I have been musing about crows, blackness, and probability since I met with Derek von Barandy and James Gibson about Hume and Bonjour last Thursday night. Let me share a snippet of my thoughts with you, as writing it down helps me to work it out in my mind.
This is not meant as an argument, but my own unorganized ponderings.
There are ten birds in a cage, five of which are white. The likelihood of me selecting a white bird with my eyes closed is 5/10. In a bird cage whose total number of birds is unknown to me, I cannot calculate the likelihood of white bird selection.
Such is the case in our world, whose total number of crows is unknown to me. If I examine 1 crow and find it to be black, my probability of selecting a black crow in the future becomes 1/X. If I examine 2 black crows, I increase my odds, but I can never reach a point at which it is true to say that my odds make it more likely that I will select another black crow for examination. For it is an epistemic possibility for me that there exist but 2 black crows in a world whose crow population remains unknown.
After selecting 2 black crows I can truthfully say that, on account of my experience, it is more likely that another black crow is found (in this case "more" is a term relating to my first trial). This is so because last time my odds were 1/X, and this time my odds are 2/X (we are assuming X is a finite number - there are only so many crows that exist at the time of the exam).
Thus, although I am able to increase my epistemic odds by examination, I am unable to know my actual odds.
Advancing from black crow selection to crow population description raises the problem I want to illumine. Suppose I want to support the claim "all crows are black". To do this I can examine one million crows, lending support to my hypothesis and perhaps rendering it a theory. The "odds" of blindly selecting a black crow after such an experiment are 1,000,000/X.
Terms like "probability" as applied to the truthfulness of my theory are problematic. I cannot say that my theory is "probably true", as I cannot express it as probabilities are expressed. What I can say is that now that my hypothesis is a theory it is relatively more probable to be true that it was when it was a mere hypothesis. I am not telling the truth if I say that my theory is "probably true".
Actual probability calculated for such a claim defeats the relevancy of such calculation. This is so for all exhaustive claims about reality. To start with, I cannot find terms to fit the probability schema. What is to be the numerator? What is to be the denominator? If this world is the numerator (i.e., if it is true that all crows are black in this world), then my numerator is 1. If I somehow know the number of possible worlds (assuming that it is a finite number), then I suppose I can use it for my denominator. I would also have to know the number of possible worlds whose entire crow population is black (never mind the difficulty in examining every crow in every possible world).
But in discovering what I can truthfully place in the numerator position I have found the relevant information. I will have had to find out already whether all crows are black in this world. In discovering this truth I have eliminated the need for me to calculate how probable it is that all crows are black (in this world).
Perhaps it would be helpful on another front to learn how narrow the parameters are that our world lies within. If the denominator of our "probability", or number of trials (i.e. number of possible worlds), is large relative to the numerator, or number of possible worlds that only have black crows, then we can count it remarkable that our world is one in which all crows are black. For example, if we can somehow learn that 12 out of 1,000,000 possible worlds have naught but black crows, then we should marvel at the fact that our world lies within the parameter of 'having only black crows'.
If we are careful, we can see that actual probabilities do not exist. If it is true that all crows are black, then the probability is 1. There is no crap shoot.
But what about the probability of this world being the one that occurred? Isn't that an actual probability? Here is where care must be taken. We must not mistake probability with possibility. Let's examine what it means for something to be possible.
There are four categories that a thing can fall into:
1. Necessary
2. Contingent
3. Possible
4. Impossible
Necessary things are those that cannot be otherwise than they are. They exist in every possible world.
Contingent things are those that can be otherwise than they are. They exist in this world, but not in every possible world.
Possible things are those that can be. They exist in at least one possible world, and they do not exist in at least one possible world.
Impossible things are those that cannot be. They do not exist in any possible world.
Although it may be true that all crows are white in some possible world, it may not be so that any crows are white in this world. What I mean is that the truth of my theory, that all crows are black (in this world), does not depend on whether the contrary is possible in another world. In fact, the truth of my theory depends on whether it is true in this world.
In discovering whether it is true in this world, I do not eliminate the possibility of its falsehood in another world. But whether it is true in this world is not probabilistic. This world is this world, and our tomorrow is not arbitrarily selected from among possibilities. Rather, tomorrow is created by the state of affairs that exist today, combined with personal determination.
Let me show you what I mean. If all crows are black in this world, and it is because of something in crow genetics that doesn't change as time advances, then it will be so tomorrow that all the crows in this world will be black. Crows will mate, the earth will rotate on its axis and advance its revolution 1/365.25th, and we will examine all new crows spawned and find them all to be black.
I say that personal determination is the other force that creates tomorrow because, as a certain set of meteorological circumstances yields a rainstorm, I can choose to operate upon the immediate sky above Los Angeles and alter the outcome of today. I could do this by creating a large fan, blowing the warm front out of the course of the cold front. While physical states of affairs are deterministic of their following physical states of affairs, personal agency can alter states of affairs. Such agency is not arbitrary, but it is not itself determined. Rather, it is determining. The nature of its ability to determine rests upon the power and authority whereby it determines, as well as its options in determining. Thus all things have as their first cause (a) choice(s) made by (a) person(s). My physics/metaphysics is not the key, however.
What is the key is that what produces tomorrow does so determiningly and according to a framework, not probabilistically and/or without boundaries. Thus, in cases that are produced within systems of pure physical causation, the outcome may be predicted. For example, once a pair of dice are thrown, if a physicist is given the opportunity to measure the velocity and spin of the dice, as well as their distance to the ground and the shape and exact physical nature of any obstacles, he is capable of predicting the outcome. The outcome is not probable, it is certain.
In systems that contain personal forces, outcomes are not produced probabilistically either. A person's choices are not made for them arbitrarily or randomly. The person is responsible for determining the choice. Moreover, he must do so with the burden of forces and compulsions influencing his will. The decision must also be one of available decisions to make, and it must be according to the laws in operation.
If you do not accept my physics/metaphysics, then it is even easier for you to see the non-arbitrary, or non-probabilistic nature of outcomes. For it may be that even personal decisions are nothing more than the tantamount of complex and layered physical phenomena.
In the case of the dice roll, outcomes are not probable, they are certain and fixed. Outcomes are, however, possible. If our epistemic situation is limited (i.e., we are not aware of the initial states and governing laws of the dice), then we call given outcomes probable according to what we know is possible. There are six sides to a die, and only one will be facing upwards at the end of the roll. We call this a probability, but it is only one epistemically. The trajectory of the dice will be determined by the person, and the rest is up to physical states of affairs that are reliable (the size of the dice and the force of gravity, etc.).
In the case of my theory that all crows (in this world) are black, it either is so or it isn't. My theory is possibly true, but it cannot accurately be said to be probably true, unless by this we only mean that we have warrant to believe in it and our warrant increases with every black crow that is found.
We therefore cannot ever elevate a theory contingent upon experience to the status of certain truth. To be rational, we must therefore choose to believe what we find to be the most epistemically probable truth (when it comes to some beliefs, warrant may consist of both empirical and logical evidence). This is what I call faith: belief in a proposition for which evidence exists, but irrefutable proof one way or the other is not observed. It is an active belief, but should not be held without reason.
When considering whether to believe in something, one ought to consider first the evidence in favor of it, and then consequences of accepting such a belief. This is what Jesus speaks of at the end of chapter 14 of Luke's gospel when He says, "Whoever does not carry his own cross and come after Me cannot be My disciple. For which one of you, when he wants to build a tower, does not first sit down and calculate the cost to see if he has enough to complete it?"
An issue entangled in this pondering is the reliability of science. Hume argued that for inductive enterprises (such as physics), in contrast to a priori enterprises (such as mathematics - within which domain we are able to fully examine just a single case of 2 + 2 equally 4 and make justified conclusions about all instances of 2 + 2), there cannot be found rational justification. In other words, why do we assume causation, and expect that the future will resemble the past? Couldn't it just be coincidence that the cue ball was accelerating South at 3 miles per hour, and when it reached the eight ball it lost its energy, and then the eight ball (unconnectedly) assumed the same amount of energy (minus friction) and continued South? What, exactly, is to assure the same "effect" in the future? The "law" that we think is governing billiard ball behavior is only a description of past experience, and causality is assumed.
A physicist will explain the mechanical issues that "caused" the transfer of energy at the time of the collision, but his world contains that same problem, on a smaller level. Why is it that atoms operate the way they do? Then - why is it that particles act the way they do? This will go on until objects get too small for us to examine at the present, and the only answer scientists can give us that they have run experiments and written descriptions of the way physical things interact with each other. They used these descriptions to predict the future, and the future did indeed resemble the past.
But we have run into our crow problem. We cannot calculate even the epistemic probability of the future without knowing about every case. Our "odds" only increase. There is never a point where we know that we have examined a majority of the cases of a physical occurrence within the universe. We can therefore never make the claim that something is "most likely". We never know how big our sample size is relative to the whole.
Bonjour's solution is to say that if we continue to find that a scientific law predicts the future, then we have reason to believe that there is something causing the outcome, and it is most likely that there exists a real reason (a determiner) that we keep on finding black crows.
But this doesn't satisfy - it begs the question. In one sense, of course something caused the cases we found. Of course something caused the crows that we found to be black. But that doesn't mean that this cause operates upon all crows.
Even if we say that it is likely that there is a reason that most or, in our case, all of the crows we found were black, we run into problems. As I illustrated above, "probable" or "likely" is a fallacious descriptive. We cannot calculate actual probability, nor does it exist as regards the truth or falsehood of a proposition (a proposition either is true or it isn't - there isn't a chance as to whether it will become true or not, as we are inquiring as to its current state). At best, Bonjour's claim can be reconstructed to specifically epistemic probability as outlined above.
It seems then, that induction has its limits and we are forced into humility when it comes to all a posteriori enterprises.
Another issue related to these musings is the reliability of physical laws and, as I will show, the a priori argument for meta-order.
One can object to my reasoning by separating my claim into two. The first would be that the extant truth of a proposition is not probabilistic. The second would be that the truth of a proposition about the future is not probabilistic.
As to my first statement, it should seem obvious (although many thinkers today inadvertently undermine with their writings). If a proposition regards the way things are - reality - then it is either true or false. Whether or not we are aware of it, reality is as it is.
The second statement is more contentious. Is a proposition that concerns the future probabilistic? I hope that by now I have made my case for why the answer is 'no'. The future is determined. Certain facets of the future are not determined yet, but they will be determined by something or someone. Pure probability is not an operating force unto itself - it is a false notion.
One might do well to say that 'if physical law (x) remains in effect throughout our next experiment, then the outcome will be the same as last time'. I like this statement. Let's explore it: can I have a priori justification for believing that if every relevant factor remains the same, an identical outcome may be produced? Certainly we trust this in science, but can we know it with justified certainty?
Even though this type of humility ('if' physical laws stay the same - allows that we do not know whether physical laws are contingent and/or consistent within this world), it still assumes a meta-order. Let's describe the application of this assumption in our case. The one who says 'if all remains, an identical procedure will produce an identical outcome' is assuming that 'if all remains, an identical procedure will produce an identical outcome'.
Although these are identical statements, the second emphasizes the structure or necessity whereby the conclusion is drawn. You see, although we are now allowing even for the strange possibility that physical laws may not apply, we are saying that it is obvious that if they do then we can produce the desired outcome again. We are assuming that our experiment will follow some order. It is clearly impossible for us to repeat a literally identical experiment under literally identical conditions and produce an entirely alien outcome.
To apprehend this IS to understand its truth, just as to understand what it means when we think that 2 + 2 = 4 is to understand that it is true. Perceiving these propositions a priori is to perceive their justification.
This brings me to what I find to be the single most foundational and profound assumption of science: that the universe is intelligible. This order that exists outside ourselves can be understood.
To complicate my undertaking I want to consider the solipsists cosmological argument. I heard about a lady who wrote a philosopher, 'I am a solipsist, and I just can't understand why there aren't more of us'... he found her statement hilarious.
Suppose that I am disembodied, and have no experience of anything other than myself. I have never seen, felt, heard, smelt, or tasted. I have perceived of nothing. I am only capable of thinking, and so I begin to do so...
"I exist." I begin, without knowing that Descartes says that I should begin here. "I know this because I am thinking. I have not always existed, and I did not bring myself into existence. There must be something that brought me into existence. I cannot conclude that it is a person, as there may be a rule that solipsis like me just pop out of nowhere uncaused. But such a rule is a cause. Maybe there is no rule - I just popped into existence from nothing, not of myself, nor of a rule. But then, wouldn't that be a rule? It would state something like 'for X amount of time, nothing will come about, then at time Y, a solips will come into existence'. I can go on thinking about what possible scenario possibly accounts for my existence, but I cannot imagine it as unordered by some account. Therefore I can say with certainty that I exist, and that some order exists outside myself. The very fact that my thoughts are linear, and I am able to construct rational, ordered sentences attests to this fact. I did not create the logic by which I am thinking."
Solips L knows that he came into being inside this permeating order, and he is subject to it. The order seems to be built in, permanent, or eternal. And so surely the order within which SL was conceived must be greater than him, for he fits inside its bounds. Certainly then, the order is personal, just as he is personal.
The equation of this order with a person is professed by John, in the first chapter of his account of the gospel:
1. In the beginning was the Word*, and the Word was with God, and the Word was God.
2. He was in the beginning with God.
3. All things came into being through Him, and apart from Him nothing came into being that has come into being.
4. In Him was life, and the life was the Light of men.
5. The Light shines in the darkness, and the darkness did not comprehend it.
6. There came a man sent from God, whose name was John.
7. He came as a witness, to testify about the Light, so that all might believe through him.
8. He was not the Light, but he came to testify about the Light.
9. There was the true Light which, coming into the world, enlightens every man.
10. He was in the world, and the world was made through Him, and the world did not know Him.
11. He came to His own, and those who were His own did not receive Him.
12. But as many as received Him, to them He gave the right to become children of God, even to those who believe in His name,
13. who were born, not of blood nor of the will of the flesh nor of the will of man, but of God.
14. And the Word became flesh, and dwelt among us, and we saw His glory, glory as of the only begotten from the Father, full of grace and truth.
15. John testified about Him and cried out, saying, "This was He of whom I said, `He who comes after me has a higher rank than I, for He existed before me.' "
16. For of His fullness we have all received, and grace upon grace.
17. For the Law was given through Moses; grace and truth were realized through Jesus Christ.
18. No one has seen God at any time; the only begotten God who is in the bosom of the Father, He has explained Him.
19. This is the testimony of John, when the Jews sent to him priests and Levites from Jerusalem to ask him, "Who are you?"
20. And he confessed and did not deny, but confessed, "I am not the Christ."
*This Greek word is logos, referencing the Greek's notion of order, logic, reason, that by which all things have existence and orderly relationships with each other.
Another man identified this logos, this personal order who became incarnate as the very order that holds all things together.
When reasoning with the Greeks in Acts 17:28, Paul says,
"In him [that is, Christ] we live and move and have our being, as even some of your own poets have said,'For we are indeed his offspring.'"
The first part of the sentence is possibly a quote of Epimenides of Crete, but the obvious quote is of Aratus's poem "Phainomena".
Then, in his letter to the believing community in Colossae Paul writes in chapter one:
"For by Him all things were created, both in the heavens and on earth, visible and invisible, whether thrones or dominions or rulers or authorities--all things have been created through Him and for Him. He is before all things, and in Him all things hold together."
Thus is can be seen that even Solipse L can perceive the existence of personal order a priori.
As to physical laws, I agree with Hume, that unless we have some perpendicular reason to believe that they will persist, we can but humbly continue to trust them. Unless...
The crow case may not be our best example. Doesn't it seem silly to say that it is a physical law that all crows are black? It doesn't seem ultimate enough. The blackness of crows may be caused by the culmination of several intersecting laws and conditions. A crow is a pretty complex being.
Could it be that if we were not epistemically restricted we might be able to perceive why it is so that physical laws are as they are. Just as I shown by experience how to do calculus (although it is an a priori enterprise), can it be that if I were shown why it is so that physical laws could not have been otherwise - that they are necessary? Is it possible that I am in a fragmented state and cannot perceive with pure rational insight such necessity?
Imagine such a case: a perfectly functioning (but limited) Solipse L. I am back in the situation described above, thinking about things. I begin to think that if something physical were to exist (all conceivability objections aside), then such stuff would behave in certain ways that make sense. Not only that order exists is perceived by me, but which order exists. In fact, the very nature of order can only be one way. Given exactly what it is that particles are made of, they are required to behave accordingly. Their behavior flows logically from their very nature.
For Solipse L to imagine a given nature for potential particles that might one day come into existence IS for him to imagine the nature of their interaction with each other. In this case, what it is that is underlying these "laws" is the pervading order that exists - the fabric of reality. Even a posteriori enterprises, such as science, if clear thinking is excersized and intellectual limits are not applied, could get to the bottom of the way things operate. In such cases, more than mere physical laws can be described, but the nature of the underlying order can be: mathematics, logic, and other purely relational domains. Summaries that accurately describe mathematics and other such necessary truths are indeed descriptions of God Himself.
In what way was creation voluntary then? Aside from the fact that creation at all was voluntary, God was creative in His creation. He made choices as to how creation was to look like and operate.
When we look at the physical laws, we see them as incomplete in a description of the universe. Not only do there seem to be laws in effect here, but there are also constants and quantities. Constants are types of forces which behave in certain stable ways, and persist evenly as time advances. Quantities are amounts that seem to have been arbitrary put in at the beginning of time. The amount of matter and dark matter, for example. Also the amount of energy and dark energy, the amount of radiation, the amount of entropy, and a few others. God made choices as to how much of what ingredient to put into the universe, as well as the velocity to start us off at. He also interacts with His creation in other ways after the initial creation.
What I find interesting is that the number line contains the infinite set of numbers. For a constant to be what it is, the "odds" or really "possibilities" for its value are literally infinite. Planck's constant, for example, could have been (in the broadly logical sense) any value at all. Its chances were 1/(infinity). That it is what it is, is something to marvel at.
But not only is there Planck's constant to consider, there are a host of others. The "odds" of them occurring in the relationship that they did to one another are [1/(infinity)] X [1/(infinity), et al. The "chances" that all the constants line up properly are staggering. When considering quantities as well, marvel should skyrocket.
Science has shown that if any given constant were to be changed a tiny bit, the effects would be devastating. The constants are finely tuned to accommodate human life.
Not only does metaphysical probability not exist, but the possibilities for worlds are infinite.
The Creator is great, and greatly to be praised.
As I continue to let my imagination run away with me as I journal, I think about other scattered issues. For instance, computers sometimes have random number generators. But, they have processes for selecting such numbers. The outcomes are unknown to us, as are the processes. They are only epistemically random. If we knew the rules and the initial states, then we would not call them random. Randomness does not exist.
Another thought: are all intelligible things produced by intelligence? When Lindsey says something intelligent, I can make sense of it. It is orderly. When we have a baby, it will probably speak some gibberish (until age two, when he will unify the theories of quantum physics with general relativity). I will tell him that his gibberish is unintelligent, because it is unintelligible. If our universe is intelligible (the fundamental assumption of science, remember), does it imply that it is produced by a Mind?
Even if chaos is possible, and if such theoretical chaos could produce something orderly or intelligible, it does not account for the existence of the order that such an effect exists within. There remains a need for a law giver.
I studied Turing Machine Functionalism for a short while a couple years ago. While there are so many issues to think about, I want to highlight that the Turing Machine Functionalists still have to admit that such machines must acquiesce to order that existed before the machines, and will persist after such machines expire. What accounts for that order?
I will tell you that it is permanent, necessary, personal, self-existent, and the initiator of the existence of everything other than itself.
More unorganized journals to come. Maybe on these matters, maybe on others.
