which **postulates the existence of an infinite set**. Since the simplest infinite set is the set of natural numbers, one cannot really say that arithmetic has been reduced to logic.

## Is the power set unique?

**Power Set Exists and is Unique**.

## What does it mean for a set to be inductive?

21-22), an inductive set is **a nonempty partially ordered set in which every element has a successor**. An example is the set of natural numbers. , where 0 is the first element, and the others are produced by adding 1 successively. Roitman (1990, p.

## How do you know if a set is inductive?

Definition 1. A set S is called an inductive set **if the empty set φ ∈ S and if a set a ∈ S then its successor a := a ∪ {a} ∈ S**. F = {C ∈ P(A) : C is an inductive set} and the right hand side is a set by Axiom 2.

## Are integers an inductive set?

Thinking about the definition of “inductive set”, you’ll find that there are lots of inductive sets, for example: the set of all real numbers, the set of positive real numbers, **the set of integers**, the set of rational numbers, and lots more.