Stagnaro Nails Probability, Ending the Fine Tuning Argument

nature, creation, flower

nature, creation, flower

In an essay in the National Catholic Register, Angelo Stagnaro, in explaining probability, hit the nail on the head. In doing so, he nailed shut the coffin of the Fine Tuning argument for the existence of God, thereby ending it. He demonstrated that valid values of probability are based on a purely logical focus, not on a material focus, such as visual observation. Thus, the relationships of probability are purely logical and cannot be predicated on material reality, whether scientifically or philosophically, as they are in the Fine Tuning argument.

The properties of material things have no relevance to probability. Material illustrations of probability are total abstractions from material reality in which the material designations of the mathematical elements of sets in the illustration, are purely nominal. Consequently, probability has no inherent relevance to material reality and cannot be inferred from material reality. The probability relationships for a set of three elephants and two lions are exactly the same as for a set of three white chess pawns and two straight pins.

In contrast, science infers mathematical relationships from measurements of the properties of material things. Stagnaro, through illustration, identified the focus of probability as solely logical.

Stargano’s Illustrated Explanation of Probability

Discussing the “Monte Carlo Fallacy”, which refers to roulette, Stagnaro states,

It’s a common notion for gamblers to believe that after a few times of falling on black, the table is “due” to have the ball fall on red. Though this is common understanding, it’s absolutely wrong. Each spin of the roulette wheel is independent of all others―no spin of the roulette wheel affects any other spins. Thus, it cannot be said that the landing on red―or black for that matter―was inevitable.

Similarly, he notes,

Six heads turning up in a row has a ⅟64 (one in 64) percent of a chance happening. A person might believe that the next flip would be more likely to come up tails but this is incorrect, illogical and unrealistic thinking. Why? Because the phenomena/event of 5-heads-in-a-row and the event 4-heads-and-then-a-tail are equally unlikely, each having the probability of ⅟32 or 0.03125 percent chance of occurring. They are both equally as unlikely.

In whatever games of chance (playing cards, roulette etc.), the players accept the implied probabilities by convention, not by inference. In a coin flip (heads and tails) the probability of each outcome is stipulated to be 1/2. For every series of outcomes, no matter what each outcome may be, the probability is the value, 1/2 raised to the power of the number of outcomes in the series. Stagnaro is properly pointing out that the probability depends solely on one’s logical focus and not on any actual material outcomes. The probability of one outcome is 1/2, the probability of two outcomes is 1/4, etc. It doesn’t matter where in a series of material outcomes or upon what limits one wishes to logically focus in a series.

Comparably, where each probability in a series is not of the same probability, the probability of a series of probabilities can be calculated for every logically prospective series of outcomes, while the length of the series is also solely one of logical focus.

The Ladykillers’ Draw

Another illustration of the purely logical focus of probability is the Ladykillers’ Draw. In the movie, The Ladykillers, none of four thugs wants to be the one to murder the old lady, so they draw from four matchsticks. Three are long. One is short. The one who draws the short stick loses. He must kill the old lady. At the start, each thug has 1 chance in 4 of losing. They draw in succession with the first two draws being long sticks. At the time of the draw, the chance of losing is not 1/4, but 1/3 for the thug, who draws second and 1/2 for the last two thugs. Does the temporal succession of drawing, which changes the probability, nullify the initial fairness of the rules of the game of probability? No, because, as Stagnaro has demonstrated, probability is based solely on the choice of a logical focus, not on material reality.

In the movie, one thug holds the matchsticks in his hand, hiding their lengths, as the other three draw in turn. It is the logical refocusing which appears to change the probability from 1/4, which in itself is merely a logical stipulation to which the thugs have agreed. The role of logical focus can be seen by changing the ‘random’ selection process. Let the matchsticks be placed in opaque coin envelopes and be distributed randomly, i.e. with no intentional human bias, among the four thugs. Then, let them open them all at once, OR, let them open them in succession with the results above. If they open them all at once, the focus yields a probability of 1/4 for each thug. If they open them successively and if the first thug, then the second, in opening his envelope, discovers a full matchstick, it appears as if the probability changes from 1/4 to 1/3 to 1/2. However, these different values of probability are based on logical focus. Indeed, all values of probability are merely a matter of logical focus, not a relationship inferable from material reality.

The Fine Tuning Argument and an Old Rejection of It

The conditions on earth are fine-tuned to support life. Fr. Robert Spitzer has succinctly stated the Fine Tuning Argument,

“The odds against all five of the anthropic coincidences happening randomly is exceedingly and almost unimaginably improbable. Most reasonable and responsible individuals would not attribute this to random occurrence (because the odds are so overwhelmingly against it), and so, they look for another explanation which is more reasonable and responsible.”

Consider a bag of marbles consisting of 1 white marble and 99 black marbles. Let a marble be randomly selected from the bag. It is black. This represents a probability of 99/100 = 0.99 = 99%. If we accept random occurrence in explanation of this selection, we must accept random occurrence in explanation of the similar selection of a white marble at a probability of 1%. It would be illogical to reject the selection of the white marble as a random occurrence (just because the odds are against it) and look for another explanation.

Let there be only one white marble in a set of 10^100 marbles, it would be illogical not to accept the selection of the white marble as a random occurrence and, therefore, look for another explanation, if one accepts probability as an explanation in any other instance, such as randomly selecting a black marble.

The Fine Tuning argument, which accepts random occurrence as an explanation at high values of probability and rejects it as an explanation at low values of probability is illogical. Richard Dawkins presented this valid refutation in 2011. He correctly noted, that there can be no value within a continuous variable, whose range is 0 to 1, which can logically divide its continuous spectrum into two different kinds of the variable. Values of the variable differ by degree, not kind.

The range of probability is 0 to 1. Probability cannot be divided into one kind of probability that is an explanation and another kind of probability that is not.

Stagnaro’s Novel Rejection of the Fine-Tuning Argument

Stagnaro has forged a novel demonstration that probability has solely a logical focus. In doing so he has implicitly undermined the Fine Tuning Argument, which draws inferences regarding material reality from material analogies of probability.

Stagnaro’s rejection of the Fine Tuning argument is not the older rejection based on the fact that probability cannot be divided into different kinds. His argument, illustrated above, is that values of probability do not depend on material reality but on logical focus. It remains, for the sake of contrast, to illustrate scientific focus. Scientific focus depends on material reality.

An Illustration of Scientific Focus

Science is the determination of mathematical relationships among the measurements of the properties of material reality. An observational focus in science is not solely logical. It involves material determination or designation. The following illustration superficially appears to be solely logical, but, in fact, depends upon the spatial location of visual observation.

Consider a two-dimensional video display in which observation does not include the frame of the display, thereby eliminating it as a frame of reference. Let the display be of two circles of equal diameter, one stationary, the other in a circular orbit about the first. Refocusing on the second as stationary would put the first in orbit, such that the two displays would be indistinguishable, given the observational conditions stipulated. These two relative motions could be recorded by video cameras, one stationary to the one circle, the other stationary to the second circle. Implicitly each camera and its corresponding stationary circle, form a reference frame. Yet, the recordings would be indistinguishable, unless the circles differed in color.

One might think that synchronizing the cameras would display a difference in phase of 180 degrees between the relative motions. For example, if the one camera starts with the circle in motion to the right of the stationary circle, then the other camera in sync would start with the circle in motion to the left of the stationary circle. However, synchronization presupposes some measure of time (another motion) independent of the relative motion stipulated. Similarly, there could be no measure of the angular velocity of the orbiting circle, because no motion is stipulated that is independent of the relative motion and could, in its independence, serve as a measure of time.

Scientific focus depends upon the material properties of both the observed and the observer.


If probability explains anything material, it must explain Fine Tuning as well.

It should be evident that scientific, i.e. material explanations, require the designation of coherent sets of material observations. In contrast, Stagnaro has shown that randomness and probability require only a logical focus on the elements of logical sets.

At the level of material reality, material conditions determine material outcomes. In probability, material conditions are irrelevant. In Stagnaro’s illustrations, no matter what the prior material pattern or, implicitly, no matter what the present material conditions, probability depends solely on logical focus. This leads to Stagnaro’s principle: Being solely logical, probability may be illustrated materially, but cannot be inferred from material reality.

Theistic philosophers, who employed the low numerical value of probability of Fine Tuning as an argument for the existence of God, have been right about the existence of God, but tragically for the wrong reason. After some initial nailing by Richard Dawkins, Angelo Stagnaro has now nailed shut the coffin of the Fine Tuning argument. May it now rest in the graveyard of the history of modern philosophy.

Endnote: The editors of the National Catholic Register should have deleted the word, percent, from Stagnaro’s essay, including twice in the quotation above, e.g. 1/32 = 0.03125 = 3.125 percent, not 0.03125 percent.

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3 thoughts on “Stagnaro Nails Probability, Ending the Fine Tuning Argument”

  1. Pingback: Probability for the Universe? New Thoughts about Anthropic Coincidences : Catholic Stand

  2. Thanks Bob, for posting this. You make a good case that probability is not “a thing,” but a method for enhancing correct predictions. Having said that, I’ll argue that as someone who has published papers involving probability considerations and taught courses involving probability, I find Stagnaro’s arguments incoherent. I’ve posted on this myself and will post on Catholic Stand to with another point of view of the Anthropic Coincidences.
    Bob Kurland

    1. Thanks for your comment. The Merriam-Webster definition of probability is the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.
      Definitions of probability, rather than solely expressing the concept, are too often couched in the language of the utility of the concept. If we strip away the implications of utility from the Merriam-Webster definition we have: probability is the ratio of a subset to a set. Of course, we do extend the word, probability, to refer to methodologies and algorithms, which employ the ratio of a subset to a set.
      From the Merriam-Webster definition, one might surmise that probability produces an event or is the explanation of an event. Events are produced and explained by the natures of things. We often don’t know the natures of things in detail, so we may employ a methodology based on probability to compensate for our ignorance.
      Another source of confusion is a disparate meaning of probability, namely the qualitative certitude of personal opinion, which is often expressed pseudo-quantitatively.
      Unfortunately, we cannot always depend upon physicists for clarity. In an online essay , a physicist used the certitude of personal opinion to illustrate the collapse of a wave in quantum mechanics. He could have used a mathematical wave familiar even to those whose education in math and physics did not go beyond trigonometry in high school. In trigonometry, the equation, Y = H = [(1/2) × cos (α)] + (1/2) is a wave, which may be viewed as generated by a rotating coin and expressing the probability of heads. Its improbability is the probability of tails, Y = T = (1/2) – [(1/2) × cos (α)]. Each wave collapses should the coin come to rest horizontally, the familiar result of the collapse of a coin flip. Each wavelength is 360 degrees. Horizontal rest yields a probability of one for heads and a probability of zero for tails, if the phase of the wave(s) is at 0 degrees at collapse. It yields a probability of zero for heads and a probability of one for tails, if the phase of the wave(s) is at 180 degrees at collapse.

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