Antiseptic,

Thanks for the explanation. As a mathematician I strictly distinguish between deduction, that is binding for everybody, and induction that is based on “common sense”, or abduction based on “best explanation”. I agree that scientific research and progress - including in social sciences - is based more on induction and abduction than on deduction, whereas in (pure) mathematics induction and abduction appear, so to say, only "in the background" of the mathematician's thinking.

I think when reasoning (about God) the problem is that both “common sense” and “best explanation” are subjective, usually understood differently by a theist and an atheist. Therefore I am skeptical about reasoning when the context is existence of God. Probably my mathematical prejudices are showing.

Are cognitive leaps, that you refer to in connection with abduction, related to Thomas Kuhn’s paradigm shifts that I can discern more clearly in social than in natural sciences, (although Kuhn coined the term for the latter)?

>> leap of the imagination, which some have referred to above as revelation<<

Is this leap something like Bernard Lonergan’s insight?

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Dear George,

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If I have understood you correctly, your personal opinion is that science will never be able to prove the existence of any god or gods. Nor will it ever be able to prove that any such entity is simply the fruit of the imagination.

That is all I need to know for now. Thank you very much.

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banjo

one small thaw..doth not a summer make
i know science..can lead to proof of god..thats where i began

it is clear that science is a way..[ta0]
but there are many ways..to god..it begins with KNOWING*..god is grace/mercy/love logic life light..dont judge and dont do collective wrath.

its a matter of finding the true 'person-al'..not person
the one true creater god..living loving good god ammong all the lies/fears..faulse-gods and false mess-angers.

Hi George,
As a mathematician friend of mine said "once it's proven mathematically, it's proven forever". The trouble is that the premises may change and anything deductively proven is only true for the premises it derives from.

Induction is the way that we fit those eternal verities into our current observed reality, but it is only by abduction that we can derive a new set of premises entirely - such as the leap from classical to quantum mechanics, or from creation theology to evolutionary biology, or from one epistemiology to another generally.

I think the point I'm making is that deductive rigour is great once we have a set of premises. It lets us talk to each other about those premises and communicate effectively.

However, it constrains us to a linear mode of development of our ideas. God is inherently non-linear.

George,
thank you for mentioning Bernard Lonergan. I hadn't heard of him previously. I'll read much more I think, but yes, it does sound a lot like what I'm struggling to express.

all extracted from

http://www.icr.org/article/7098/

<<seldom will you hear an evolutionary tale...of the origin of mathematics..because it just isn’t possible.

Numbers cannot have evolved..
because numbers..;cannot change.??

<<laws of mathematics do not change with time.
Therefore,..they existed before people existed.

So they obviously cannot be a creation..of man.!

The equation 2+3=5..was true long before any human being thought about it, realized it, or wrote it.

<<we would ask,..“From what did numbers evolve?
What were numbers before they were numbers?
When did the physical universe..begin obeying mathematical laws?”

Or how about..the irrational numbers?
When did these numbers begin obeying..mathematical laws?

Did laws of mathematics..*evolve first,
and then numbers later?..Or was it the reverse?

If these sorts of questions sound silly,..it is because they are.
The evolution of numbers*..makes no sense whatsoever.

7 has always been 7,..just as 3 has always been 3.
Likewise,..the expression..2+3=5..was as true at the beginning of time..as it is today.

And yet laws of mathematics are conceptual in nature.
Concepts exist in a mind;..they are objects of thought...So how can a conceptual entity like math exist..*before any mind is around to think it?

Numbers are a reflection of God’s thoughts...Numbers existed before people..because God’s thoughts..*existed before people.

Laws of mathematics..are a reflection*..of how God thinks about numbers...The internal consistency of mathematics is a reflection of the internal consistency..*within the Godhead.

The invariant nature..of mathematics
is a reflection..of the unchanging nature of God.

Since God is beyond time..(2 Peter 3:8),..His thoughts do not change with time!..and,thus,..neither do laws of mathematics.

Laws of mathematics apply everywhere..because God is omnipresent(Jeremiah 23:24).

Laws of mathematics are absolute because God is sovereign and does not change His mind (1 Samuel 15:29)...Laws of mathematics are real and,..*yet,.not physical—just as God is real..and not physical/..in His essential nature.

Whether it is the intricate workings..of a living organism,
or..the existence of the solar system,..gradual change over time is considered to be the “creator”—not God...They promote the idea,..that if you just give it enough time,..lol..then the impossible becomes inevitable..through gradual,..naturalistic change.

Of course, there are many reasons to reject such conjectures