I don’t know if this will go anywhere interesting, but…

Discussions about proving the existence of God often simply assume that the notion of “proving something” is clear and simple.  But is it?

The question that follows may be too general, but consider it just the beginning of the inquiry.

What does it take to prove something?

When one looks at the variations on “the five ways” of Aquinas as instances of (attempts, at least at) proofs for the existence of God, it looks as though what is sought is a sound argument that has “There is a God” or “God exists”, or something equivalent, as its conclusion.  Logic texts, and Intro to Philosophy texts typically define “sound argument” as an argument in which all of the premises are true and is valid.

If what it takes to prove something is a sound argument for that something, the following would be a proof that I currently live in a state in the United States that has 67 counties:

1.  If the state Elizabeth currently resides in is Pennsylvania, then the state Elizabeth currently resides in has 67 counties.
2.  The state Elizabeth currently resides in is Pennsylvania.
——
3.  The state Elizabeth currently resides in has 67 counties.

The above is a sound argument that has as its conclusion the statement that the state I currently live in has 67 counties.

Is this a proof of the conclusion?  If not, what would make it a proof of that conclusion, or, if the example is not even close to being a proof, what would it take to prove that conclusion?

cheers,

Elizabeth

The basic problem here is that we have two meanings for the word “proof”. The first is a definition in terms of logical form, along the lines you suggest. A logical proof is a valid argument with true premises. The problem is that this doesn’t say anything very useful about whether the argument provides good information or not. Indeed, it’s necessarily the case that in any logical proof, the conclusion contains no more information than the premises themselves.

In this sense, any (valid) proof of X establishes that if these premises are true, X must follow of necessity, because X is simply the premises restated.

Our other sense of “proof” is the everyday notion that we find in court cases, scientific analyses and the like. It is by far the most dominant usage of the term. In this secondary usage, what a “proof” amounts to is something like an inference to the best explanation. When Holmes ‘proves’ that Moriarty is the murderer, he doesn’t do it by assaying a long analysis in logical form, what he does is to look at the evidence provided him, and infer that Moriarty’s having been the murderer is the best (simplest, most likely) explanation of that evidence.

And then anyone who disagrees with Holmes’s analysis will go at that same evidence and show how Holmes’s analysis wasn’t optimal, or provide other evidence. Here think of the masterpiece film 12 Angry Men for an example. Logical form virtually never comes into it.

Elizabeth - 28 April 2011 05:54 AM

Is this a proof of the conclusion?  If not, what would make it a proof of that conclusion, or, if the example is not even close to being a proof, what would it take to prove that conclusion?

cheers,

Elizabeth

A valid drivers license would work along with a couple of references to the number of counties for the state in which you live.

Now if God would only produce a valid drivers license. 

The kind of logic Elizabeth is talking about is called “deductive reasoning.”  The kind DougSmith is talking about that is used in science and court cases is called “inductive reasoning.”  Sherlock Holmes uses misleading terminology according to today’s definitions.  Maybe the language has changed since it was written, but when Sherlock Holmes says “brilliant deduction” he is really talking about induction.

brightfut - 28 April 2011 01:03 PM

The kind of logic Elizabeth is talking about is called “deductive reasoning.”  The kind DougSmith is talking about that is used in science and court cases is called “inductive reasoning.”  Sherlock Holmes uses misleading terminology according to today’s definitions.  Maybe the language has changed since it was written, but when Sherlock Holmes says “brilliant deduction” he is really talking about induction.

No, it’s actually called “abductive reasoning”. Inductive reasoning is reasoning to the future based on the past. Abductive reasoning assumes inductive and deductive reasoning, but it’s not the same form as either. It’s not like Holmes can say, “in the past every time there was this evidence, Moriarty was the murderer”, which is what he’d need for this to be strictly a case of inductive reasoning.

Abductive reasoning = inference to the best explanation

Would the term “inductive argument” be more accurate?  Inductive Argument:  One of the two major types of argument traditionally distinguished, the other being the deductive argument.  An inductive argument claims that its premises give only some degree of probability, but not certainty, to its conclusion. (Introduction to Logic; Irving M. Copi)

brightfut - 28 April 2011 01:58 PM

Would the term “inductive argument” be more accurate?  Inductive Argument:  One of the two major types of argument traditionally distinguished, the other being the deductive argument.  An inductive argument claims that its premises give only some degree of probability, but not certainty, to its conclusion. (Introduction to Logic; Irving M. Copi)

An inductive argument is an example of induction. Everything you’ve quoted from Copi is correct, but irrelevant to the main point. Recall that you’re reading from a book about logic, not epistemology or philosophy of science. Inductive arguments can and have been formalized in various ways, e.g., following Bayes. Abductive arguments have not, at least not in any rigorously worked out fashion, so you typically won’t find mention of them in books about logic.

Elizabeth - 28 April 2011 05:54 AM

I don’t know if this will go anywhere interesting, but…

Discussions about proving the existence of God often simply assume that the notion of “proving something” is clear and simple.  But is it?

It is, except when people use deliberately deceptive language.

Note that science is really geared toward disproofs, not proofs, in a logical sense. If someone comes up with a scientific theory (like Newton’s laws of motion) then the tests are designed to find ways to force those theories to fail, not to succeed. Theories that prove to be very hard to disprove become respected, but never fully “proven.”

Many modern definitions of God are specifically designed to be immune to disproof; they become essentially meaningless from a logical point of view (hence the problem of people using deliberately deceptive language). Things like God existing outside of the universe and things like that. However, when someone makes a claim on an action by God, like response to prayer, this becomes testable as long as there is a test that could logically disprove the claim. For Newton’s #3 law, that would be observing an object blatantly change momentum without any outside interference. For prayer, that usually involves comparing the effect of prayer vs. the effect of no prayer in the same situation. And this has been done many times, of course, and prayer has been shown to be nothing more than a placebo. Newton’s Third Law of Motion has proven to be much more robust and harder to disprove.

I don’t understand what the difference is between the type of reasoning used in abductive arguments and those of inductive arguments.  Both are using statistics from one area to make generalizations to another area.  Abduction sounds like induction used to predict the future.  All statistics come from the past.  In this sense all inductive arguments could be looked at as abductive arguments.  I can see that some people could claim that some statistics apply to the present even though they were collected in the past.

brightfut - 29 April 2011 08:16 AM

I don’t understand what the difference is between the type of reasoning used in abductive arguments and those of inductive arguments.  Both are using statistics from one area to make generalizations to another area.  Abduction sounds like induction used to predict the future.  All statistics come from the past.  In this sense all inductive arguments could be looked at as abductive arguments.  I can see that some people could claim that some statistics apply to the present even though they were collected in the past.

This isn’t the thread to get into a long discourse about the difference. An inductive argument doesn’t look for an explanation, instead it looks for a regularity. The sort of argument given by Holmes or indeed Einstein is not inductive, although it may depend partly on induction. To say they are simply inductive arguments is to oversimplify to the point of falsification.

For more (written at a semi-pro level so perhaps not the best intro) see the SEP on abduction.