that's not really a counter to kant, that's more saying you prefer empiricism to kantian idealism as a means of ascertaining "triuth."  what is truth?  subjective or objective?  i think kant would argue that even a widely held truth is still truth colored by human perception and thus ultimately subjective.  i'm pretty sure the scientific method was the very thing kant was criticizing.  how does the scientific method get us beyond the limitations of our perception that kant observes?  is there really such a thing as true objectivity, i.e., "pure reason," untouched by any sort of pre-conceived notions?  are kant's posited "limitations" of reason fallacious?  if not, how can one really speak in terms of universals at all?

i wasn't implying heisenberg's principle was supernatural.  i just recall dr. hawking making a comment in "brief history" that the uncertainty principle makes the idea of a deterministic universe impossible.  while this doesn't bode well for theists (of a certain stripe anyhow), it also doesn't bode well for the omnipotence of human reason, which during the enlightenment was taken by many thinkers as a given.  i don't propose you or your colleagues take it as a given, i just thought i'd touch on the issue.

"Mine is the placement of modern religion next to ancient religion in terms of status. They are equally valid in their assertions and explanations."

that's very interesting, in that it's the exact opposite of what nietzsche wishes to accomplish, particularly in "the birth of tragedy" and "the gay science."

as for the origins of the universe, i'm afraid i have no astrophysicists handy, but i'm not interested in how it "was."  i only wanted a clarification of sapient's remark.  of course you cannot provide that.

i appreciate your candor, though i've never heard hawking called a "shit disturber" before.  did you mean "distributor"?  do you think hawking has a religious agenda or what?

nietzsche in "the birth of tragedy" lauds wagner because wagner represents a return to classical religion, or what he calls "dionysian" religion.  through communal religious festivals and gods that are approachable to humans, we can overcome the fear of death, which is one of schopenhauer's requirements for a proper religion.  while of course nietzsche later broke with wagner, one can still see the communal religious trend in later works.  i would recommend julian young's "nietzsche's philosophy of religion."  he goes against the grain of classic nietzsche scholars in saying that nietzsche, while of course anti-christian, was not necessarily anti-religious, and indeed saw that a return to ancient greek religious modes (in a modern context) would be beneficial for mankind's survival and "evolution" (not necessarily in a darwinian sense; nietzsche hated darwin).  it's interesting reading and i agree with many of his interpretations.

then what are your views on pantheism and/or monism?  it's well known among classics scholars (it was one of my majors) that at least by the time of the apogee of greek civilization, very few greeks probably believed their myths literally but held them as representations (though not entirely in the sense of what we would call "fairy tales&quot of higher truths and that we are actually all "in god."  there is also the parallel example of brahman in hinduism.

in fact, is this in substance any different from the typical atheist's position that it is the universe that is (in some sense) infinite and "creates" through observable means?  is it absolutely necessary to the atheist position that this universe have no consciousness of its own?

The main problem I have with pantheism is that it seems to introduce an extra "magic" variable where it's not called for. Please understand: I'm a strong atheist and positivist. My bet is on the scientific method for solving problems of the nature of reality. I may be an extreme example of the views expressed on the site or by atheists in general.

After reading the rest of your post, I'm not sure which "monism" you mean. You mean like "everything is one" or something along those lines?

Yeah, that's the sense I mean. It's also the way I understand modern religions: as representations of hope and fear elaborated.

I haven't seen that assertion, so I'm not sure what you mean. To the best of my knowledge, we've found out that the universe is expanding, but I'm not sure about the creation part.

I'd say so, since the consciousness of the universe is a weak hypothesis. Tell me how this consciousness would work in your theory, and maybe we can discuss it, but I'm having a hard time seeing why an extra-physical "consciousness" is necessary to the explanation of the universe in general.

natural,

i'm not exactly sure why, but your aphorism strikes me as almost confucian in style.  bravo.  those are good questions.  how does science tell us consciousness evolved?  i know fundies say they have no explanation, but do they?

"That's the strong atheist position as far as I'm concerned: probably no flying walruses, and probably no gods."

fair enough.  i think i understand your position.  still, what would you say to those very respected thinkers throughout history, among them kant, schopenhauer, nietzsche, jung, and eliade, who said that religion is an important human survival mechanism?  i believe it was jung specifically who said something along the lines of "every society needs a myth to live."  i recall in the nightline debate that sapient said that morality is an important survival mechanism.  is it not also true that the majority of humanity cannot conceive of morality without a big daddy to be accountable to?  aren't you working against humanity's survival?  is everyone ready for the knowledge that there's nothing out there?

in fact, how would you answer camus's big question: why not kill ourselves?

It's true that most of humanity has been conditioned to only accept an externally-imposed morality. However, absent theism, why would they not simply accept natural humanist morality? We have no evidence that external morality is required, just that it's how it is currently.

I think humanity is growing up, and is almost ready to give up our belief in Santa Claus. Almost.

Because life is fun? It's good to have fun? It's good to help others have fun?

ah, i see you already nailed it. 

"However, absent theism, why would they not simply accept natural humanist morality?"

do you ever think we'll really have a chance to find out?

"Because life is fun? It's good to have fun? It's good to help others have fun?"

why put question marks after those?  those are goddamn good responses, and the most honest i've heard in a while.  in fact, i think you should've stopped with the first.

I don't believe Kant intended to lead to solipsism. I'm just getting back into philosophy because of the RRS, so I haven't had time to go back and re-read Kant recently. My memory of Kant is about 20 years old, so it might very well be faulty. But, as I recall, he intended to refine an epistemology that allowed for deductions of reality, based on analytic truths, which were based on logic, and on synthetic truths, which were combinations of analytic truths and observation of reality.

It was his innate distrust of the epistemology of the scientific method that led him there, I think. And looking back at the time, no wonder. Science was still in its infancy. Newton had just changed the scientific ontology in the same way that quantum mechanics changed the Newtonian-based ontology a couple of hundred years later. Hume, Locke, Kant, Spinoza, and all the rest were trying to cope with this new ontology. I'm not entirely sure if Kant was trying to refute rationalism and empiricism, or combine them.

Well, I think the RRS is different for each of us. For me, it's a place where I can feel as if I'm part of a rational group of people. I also get to engage in intellectual (and some not-so-intellectual) discussions. Such as this one. I learn quite a bit. As I said, my last study of philosophy had been 20 years ago. These discussions are forcing me to go back and re-read -- and re-evaluate based on my greater maturity -- philosophy. And that is good.

Kelly and Sapient have different goals, I'm sure. They certainly want to confront religous beliefs head-on. Near as I can tell, it's not because they are against religious belief per se; it's more that religous belief is hurting our chances to progress beyond our current state. Of course, that's my understanding of their motives. Maybe they just enjoy being snarky.

Insert big grin here.

Will and I seem to be very similar in belief and temperament. He's a bit less snarky than me, but that's mostly because he holds it in reserve for really deserving moments. Me, I just like to be funny.

For me, it's not just probabilities. It's about perception. We have perceived only one realm, the natural reality around us. There are certain arguments for a quantum-computer nature of the universe, which perhaps even allows for a universal consciousness. This is the only definition of God that I can accept as even remotely possible. However, the chances of such a Spinozan naturalistic pantheistic God is so remote, I consider it highly improbable. And until there is some sort of evidence, it is (as Will said about God in general) completely irrelevent. Any further speculation on the nature of God is just that: speculation.

Any other definition of God has to prove something even more unlikely: a realm that is separate from, but intersecting with, ours. The likelihood of that is so remote, it is essentially impossible.

Anyway, that's my position. It's not a convincing argument against God, but for me, it is more than sufficient to give me a hard-atheist perspective.

Submitted by todangst on April 22, 2007 - 6:00pm.

Why the "Problem of Induction" really isn't a problem. (And why theists don't even get it right)

What is Inductive Logic?

Gregory Lopez and Chris Smith

We can define any type of logic as a formal a priori system (axiomatic) that is usually employed in reasoning. In general, if we feed in true propositions, and follow the rules of the particular system, the logic will crank out true conclusions.

We can define 'induction" as a thought process that involves moving from particular observations of real world phenomena to general rules about all similar types of phenomena (a posteriori). We hold that these rules that we generate are probably, but not certainly, true, because such claims are not tautologies.

Inductive logic therefore, is a formal system that can be distinguished from deductive logic in that the premises we feed into these arguments are not categories or definitions or equalities, but observations of the real world - a posteriori world. Inductive logic therefore, is the reasoning we do every day while working in the real world - i.e. the probabilities that we deal with while making judgments about the world. We can think of it as learning from experience and
applying our prior experiences to new, but similar, situations.

History

Inductive logic is basically a form of probability. While human beings have used intuitive forms of inductive reasoning all throughout history, probably theory was first formalized in 1654 by the mathematicians Pascal and Fermat - during their correspondence over the game of dice! In their attempts to understand the game, they created a set of frequencies - or possibilities that described the likelihood for particular rolls of the dice. In doing this, they accidentally set down the basics of probability theory.

It was only a short time later, in 1748, that someone noticed a problem in probability theory - that it included the presumption that the future would be just like the past, yet this assumption could not in of itself provide a sufficient condition for justifying induction, seeing as there is no valid logical connection between a collection of past experiences and what will be the case in the future. Hume's Inquiry Concerning Human Understanding" is noted, even today, for pointing out this problem - the "problem of induction". However, few realize that a solution to the problem appeared only a few years later: In 1763, Thomas Bayes's presented a theorm that unaware to him, could be used to provide a logical connection between the past and the future in order to account for induction. More recently, Kolmogorv (1933) axiomized probability theory, which means that he gave probability theory an axiomatic foundation. Induction, therefore, while a probabilistic enterprise, is founded on a deduced system:

The three axioms of formalized probability theory:

1. The probability of any proposition falls between 1 and 0.

2. Certian propositions have a probability of 1

3. When there is no overlap, P(P or Q) = P(P) + P(Q)

and the definition of conditional probability:

P(P/Q) = P(P & Q)/P(Q)

If you accept these axioms, you must accept Bayes Theorem. It follows logically from the axioms.

These are the key points to the history of induction as far as the formal origins and formal supports for induction. I will cover these points in more detail below. But first, let's look at the different types of inductive logic.

Types of Inductive Logic

Let's do a brief review of some kinds of Inductive Logic

Argument from analogy . This occurs when we compare two phenomena based on traits that they share. For example, we might hold that Object 'A' shares the traits w, x and y, with with object 'B,' therefore, object A might also share other qualities of object B.

Statistical syllogism. This inductive logic is similar to the argument from analogy. The form of the logic follows: X% of "A" are "B", so the probability of "A' being "B" is X%

Example: 3% of smokers eventually contract lung cancer. John Doe is a smoker, therefore, he has a 3% chance of contracting lung cancer.

Generalization from sample to population The best example of this inductive logic would be a poll. Polls rely on random samples that are representative of a group by virture of their random selection (i.e. the fact that every person had the same chance of being chosen for the sample).

On my website, I will also discuss John Stuart Mill's Method of Causality. For now, let's return to the aformentioned "problem of induction" and take a deeper look both at the problem of induction, and some solutions for this problem.

The problem of induction

You've probably heard about Hume's famous 'problem of induction"

How do we know that the future will be like the past?

Or... more comedically

How do we know that the future will continue to be as it always has been?!

Consider the following example: we observe two billiard balls interact. From this, we observe that they appear to obey a physical law that could be presented in the formula: F=ma - Force = Mass X acceleration. From this observation, we then generate a general law of force. However, the problem then arises: how can we hold that this law will really apply to all similar situations in the future? How can we justify that this will always be the case?

If we argue that "we can know this, because the balls have always acted this way in the past" we are not really answering the question for the question asks how how we know that the balls will act this way in the future. Of course, we can then insist that the future will be just like the past, but this is the very question under consideration! We might then insist that there is a uniformity of nature that allows us to deduce our conclusion. But, how do we know that nature is uniform? Because in the past it always seemed so? Again, we are simply assuming what we seek to prove.

So, it turns out that this defense is circular... we assume what we seek to justify in the first place, that the past will be like the future. So this argument fails to provide a justification for induction.

But this in itself is not the whole story, in fact, if we stop here, we get the story all wrong. You see, the 'uniformity of nature' is in fact a necessary condition for induction but it could never be a sufficient justification of inductive inference anyway. The actual problem of induction is more than this: it is the claim that there is no valid logical "connection" between a collection of past experiences and what will be the case in the future. The classic "white swans" example serves: the fact that every swan you've seen in the past was white means simply that: every swan you've seen has been white. There is no logical "therefore" to bridge the connection "all the swans I've seen are white" to "all swans are white" or "the next swan I encounter will be white".

So, yes induction presupposes the uniformity of nature, but while this is a necessary condition for induction, the UN is not sufficient to justify inductive inferences epistemologically. So, any attempt to solve the problem by shoring up the 'uniformity of nature' will never work to begin with. When the next swan turns out to be black, it shows your statement "all swans are white" had no actual "knowledge" content. What you've done is presupposed nature to be uniform, but not in fact justified any particular inductive inference you may wish to make.

So,solving the 'problem' of induction is more than just trying to find a way out of the 'circle' of uniformity of nature/justifying induction. There is a problem that needs a solution. Interestingly, many critics seem to believe that the story ends here - that there simply is a problem, and that all solutions are merely circular. But this is untrue. There are responses to the problem.

Since it was Hume who first uncovered this problem, let's begin by looking at his response:

David Hume's Response: This assumption is a 'habit'

Hume's answer was that we had little choice but to assume that the future will be like the past..... in other words, it was a habit born of necessity - we'd starve without it! And, given that there was nothing contradictory, logically impossible or irrational to holding to the assumption, this utility of induction was seen to support the assumption on a pragmatic basis. This is a key point lost upon many people: there is nothing illogical or irrational about assuming that induction works, nor are there any rational grounds for holding that 'induction is untrustworthy'. The fact that I cannot be absolutely certain that the sun will rise tomorrow does
not give me any justification in holding that it will not rise tomorrow! This error is called the fallacy of arguing from inductive uncertainty.

But merely holding that an assumption is 'not irrational' is not a satisfying enough answer for many. Hume himself stated: "As an agent I am satisfied but as a philosopher I am still curious." So let's continue our search for an answer to the problem.

What is the Basis for Inductive Logic? - An examination of Probability Theory

Curiously, the axiomatic foundations for inductive logic only tell us how a probability behaves, not what it is. So let's begin our examination by first defining what we actually mean by saying the word "probability".

Three common definitions:

Classical - the classical definition describes probability as a set of possible occurrences where all possibilities are 'equally likely' - but a problem arises from this definition. For example, how do you define "possibility" in a univocal manner? Is an outcome 50/50 (either it happens or it does not) or is an outcome actually 1/10, 1/100? In many cases there are possible reasons for each choice. So let's look at another definition.

Frequentist - the 'frequency' is the probability for a given event, that is determined as you approach an infinite number of trials. For example, as with the central limit theorm, you could learn what a probability might be for the roll of a 7 on a pair of dice, after rolling them for a large number of trials. This is the most popular definition, including in science and medicine. This view is backed up by axiomatic deduced probability theory (based on infinite trials (like coin flips)) the law of large numbers. The frequency converges to the probability when we reach infinity. But there are problems here as well: does the limit actually exist? Do we ever really know a probability, since we can't do things infinitely? Also, this method gives us very counterintuitive interpretations. For example, consider a 95% confidence
interval - often this is read to mean that 1 out of every 20 such studies is in error. In
actuality, what this means is that if the experiment were repeated infinitely, you'd get the real mean 95% of the time. This is hardly what people think when they read a poll.

Finally, we can't apply this method to singular cases. 'One case probabilities' are "nonsense" to the frequentist. How do we work out the probability of the meteor that hit the earth to kill the dinosaurs?
We can't repeat this experiment infinitely! We can't repeat it once! We see the same problem with creationist arguments for our universe that attempt to assign a probability to the universe.

Subjective probability - Here, probability is held to be the degree of belief in an event, fact, or proposition. Look at the benefits of this model. 1) We can more carefully assign a probability to a given situation. 2) We can apply this to method 'one case events'. 3) This manner of defining probability gives us very natural and intuitive interpretations of events that fits with our use of the word "probably", circumventing the problems of frequentism.

MOST IMPORTANTLY: Allows us to rationally adjust our beliefs "inductively" by use of probability theory, which is a mathematically deduced theory, so we can latch on our beliefs onto a deductive axiomatic system. Here then, for many, is the solution to Hume's "problem" - induction is no longer merely "not irrational', but instead, can be seen as resting upon a firm deductive foundation.

How does it work?

How do you get a 'number' or probability, for subjective probability? Let's use the concept of wagering.... What would you consider to be a fair bet for a particular outcome? Is X more probable then getting Y heads in a row in your view? In brief, this is how the method works.

Subjective probability and frequency are linked by the "Principal Principle" (David Lewis) or Ian Hacking's "Frequency Principle" (his book cover appears at top). Subjective probablity is justified by a reductio argument: if your subjective probabilities don't match the frequency, and you know nothing else, you have no grounds for your belief.

A question may arise: How can we reason anything if probability's subjective? Well, it is true that you can just choose any starting ground you desire, HOWEVER, your choice must follow laws of probability, or else you're susceptible to 'Dutch Book Arguments' - what this means is that if your degrees of belief don't follow the laws of probability, you are being inconsistent and incoherent. You can choose to believe what you want, but at the risk of being incoherent. The beauty of this method is that a starting point is not necessarily very important: given differing
starting probabilities, based on different subjective evaluations, two very different people who are shown enough of the same evidence will have their probabilities converge to the same value (a LAW OF LARGE NUMBERS) by probability theory - beliefs will converge to a similar value!

Being a subjectivist who wants to use probability as a basis of induction leads us to focus on a certain way of doing things using, Bayes' Theorm

BAYES' THEOREM

The simplest form of Bayes' Theorem:

where:

H is is the hypothesis. This is a falsifiable claim you have about some phenomena in the real world
E is the evidence This it the reason or justification you have for holding to the
hypothesis. It is your grounds.

P(E|H) is called the likelihood : it is also the probability of E given H. In other
words, it is the probability that the evidence would occur if the hypothesis were true.

P(H) is called the prior, or prior probability of H. It is the probability of the
hypothesis being true without taking additional evidence into consideration. In other words, it is an unconditional probability. When I call something, "the prior" without qualification, I mean this probability.

P(E) is called the prior , or prior probability of the evidence E. It is the probability of E occurring regardless of H being true. This probability can be broken down further into the partition , as explained below.

The denominator of Eqn. 1 can be broken down as:

where H is the compliment of H, AKA not-H, and S is the sum over all independent hypotheses. This is sometimes called the partition. The top form is used when one is only considering whether a hypothesis H is true or false. The bottom form is more general, and holds for several independent hypotheses.

Plugging these into Eqn. 1 yields either:

which is useful when considering one hypothesis, being either true or false - this denominator of the right side of the equation multiplies the probability of the hypothesis being true against the probability of the hypothesis being false.

or it yeilds:

which is useful when considering how some evidence supports several independent hypotheses.

This, in a nutshell, is a possible foundation for Inductive logic. For more on this concept, try Wikipedia's entry on Bayesian Inference

Some notes on Bayes' himself:

Rev. Bayes may have (but not definitely) disagreed with "subjective probability". He derived his equation in order to answer a weird problem, which is briefly (and IIRC - no resources with me right now) as follows: you have a pool table of a known size. You draw a line across it parallel to one of the edges (I forget if it's the long or short edge). But you don't know where along the pool table the line's drawn. Now, you place a billiard ball on the table "at random" (equal probabilities of it being anywhere on the table), and you get a yes or no answer to the following question each time you do it: "is the ball to the left of the line?". Repeat this process a few times. With this problem, Bayes derived his equation and used it to find the probability that the
line is drawn at distance X from one side of the table: i.e. the probability that the line is X away from one side of the table.

So, whiles Bayes' theorm can be called upon to solve the problem of induction, Bayes wasn't really concerned with induction. He laid the mathematical foundations, however, for it to be "solved" (many people still today say that Bayesianism isn't really a solution, but a circumvention, of the problem of induction - a very technical point, however. And some object to Bayesianism altogether). The mathematician Pierre Laplace was the one who took up subjective probability and ran with it: he calculated the probability of the mass of a planet with it, and even calculated the probability that the sun would in fact rise tomorrow. There were, however, fatal flaws in his argument which led subjective probability to be all but abandoned. The frequentists took up the ball, and ran with it, until the mathematician Bruno De
Finetti picked up Laplace's torch, leading to "Bayesianism" almost as we know it today.

Conclusion

Lopez believes that both classical and Bayesian statistics answer the problem of induction, as they are both founded on a priori deductive systems. Thus, he ultimately believes that the problem of induction is only a problem if one wishes to find certainty in a belief, and nothing more. It completely discounts degrees of belief.

Degrees of belief is most directly addressed by the Bayesian view. However, the frequentist interpretation still has some power against the problem of induction in my view as well.

Two Further notes:

As already stated above, Christian Presuppositionalists often state the Problem of Induction incorrectly, confusing it with the assumption of a Uniformity of Nature, an error made even more comical when one considers that there solution is an assumption of the Uniformity of "God"!

However, they commit yet another serious blunder: it is a mistake to hold that a failure to provide an adequate justification for induction leaves us without any grounds to rely on induction other than 'faith': The fact one cannot prove something to be correct doesn't imply that one cannot know that the system is correct. A child is unable to prove his name, does this mean he does not know it? Knowledge and proof are two different philosophical concepts. The Problem of Induction relates to philosophical justification.

In short - no matter how one ultimately slices it, the mathematics of probability and statistics ultimately does away with the problem of induction - Bayesian or not.

More Comments on the Problem

Quite frequently I encounter people who equate lack of certitude with giant inferential leaps. Science deals with probabilities, often quite high probabilities, but not certitudes. It is one of the strengths of the scientific method as it acknowledges a chance of error(while maintaining rigorous standards to establish provisional acceptance of propositions). "It is a mistake to believe that a science consists in nothing but conclusively proved propositions, and it is unjust to demand that it should It is a demand only made by those who feel a craving for authority in some form and a need to replace the religious catechism by something else, even if it be a scientific one. Science in its catechism has but few apodictic precepts; it consists mainly of statements which it has developed to varying degrees of probability. The capacity to be content with these approximations to certainty and the ability to carry on constructive work despite the lack of final confirmation are actually a mark of the scientific habit of mind." -- Sigmund Freud

Usually when people talk about how induction is "flawed," they mean that it's not
truth-preserving like deduction. You don't get certainty from true premises. I.e.: Holding an inductive claim as if it were a series of equivalencies is an error.

I think that the problem of induction is only a problem because: a) Some people look for certainty in it, and b)historically, the problem arose before probability theory was mature. If you don't look for certainty, and you know about modern probability and statistics, the problem of induction is not a problem at all. The whole (deductively-created) theory of probability and statistics is dedicated to telling us something about "populations" from "samples." It's made for induction.

Another possible solution: Can we assume that nature has a Uniformity?

As already mentioned previously, the assumption of a uniformity of nature is a necessary but not a sufficient condition for building inferences from the past to the future. So the assumption is not only circular, it fails to provide a justification for such inferences. In addition, Howson & Urbach point out, assuming a uniformity of nature is doubly a nonsolution, since it's a fairly empty assumption. For how is nature uniform? And what, really, are we talking about. What would really be needed are millions upon millions of uniformity assumptions for each item under discussion. We'd need one for the melting temperature of water, of iron, of nickel, etc, etc. For example "block of ice x will melt at 0 Celsius;" for these types of assumptions actually say something. Furthermore, the uniformity of nature assumptions fall prey to meta-uniformity issues - for how are we to know that nature will always be uniform? Well, we have to assume that too. And how do we know that the uniformity of nature is uniform? Ad infinitum. So, to "solve" the philosphical problem of justifying induction by uniformity of nature solutions doesn't really work.

Quantum entanglement. Quantum computing.

So, to continue with the Captain's examples: it actually furthers our "conquering" of the universe, as it furthers our understanding of the universe. The closer our models are to the fundamentals of the universe, the closer we are to "conquering" it.