Posts tagged ‘logic’

May 27th, 2013

Q&A 24: Induction, Deduction, and Falsifiability

by Max Andrews


Hello Max,

I did have a few questions in regards to the nature of scientific explanation and furthering (or ‘advancing’, if you prefer) scientific knowledge. Hume had recognized that the problem of induction can not be justified by an inductive rule (that would be circular) or a deductive rule (or else the principle wouldn’t be inductive – we cannot deduce the truth of induction from the axioms of logic). This of course being Hume’s fork.

However, does Karl Popper’s interpretation of scientific methods being deductive (or falsifiable) solve this problem more so than science on the inductive interpretation? In short, Im just curious if we are reasonable in rejecting Hume’s skepticism, but sound in still adhering to science hinging off of induction.


Hi Steven!

I did a lot of work on this question in my MA thesis. My full answer is a bit long but I hope it’s easy to follow. For the Reader’s Digest version, I’d say that I’m not a fan of deductive arguments and I prefer inductive arguments. (Actually, I love abductive arguments much more but that’s another issue!) I’m very sympathetic to Popper’s criterion of falsifiability but it’s not a necessary condition for science–it’s just preferable. I’ll try to contextualize and elaborate on some of the hidden talking points in your question so some of the readers can follow along.

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.  

April 22nd, 2013

Q&A 19: Calvinism and Free Will

by Max Andrews


Hey! My name is Josh. I’m a young college student by day (and christian apologist by night, jokes). But in my personal life, apologetics is important to me.Aside from that, I have a question I think you could help me with. I’m a Calvinist (hold the tomatoes) because I think, Biblically, it’s the most accurate putting together of scriptural truth (basically the best systematic theology). My problem is this:
Total Inability and free will. How are we morally responsible if we cannot choose otherwise? And since no one seeks God (Romans) and no one can come to Christ unless the Father brings them (John 6), how is it that we can really talk about free will? How would this be the best possible world where most free creatures choose Christ, when they cannot choose Him unless He first removes their inability? It seems that it doesn’t matter what world God created becaue technically speaking, He could remove the inability from all people, resulting in everyone freely choosing Christ. I hope my questions make sense. I’m eager to hear your response.Keep up the good work. I love your website!God Bless :)



Thanks for your question. Since I’m not a Calvinist my answer will probably be a little different from what you were anticipating. First, I’ll respond to you question from within the Calvinist system (as best as I can). Then I’ll give you  my response and thoughts on the issue as a Molinist.

April 6th, 2013

An Abductive Fine-Tuning Argument

by Max Andrews

The fine-tuning argument argues that when physics and the laws of nature are expressed mathematically their values are ever so balanced in a way that permits the existence of life. I’m merely arguing that the universe is finely tuned for the essential building blocks and environments that life requires.

  1. Given the fine-tuning evidence, a life permitting universe (LPU) is very, very unlikely under the non-existence of a fine-tuner (~FT): that is, P(LPU|~FT & k) ≪ 1.
  2. Given the fine-tuning evidence, LPU is not unlikely under FT (Fine-Tuner): that is, ~P(LPU|FT & k) ≪ 1.
  3. Therefore, LPU strongly supports FT over ~FT.[1]

Defense of 1: Given the fine-tuning evidence, a life-permitting universe is very, very unlikely under the non-existence of a fine-tuner.

So what are some of the evidences for fine-tuning?

  1. Roger Penrose calculates that the odds of the special low entropy condition having come about by chance in the absence of any constraining principles is at least as small as about one in 1010^123.[2]
  2. Strong Nuclear Force (Strong nuclear force coupling constant, gs = 15)
    1. +, No hydrogen, an essential element of life
    2. -, Only hydrogen
      read more »

April 5th, 2013

An Abductive Thomistic Cosmological Argument

by Max Andrews

The following argument is an abductive Thomistic cosmological argument from contingency, which I presented at my recent Ratio Christi debate.

  1. There are contingent constituents to the universe.
  2. Given the contingent constituents of the universe, the existence of the universe (U) is very, very unlikely under the hypothesis that these constituents are themselves uncaused or self-caused (~Cu): that is, P(U|~Cu & k) ≪ 1.
  3. Given the contingent constituents of the universe, the existence of the universe is not unlikely under the hypothesis of a first uncaused cause (Cu): that is, ~P(U|Cu & k) ≪ 1.
  4. Therefore, U strongly supports Cu over ~Cu.

The constituents of the universe include galaxies, planets, stars, cars, humans, leptons, bosons, and other particles. For the constituents of the universe to be uncaused that would mean it is metaphysically necessary. For something to be metaphysically necessary that means that it could not have failed to exist—it exists in every possible world.

For something to be self-caused it must be simultaneously antecedent to itself to produce itself as its own effect. But this contradictory. This would be akin to the ultimate bootstrapping trick.

March 26th, 2013

Q&A 16: How Robust Are Theistic Explanations?

by Max Andrews

Q&A GraphicQuestion:

Hello Max,

I’m currently reading on philosophy of religion, and I came across your site. You admit to being a “staunch proponent of abductive arguments”. It made me curious as to what your thoughts were regarding arguments against theistic explanations (such as those given in Gregory Dawes’ Theism and Explanation). For example, theistic explanations don’t fulfill explanatory virtues such as being part of successful research program (most theistic explanations failed in the past), being informative (they don’t describe in great detail the mechanisms involved in divine activity), being testable, being coherent with our background knowledge (arguably, all our knowledge involves embodied minds, so positing a disembodied one is theoretically costly), and having ontological economy (theistic explanations posit a radically new set of substances). 
Furthermore, given God’s omniperfection, we can expect that he will fulfill his intentions in the best possible way. But to the extent that the phenomena to be explained don’t seem to be the product of the best possible way of being actualized, it is to that extent we can doubt that God’s activity is the explanation for that phenomena. We need good reason to think the phenomena to be explained was actualized in the best possible way; otherwise, the theistic explanation won’t work.
read more »

February 25th, 2013

Q&A 12: How Can We Know God is Good and Not a Sadist?

by Max Andrews


Mr. Andrews,
Philosophically, How can we know God is good and not like some form of a sadist who will just torture everyone in hell when they die? Didn’t CS Lewis once try to argue that evil is not created but a lacking of good, could you shed some light on this? Couldn’t it just be said the other way around too, that good is lacking evil? Then who knows what sort of entity (good or evil) ultimately rules the universe? What philosophical reason is there to believe that God is the entity that is all powerful and all good?

February 18th, 2013

Q&A 11: Is the Belief in Free Will a Properly Basic Belief? Defeaters?

by Max Andrews


Is the properly basic belief that I have free will indefeasible? I’m thinking of the fact that a properly basic belief can be defeated, but was wondering how far that goes. So can someone ever provide a defeater for the idea that we have free will? The thought came to me again when I was listening to a podcast by Glenn Andrew Peoples and he made a comment about how we should give up the idea of free will if a good enough theory (of mind) came along that denied free will. I disagree with Glenn on this but was wondering if you ever could be presented with defeaters for free will. I can sort of see an undercutting defeater might but not a rebutting defeater.



For those who may not be familiar with the issue, a properly basic belief is a belief that is held via non-doxastic justification, which is self-evident to the subject. For example, a properly basic belief is the belief that I am a mind or that there is an external reality beyond myself. The first question is whether or not free will is a properly basic belief–and I think not.

February 15th, 2013

Is This a Possible World?

by Max Andrews

So, I gave a pop quiz to my class today because I asked them if they had any questions about any of the material we’ve been recently going over (logic) and no one had any questions. Because of their confidence I gave them a quiz, which resulted in very interesting answers. One of the questions was to describe some possible world. Simple enough, right? If they knew what a possible world was they could write something simple down like “there are pink elephants” or “my shirt is red instead of blue.” However, I got this very interesting one that made me think. Think about it and let me know how you would respond to this scenario. It assumes a lot about knowledge, minds, God, etc.

In a possible world there is no predictability. Nothing that happens once happens again a second time. There is no way to know what is going to happen but there is also no such thing as knowing because there is nobody to know anything since a being would require repeated processes to function and remain functioning.

February 8th, 2013

How to Construct a Cumulative Case Argument

by Max Andrews

The cumulative case uses the prime principle of confirmation: Whenever we are considering two competing hypotheses, an observation counts as evidence in favor of the hypothesis under which the observation has the highest probability. This principle is sound under all interpretations of probability.  Each argument must be taken on its own grounds and one cannot arrive at “God” at the end of each argument.  The conjunction of arguments is what is needed to make a cumulative case for the existence of God.

The Likelihood Principle of Confirmation theory states as follows.  Let h1 and h2 be two be competing hypothesis (in this case the existence of X and ~X, with X being a first cause, fine-tuner, etc.).  According to the Likelihood Principle, an observation e counts as evidence in favor of hypothesis h1 over h2 if the observation is more probable under h1 than h2.  Thus, e counts in favor of h1 over h2 if P(e|h1) > P(e|h2), where P(e|h1) and P(e|h2) depict a conditional probability of e on h1 and h2, respectively.  The degree to which the evidence counts in favor of one hypothesis over another is proportional to the degree to which e is more probable under h1 than h2: particularly, it is proportional to P(e|h1)/P(e|h2) .  The Likelihood Principle seems to be sound under all interpretations of probability.  This form is concerned with epistemic probability.