>...Your statement about validity in deductive logical structures is, of

Robert,

>course, entirely correct, so long as we are speaking of formalized

>deductive arguments. My attempt was to look at the issue of the use of

>deductive vs. inductive arguments as applied within particular fields of

>study, especially our conversations concerning the HJ, etc. Here there

>would seem to be some additional traps we need to avoid.

>

>One of these has to do with the derivation of premises. Most of the work

>in the 20th century looked only at the relationship of premises to

>conclusions, and also at the so-called "meaningfulness" of particular

>logical statements (ie., does a particular statement have to be true in

>order to be meaningful, about which the consensus is clearly no, it

>doesn't). But in the philosophy of science, beginning with Bertrand

>Russell and continuing through Karl Popper and his successors, there has

>been concern about the derivation of premises in and of themselves,

>particularly as they impact scientific inquiry. I presume we don't need

>here to go into all the issues of "verification" vs. "falsification" and

>so I will not. Suffice to say, however, that, as applied to the use of

>deductive arguments, if the premises are not "checkable" in one way or

>another, then there can be no confidence in the meaningfulness of the

>conclusion, even if the structure of the argument itself is valid.

Can I join in? I agree mostly with what you are writing here, but the

problem here is what does "checkable" mean? For example, in what sense are

the foundational axioms of Euclidean geometry "checkable"? For thousands of

years, people "checked," and it seemed to "check out."

>The reason this is important is that premises are the level of statement

I agree with the above. This is not a new problem. In fact, its an

>in which assumptions and world-views are actualized. And because this

>seems to be the case, the way each premise is formulated will depend on

>what the formulator believes to be possible or even conceivable. One can

>draw a premise very narrowly, if one does not accept possibilities outside

>a relatively narrow range; alternatively, one can draw a premise much more

>widely, allowing for previously unconsidered or even "inconceivable" (by

>others) possibilities. For instance, if I am attempting to make a

>deductive argument for or against the possibility of life on other

>planets, my own assumptions as to whether I believe in the possibility of

>such life will affect how I will draw my premises. If I believe in the

>possibility of non-terrestrial life, then I will formulate my premises one

>way, if not, then in another. The resulting conclusion, if derived

>correctly, will be valid, but if I have "cooked" the premises, then the

>argument itself cannot be meaningful.

ancient problem, that has been handled in a number of different ways. The

purest example of this that I can think of is Euclidean geometry, which is

based on strict logic. The entire structure of Euclidean geometry was based

on a very small number of assumptions or axioms that were regarded as so

fundamental as to be "uncheckable," to use your phrase, but were a matter

of consensus (e.g., things on the level of "The shortest distance between

two points is a straight line"). An amazingly elaborate set of theorems

could be derived, using strict logic (much more strict than 99.9% of what

is written on this list), from this small number of initial assumptions.

Euclidean geometry was regarded as gospel truth for close to 2000 years,

more or less until Einstein's theory of relativity(?) challenged a few of

those basic assumptions. A field of non-Euclidean geometry then arose to

deal with certain difficult matters of an astronomical nature. A key reason

for the acceptance of non-Euclidean geometry in certain circumstances was

that there were certain extreme situations where the extrapolation of

Euclidean geometry didn't work adequately, but the newly emerging field of

non-Euclidean geometry could handle just fine. I think the challenge was

also conceived at the level of the basic assumptions-- Einstein posited

that the universe was not really linear, but warped in odd ways such that

the shortest distance between two points was not necessarily a straight

line. However, the number of people these days who use non-Euclidean

geometry for anything other than a classroom exercise is vanishingly small.

99.9% of humanity still uses Euclidean geometry. When you hire someone to

come survey your property, he/she will use Euclidean geometry.

Other examples can be drawn from the cases Thomas Kuhn used 30 years ago.

For example, the Ptolemaic system of navigation assumed that the Earth was

the center of the universe. It, too, was based on a very small number of

initial assumptions, with which most people agreed. The system was a bit

elaborate, with all those epicycles to worry about & such, but navigators

had developed the whole system to a high degree of accuracy. When

Copernicus challenged the central assumptions of the Ptolemaic system, he

did NOT do so by presenting more accurate navigational charts. He also did

not (initially) win converts by presenting a navigational system that was

easier to use. And it was arguable that his system was conceptually

simpler: what could be simpler than that the Earth was the center of the

universe? If the Earth was not the center, what was? So it took a while for

the Copernican system to be accepted. But I think it eventually won out

because it could predict some astronomical phenomena more accurately than

the old system-- although not enough better to help navigators all that

much. In what way were the foundational axioms of the Ptolemaic system

"checkable"?

>...To refer to an "invalid premise" therefore is to refer to a premise in

In general, I agree. It seems like Wykestra is looking at some of the

>which unexamined assumptions have creeped in to the statement as

>formulated. Now, this may be egregious enough to be recognized as some

>sort of deductive fallacy--primarily assuming the conclusion as part of

>the premise--but it need not be so obvious. Once again building on

>Stephen Wykestra's work in this area, which suggests that we all have what

>he calls "canopies of assumptions" within which we conduct our study, we

>cannot assume that any premise is neutrally drawn until it has been proven

>to be so. Wykestra himself believes that most such premises cannot stand

>up to this test, and I tend to agree with him.

>

>As applied to our own discussions here, part of what we need to look at is

>how our prior assumptions affect the pursuit of our own research and how

>it is reported out.

things that Kuhn included as part of a particular "normal science,"

including its "paradigms."

> Does one assume that there really was an HJ, or not?

This can be either an assumption, or a datum to be evaluated. One of the

characteristics of the growth of knowledge is that one person's conclusions

become someone else's assumption. But this is not, of course, a question

of science. To many of us, myself included, I simply assume that *an* HJ

existed. I am willing to make this assumption because if we do not accept

the historicity of Jesus, using the same standards of evidence applied to

the rest of humanity at the same time would result in the discovery that

there were very few people in the first century who actually existed, and

that many of the persons accepted as historical in our textbook would have

to be expunged. However, I know that some people are not satisfied with

the assumption that there was an HJ. Some of them might prefer the

assumption that the HJ *did not* exist. Others may actually have an "open

mind," and may be consumed by an interest in determining whether an HJ

actually existed. I do not choose to expend my time in such labors.

>...Thus, in any use of deductive reasoning, the premises must necessarily

You seem to regard deduction as problematic, and induction as preferable.

>be checked out. But it is just here that we are confronted with problems

>perhaps insurmountable.

It is clear that you *prefer* induction. You *like* it. But your arguments

in favor of it sound to my ear more like rationalizations of something

already decided rather than actually checking out the assumptions of each.

The main difference, it seems to me, is that induction of the kind you

refer to sweeps all the problems under the rug where you feel free to

ignore them, whereas in deductive arguments everything is on the table, but

you worry about the necessity to check everything out. Are you equally

concerned with checking out the assumptions of the theory of electricity

before turning on any of the light switches in your house or turning your

computer on? How will you check out the Copernican theory of the universe?

How will you check out Euclidean geometry? The fact is that most of us take

many of these things for granted. Otherwise, we'd never make it out the

door in the morning. We only become concerned about checkability about

certain things that suddenly jar our sense of complacency. I think we need

both induction and deduction.

Bob Schacht

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