Posts tagged ‘infinity’

July 8th, 2015

Paper: Defending the Possibility of an Actually Infinite Universe

by Max Andrews

Cambridge Max Andrews 2015On July 2, I will be presented my first philosophy of mathematics paper at Tyndale’s conference at Cambridge University.

Below is the abstract for “The Extent of Existents: Ontologies and Infinities”.

Abstract: There seems to be an intrinsic rationality to the universe that is not simply extrinsically projected by the knowing subject. The consilience between mathematics and physics is inherent to nature and is inductively depended upon by every person. What makes the question of infinities interesting is whether there actually are such existent sets. Theists are often inclined to deny that actual infinites exist and explain such things as useful fictions of conceptually existent in the mind of God—but there can be no actual infinite set (ℵ) of existents [or anything]. I will, of course, address the concrete or abstract nature and [the so-called] indispensability of such sets but that is a peripheral concern, as the infinite set of quarks or strings does not necessarily depend on the existence of the correlate abstracta. I will then survey some rejoinders such as Hilbert’s Hotel and other ‘incoherence’ arguments against actual infinites and how they are limited in applicable scope. Cantorian and ZFC semantics will be used, as they are mathematically canonical. I will conclude that theists are wholly consistent in their philosophy of mathematics and science, which will, in turn, compose a stronger theology of nature by affirming actual infinites. A theological and scientific consilience will be argued from the Thomas Aquinas’ doctrine of variety and G. W. Leibniz’s principle of plenitude. I will conclude that having a theology and philosophy that permits an actual infinite set of existents will not conflict with [examples in] theoretical physics such as many cosmological models and some mechanics in quantum physics—though this is not to be considered a driving motivator; rather, it’s an example of some of the consequences for one allowing the possibility of an actual infinite of existents to one’s ontological framework.

May 31st, 2015

Cambridge Paper Preview: Extent of Existents

by Max Andrews

This July I will be presenting my first philosophy of mathematics paper at Tyndale’s conference at Cambridge University. Please Consider Helping! I’m almost at the goal for grants and donations to pay 100%. For insight on my response paper to the plenary speak see my earlier post.

So far, in brief discussions with others, this paper seems a bit controversial since I’m defending the possibility of an actual infinite set of things existing. Below is the abstract for “The Extent of Existents: Ontologies and Infinities”.

Abstract: There seems to be an intrinsic rationality to the universe that is not simply extrinsically projected by the knowing subject. The consilience between mathematics and physics is inherent to nature and is inductively depended upon by every person. What makes the question of infinities interesting is whether there actually are such existent sets. Theists are often inclined to deny that actual infinites exist and explain such things as useful fictions of conceptually existent in the mind of God—but there can be no actual infinite set (ℵ) of existents [or anything]. I will, of course, address the concrete or abstract nature and [the so-called] indispensability of such sets but that is a peripheral concern, as the infinite set of quarks or strings does not necessarily depend on the existence of the correlate abstracta. I will then survey some rejoinders such as Hilbert’s Hotel and other ‘incoherence’ arguments against actual infinites and how they are limited in applicable scope. Cantorian and ZFC semantics will be used, as they are mathematically canonical. I will conclude that theists are wholly consistent in their philosophy of mathematics and science, which will, in turn, compose a stronger theology of nature by affirming actual infinites. A theological and scientific consilience will be argued from the Thomas Aquinas’ doctrine of variety and G. W. Leibniz’s principle of plenitude. I will conclude that having a theology and philosophy that permits an actual infinite set of existents will not conflict with [examples in] theoretical physics such as many cosmological models and some mechanics in quantum physics—though this is not to be considered a driving motivator; rather, it’s an example of some of the consequences for one allowing the possibility of an actual infinite of existents to one’s ontological framework.

May 15th, 2015

Tyndale Cambridge: Presenting on Divine Foreknowledge and Human Freedom and Actual Infinites

by Max Andrews

This July, at the Tydale philosophy conference at the University of Cambridge, I’ll be doing a response paper to ”Can Divine timelessness reconcile libertarian human freedom and divine knowledge of future human actions?”. This was a prize winning paper with Tyndale and I will be responding to this year’ plenary speaker, who will be presenting this paper.

Abstract:

An age-old problem for theists is the apparent irreconcilability of God’s omniscience with libertarian human freedom. If God knows what I will do tomorrow, and is infallible, then it appears that I am unable to refrain from acting in accordance with this knowledge. The pervasiveness of this problem is an important reason for many philosophers (from Boethius, Augustine and Aquinas, through to Helm, Leftow and Stump) holding that God is timeless. I will explain how a timeless God is alleged to avoid the sting of the freedom-foreknowledge dilemma, before demonstrating why I believe that this account fails.

September 14th, 2014

Podcast: What Kinds of Multiverses are There?

by Max Andrews

Podcast: https://soundcloud.com/sententias/eavesdropping-ep25-levels-of-the-multiverse

Contemporary physics seem to indicate that there are good reasons, theoretically and physically, for an idea that there is a plurality of worlds. This concept has come to be understood as the multiverse. The multiverse is not monolithic but it is modeled after the contemporary understanding of an inflationary model of the beginning of this universe. Max Tegmark has championed the most prominent versions of the multiverse. Tegmark has made a four-way distinction.

Levels of the Multiverse

June 9th, 2013

The Philosophy of Science Directory

by Max Andrews

This is a compilation of posts, which focus on the philosophy of science. These posts will cover a broad spectrum within the philosophy of science ranging from multiverse scenarios, scientific theory, epistemology, and metaphysics.

  1. MA Philosophy Thesis: “The Fine-Tuning of Nomic Behavior in Multiverse Scenarios”
  2. Natural Law and Scientific Explanation
  3. Science and Efficient Causation
  4. Which Comes First, Philosophy or Science?
  5. The Postulates of Special Relativity
  6. There’s No Such Thing as Creation Science–There’s Just Science
  7. Time Travel and Bilking Arguments
  8. “It’s Just a Theory”–What’s a Scientific Theory?
  9. Exceptions to a Finite Universe
  10. Teleology in Science
  11. Duhemian Science
  12. The Relationship Between Philosophy and Science
  13. The History of the Multiverse and the Philosophy of Science
  14. Where’s the Line of Demarcation Between Science and Pseudoscience?
  15. Miracles and the Modern Worldview
  16. Mass-Density Link Simpliciter
  17. Scientific Nihilism
  18. Q&A 10: The Problem of Defining Science
  19. Q&A 6: Scientism and Inference to the Best Explanation
  20. The Quantum Universe and the Universal Wave Function
  21. The History and Macro-Ontology of the Many Worlds Interpretation of Quantum Physics
    read more »

May 14th, 2013

Infinity + 1 = ?

by Max Andrews

When we think of infinity we usually think of the usual two categorical distinctions:  a potential infinite and an actual infinite.  A potential infinite suggests that infinity is only an idea or a concept but doesn’t actually exist in the Platonic sense or in the physical sense. In any set, one may always be added.  An actual infinite is the notion that there exists such a set, Platonic or physical, whichis infinite.  A potential infinity may be symbolized by a lemniscate:  ∞.  An actual infinite can be depicted by the aleph-null or aleph-nought:  ℵ0 (The Hebrew letter aleph with a subscript zero).

First, let’s have a brief refresher on set theory. A set is any collection of things or numbers that belong to a well-defined category.  In a set notation, this would be written as {2, 3, 5, 7, 11} being the first five prime numbers, which is a finite set of things.  Let’s simply signify this set as S.  There is a proper subset (SS) of S.  There are members in S that are not in SS, but no member of SS that is not in S.  

December 10th, 2012

Q&A 1: Kalam and The Flying Spaghetti Monster

by Max Andrews

Hey Max,

I guess since I requested the Q&A section, I’ll start it off!

I recently had a conversation with an atheist in which I walked him through the Kalam Cosmological Argument. This inevitably led into a conversation about what criteria a “first cause” must meet. It was difficult for me to explain, and for him to understand how God exists as a necessary being, or out of His own nature.

The atheist resorted to a version of  “Flying Spaghetti Monster” argumentation, in which he said, “How do we know that the first cause wasn’t a giant pink unicorn, or that two universes didn’t just mate and form ours?”. For obvious reasons, his argument is absurd. But what’s the best way to explain the concept of the first cause, and why it couldn’t be a “giant pink unicorn”?

Thanks a lot,

Richie Worrell (USA)

Richie,

I’m always amazed at some of the philosophical lunacy some atheists come up with. The mockery of using phrases like “flying spaghetti monster” or a “giant pink unicorn” weren’t originally developed in response to the kalam. They were developed in response to intelligent design suggesting the designer could be a spaghetti monster. I recall Dawkins using it several times and it has gained popularity in response to the ontological argument.

Nonetheless, let’s accept his flying pasta, pink unicorn, and sexual universes for the sake of discussion. Let’s recap the the kalam argument:

  1. Whatever begins to exist has a cause of its existence.
  2. The universe began to exist.
  3. Therefore, the universe has a cause of its existence.
    read more »

February 8th, 2012

Word of the Week Wednesday: Multiverse

by Max Andrews

The Word of the Week is: Multiverse

Definition: The term to designate the existence of many worlds or universes.  Contrary to just one world, a uni-verse, there are many worlds, a multi-verse.

More about the term: The multiverse is not monolithic but it is modeled after the contemporary understanding of an inflationary model of the beginning of this universe suggesting a plurality of worlds.  Max Tegmark has championed the most prominent versions of the multiverse.[1]  There are four levels of the multiverse.

  1.  Level One:  The level one is, for the most part, more space beyond the observable universe.  So, theoretically, if we were to go to the “edge” of the universe there would be more space.  Having this model as a version of the multiverse may be misleading because there is still only one volume, landscape, or system involved.  A generic prediction of cosmological inflation is an infinite space, which contains Hubble volumes (what we see in our universe) realizing in all conditions—including an identical copy of each of us about 10^10^29 meters away.[2]
    read more »

January 17th, 2012

William Lane Craig’s “J. Howard Sobel on the Kalam Cosmological Argument”–A Review

by Max Andrews

A Review of William Lane Craig’s “J. Howard Sobel on the Kalam Cosmological Argument.” Canadian Journal of Philosophy 36 (2006): 565-584.

William Lane Craig formulates retort to J. Howard Sobel’s objection to kalam as he typically formulates it.[1] Premise 1 seems obviously true—at least, more than its negation.  To suggest that things could just pop into being uncaused out of nothing is to quit doing serious metaphysics and is a premise that Sobel acknowledges to be true.  Sobel’s objection is with 2—that the universe began to exist.  This would then run into an infinite regress, which is philosophically and mathematically untenable.  Because an actually infinite number of things cannot exist, the series of past events must be finite in number and, hence, the temporal series of past, physical events is not without beginning.[2]

December 31st, 2011

An Outline of Tegmark’s Four Levels of the Multiverse

by Max Andrews

Contemporary physics seem to indicate that there are good reasons, theoretically and physically, for an idea that there is a plurality of worlds.  This concept has come to be understood as the multiverse.  The multiverse is not monolithic but it is modeled after the contemporary understanding of an inflationary model of the beginning of this universe.  Max Tegmark has championed the most prominent versions of the multiverse.[1]  Tegmark has made a four-way distinction.

Tegmark’s first version of the multiverse is called the level one multiverse.  The level one is, for the most part, more space beyond the observable universe.  So, theoretically, if we were to go to the “edge” of the universe there would be more space.  Having this model as a version of the multiverse may be misleading because there is still only one volume, landscape, or system involved.  A generic prediction of cosmological inflation is an infinite space, which contains Hubble volumes (what we see in our universe) realizing in all conditions—including an identical copy of each of us about 10^10^29 meters away.[2]