Posts tagged ‘conjunctive probability’

March 26th, 2012

VT Debate–The Problem of Gratuitous Evil

by Max Andrews

One of the objections made by one of the atheists in the VT debate on the existence of God was William Rowe’s form of the problem of gratuitous evil:[1]

  1. There exist instances of intense suffering that an omnipotent, omniscient being could have prevented without thereby losing some greater good or permitting some evil equally bad or worse. (Factual premise)
  2. An omniscient, wholly good being would prevent the occurrence of any intense suffering that being could, unless that being could not do so without thereby losing some greater good or permitting some evil equally bad or worse. (Theological premise).
  3. Therefore, There does not exist an omnipotent, omniscient, wholly good being.

Or, simply put:

  1. There are unnecessary evils.
  2. God would prevent evils without losing some greater good.
  3. Therefore, God does not exist.
    read more »

March 25th, 2012

What if God Commanded You to do Something Wrong?

by Max Andrews

While at the VT Debate on the existence of God one of the atheists’, in passing, briefly mentioned the Euthyphro dilemma. Does God command something because it’s good or is it good because God commands it?  The first horn makes goodness apart from God and the second makes goodness arbitrary. This came up in the Q&A as well.  What if God commanded you to strap a bomb to your chest and blow other people up or rape others?  As an advocate of divine command theory the response to this question is a bit more nuanced then any prima facie answer. (Also, see my moral argument I presented at this debate).

The proponent of divine command theory (DCT) claims that whatever God commands to any moral agent becomes a moral obligation.  Formulations of the commands are given symbolic form by David Efird as:[1]

(RIGHT)                      ∀ϕ☐(Rϕ ≣ Cgϕ)

(WRONG)                   ∀ϕ☐(Wϕ ≣ Cg~ϕ)

(PERMITTED 1)            ☐(~Eg ⊃ ∀ϕ~Wϕ)[2]

(PERMITTED 2)            [(∃ϕ☐Cgϕ ∙ ∃ϕ☐Cg~ϕ)] ∙ [(∃ϕ☐~Cgϕ ∙ ∃ϕ☐~Cg~ϕ)]

*∀= for all…, ☐=necessarily, ◊=possibly.  For instance, RIGHT is read as for all actions, ϕ, ϕ is right if and only if God commands ϕ.

March 24th, 2012

The Fine-Tuning Argument and Random Sampling

by Max Andrews

One of the objections raised by an audience member at the VT debate on the existence of God was against the fine-tuning argument and probability (for my method of argumentation please see: VT Debate-My Method of Argumentation).  In statistics a random sample drawn must have the same chance of being sampled as all the other samples.  The objection was based on this problem.  Since we know of only one universe we don’t know what the range of values for the constants and physics could be.  This was also brought up in conversation with both atheists after the debate.  Since we don’t know how narrow or broad these ranges could be there’s no way of drawing out any probability based argument from fine-tuning.  The thing is that we can know what other universes would be like if the values were different.  If our natural laws have counterfactuals that are in any way incoherent then this is an appropriate sampling.  Also, to make this objection and advocate that we just so happen to live in a life permitting universe in the multiverse then this objection cannot be made since the claim that we happen to life in a life-permitting one amongst countless others suggest we can know what the other samplings are.  For instance, here are a few examples:

March 24th, 2012

VT Debate–The Moral Argument

by Max Andrews

The following is David Baggett’s moral argument* for the existence of a perfectly moral person I used in the VT debate on the existence of God. (I highly recommend Baggett’s book co-authored with Jerry Walls Good God: The Theistic Foundations of Morality.) This version of the moral argument is an abductive version. I believe this argument, when used in an abductive form, is the strongest form of the argument. You’ll usually see it in a deductive form, a la William Lane Craig. For my method of argumentation please see: VT–My Method of Argumentation.

  1. There are objective axiological/moral facts that obtain.
  2. Either the world alone or the world and a perfectly moral person best explain these facts.
  3. It is the case that the world and a perfectly moral person best explain these facts.
  4. Therefore, the world and a perfectly moral person best explain these facts.

In essence, it seems that there are objective moral facts and this asks the question, “What’s the best explanation for these facts?”

March 24th, 2012

VT Debate–The Fine-Tuning Argument

by Max Andrews

The following is Robin Collins’ fine-tuning argument for the existence of a fine-tuner I used in the VT debate on the existence of God.  This version of the fine-tuning argument is an abductive version.  I believe this argument, when used in an abductive form, is the strongest form of the argument.  You’ll usually see it in a deductive form, a la William Lane Craig.  For my method of argumentation please see: VT–My Method of Argumentation.

The fine-tuning argument argues that when the physics and the laws of nature are expressed mathematically their values are ever so balanced in a way that permits the existence of life.  This claim is made on the basis that existence of vital substances such as carbon, and the properties of objects such as stable long-lived stars, depend rather sensitively on the values of certain physical parameters, and on the cosmological initial conditions.[1]  I’m merely arguing that the universe/multiverse is fine-tuned for the essential building blocks and environments that life requires for cosmic and biological evolution to even occur.

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

March 23rd, 2012

VT Debate–The Thomistic Cosmological Argument

by Max Andrews

The following is Thomas Aquinas’ cosmological argument from contingency I used in the VT debate on the existence of God.  This version of the cosmological argument can be traced back to antiquity originally advocated by Plato and Aristotle.  For my method of argumentation please see: VT–My Method of Argumentation.

  1. What we observe and experience in our universe is contingent.
  2. A network of causally dependent contingent things cannot be infinite.
  3. A network of causally dependent contingent things must be finite.
  4. Therefore, There must be a first cause in the network of contingent causes.

In this context, what I mean by contingent is that if X is contingent then X owes its existence to something else. For a thing that has the potentiality of movement cannot actualize its own potential; some other thing must cause it to move.  The universe consists of a network of causes. A was caused by B, but only because B is caused by C, and so on. We know of nothing that spontaneously initiates its own causal activity. (Even supposed quantum indeterminacy requires a state of affairs, or preceding causal conditions, such as the governance of the laws of nature, for the event to occur).  This is a hierarchical network of causation and not temporal.  Note that nothing here turns on our having to know about everything.

March 23rd, 2012

VT Debate–My Method of Argumentation

by Max Andrews

The topic of the VT debate was “Does God Probably Exist, or Not?”  I used a cumulative case approach for my arguments.  Below is my opening statement:

This evening we will be defending the proposition “God probably exists.”  We will present three different arguments for theism. To defend our case we will be using 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.