The Roles of Logic and Science in Questions of Theology

[_marg]

Marg,
I have taught logic before as part of some math courses.
Just wondering? Suppose you were in my class and we were going over these issues and I was trying to explain the whole thing about the role of stipulative definitions in deductive arguments. What do you think I should do at this point if you were in one of my classes where I teach logic and you kept not getting this point?

I have never quite had that situation but I am trying to picture exactly how patient I should be.

Once in a while someone might think it is me that doesn't get it but then I can just drag another professor into my office and it becomes clear that what I am saying is just standard stuff--the student is convinced.

Does math always allow for the nul or the non existence of things? Is it possible that conceptually the same problem doesn't exist for numbers as for conceptual things?

I brought up something before in a previous and you didn't appreciate what I was trying to get at. With conceptual ideas, the idea has to come before the concept of that thing as being non existent comes. There is no such thing as the universal non existence of something without first that something being conceived. Now I don't know if math deals with that conceptually.

As far as what to do, well you don't hold up a class over one person's questions. What you can say is "I've done my best to explain and I don't think I can add anything more to it"

by the way, as far as this discussion goes this one point of whether or not the def'n assumes God is a minor point relative to the whole discussion. You are the one focussing one it. JAK had mentioned the entire argument assumes God. And that goes back to a discussion with CC he had. I'd have to look back for the exact words. Later JAK mentioned that within the context of the entire argument the def'n assumes god. And you then focussed on that and asked me my thoughts on that.

I understand your point of technically setting up a def'n in a closed reasoning system, defining terms and working from there. But there is something a little more to this discussion that that...there is the concept of "existence" Implicit in any definition within a closed reasoning system, is that the thing being defined has properties. In order to be defined it must have properties. One can not define the properties of things which don't exist conceptually or otherwise.

My focus certainly is not on the def'n section of this argument. But since that was your focus I wanted to flesh it out more.

[_Tarski]

JAK had mentioned the entire argument assumes God.

Well, he is quite worng about that. The problem does not lie with an inappropriate assuming of the existence of God either in the usual meaning (whatever that may be) or in some meaning connected with Godel's technical definition.

Does math always allow for the nul or the non existence of things? Is it possible that conceptually the same problem doesn't exist for numbers as for conceptual things?

I don't understand what you are saying ( I suspect you don't either). You once claimed that numbers only exists as concepts. So now what do you mean?


It may interest you to think about the concept of the so called "empty set" (http://en.wikipedia.org/wiki/Empty_set).

By the way, if history had been just a bit different we might be calling this the "vacuous set" instead of the "empty set". Then we would have to say that the vacuous set exists. I'm am sure that would irk you to no end.

by the way, it might actually be called the vacuous set somewhere or in another language.

[_marg]

JAK had mentioned the entire argument assumes God.

Well, he is quite worng about that. The problem does not lie with an inappropriate assuming of the existence of God either in the usual meaning (whatever that may be) or in some meaning connected with Godel's technical definition.

Well at this point Tarski I think you are wrong. I'm going to quote from the course I mentioned I have been listening to..the one by Prof J. Hall..Philosophy of Religion.

"There are certain sentences, predicative sentences “All swans are either white or black, all humans are moral etc. where in order to figure out whether the predication is being made, predication of mortality to humans, predication of white and black to swans, in order to figure that out involves field work. The proposition puts together or synthesizes new information. Proposition says more than what it included in the very def’n of it’s subject term.
Being either white or black, being mortal is not part of the def’n of swan, the def’n of human being necessarily.

Suppose I said a bachelor is an unmarried male of marriageable age or all bachelors are unmarried. Well if def’n of bachelor is unmarried male of marriable age, then the statement all bachelors are unmarried is analytic. That is you may discover the truth of the predicate by simple analysis of the meaning of the subject.

Analytic you can discover the truth by analysis alone.
Synthetic requires field work.

Consensus in 20th century is that any statement that can be known a priori, independent of experience must of necessity be analytic. That is we must be able to discover its truth by analysis of the subject term. That any statement that is synthetic, any statement that delivers new information is of necessity a posteriori. It’s going to use reason with the fuel working with raw material provided by experience.

Point: If the ontological argument is a priori and if truth of conclusion is discovered by analysis of what is contained in subject term alone, what we have here is a circular or question begging argument. It presumes the very thing it sets out to prove."

previously: Does math always allow for the nul or the non existence of things? Is it possible that conceptually the same problem doesn't exist for numbers as for conceptual things?

Tarski: I don't understand what you are saying ( I suspect you don't either). You once claimed that numbers only exists as concepts. So now what do you mean?

What I am saying Tarski is numbers don't care whether things exist or not. But sentences with subject and predicate assume the subject exists conceptually. Sentences with subjects refer to some thing...even if just conceptual.

It may interest you to think about the concept of the so called "empty set" (http://en.wikipedia.org/wiki/Empty_set).

Correct math can address the empty set but that wasn't an option given in the def'n by Godel, no empty set was allowed as part of the def'n, to replace the God in God-like..

By the way, if history had been just a bit different we might be calling this the "vacuous set" instead of the "empty set". Then we would have to say that the vacuous set exists. I'm am sure that would irk you to no end.

Why would I be irked? I don't understand your point.

by the way, it might actually be called the vacuous set somewhere or in another language.

[_marg]

by the way Tarski,

Is it possible that symbolically what Godel's argument is saying is that conceptually "ultimate universal knowledge" or a "platonic ulimate reality" necessarily exists? An ultimate platonic reality would be a positive. It's got to be better than an absence of ulitmate platonic reality. And conceptually "ultimate univeral knowledge" necessarily is impossible to not exist. But that doesn't mean there is an entity with properties which has that knowledge. However when people translate that conception into words and in particular use a God...the value laden word "God" gives the argument theological weight it shouldn't have. It turns the conception of "ultimate univeral knowledge/platonic reality/ knowledge" into an entity with properties of existence.

[_Tarski]

by the way Tarski,

Is it possible that symbolically what Godel's argument is saying is that conceptually "ultimate universal knowledge" or a "platonic ulimate reality" necessarily exists? An ultimate platonic reality would be a positive. It's got to be better than an absence of ulitmate platonic reality. And conceptually "ultimate univeral knowledge" necessarily is impossible to not exist. But that doesn't mean there is an entity with properties which has that knowledge. However when people translate that conception into words and in particular use a God...the value laden word "God" gives the argument theological weight it shouldn't have. It turns the conception of "ultimate univeral knowledge/platonic reality/ knowledge" into an entity with properties of existence.

You are right about one thing. If an average person thinks that what Godel had attempted to prove exists is automatically all that we normally think of when we use the word God, then that person has another thing comming.

An ultimate platonic reality would be a positive. It's got to be better than an absence of ulitmate platonic reality

That's the idea, but even on it's own terms I think Godel's proves fails to be convincing. I am no more convinced that Godel has proven the existence of anything at all than you are. We are only disgreeing about what went wrong.

[_Gadianton]

Of historic interest concerning JAK's opening words and accusations.

Within 1 hour of CC posting on Godel, JAK had made his first accusation of assuming conclusions. But that accusation was merely 7 minutes after his analysis of Armstrong. Is it reasonable that JAK familiarized himself with Godel in one hour -- but most likely 7 minutes?

As some of the lurkers may be curious, note JAK's instructive paragraph:

To accept the ontological arguments of Gödel, requires an irrational leap. His ontological argument has often been said to ascertain God's existence by a philosophical sleight of hand or a ruse of words. Gödel’s arguments are flawed, if by nothing else, his assumptions absent evidence. The minutia of his arguments tends to be intimidating. In any case, they are not transparent and philosophers today do not accept (universally) his assumptions and application of those assumptions to agree with Gödel’s conclusion.

Note the bold is plagiarized from here:

http://www.apollos.ws/ontological-argument/

But also note that the "HIS" reads from the article "THE". JAK's original misuse of copyrighted material also betrays that he thinks "the ontological argument" had its origin in Godel. How funny.

[_Tarski]

JAK had mentioned the entire argument assumes God.

Well, he is quite worng about that. The problem does not lie with an inappropriate assuming of the existence of God either in the usual meaning (whatever that may be) or in some meaning connected with Godel's technical definition.

Well at this point Tarski I think you are wrong. I'm going to quote from the course I mentioned I have been listening to..the one by Prof J. Hall..Philosophy of Religion.

"There are certain sentences, predicative sentences “All swans are either white or black, all humans are moral etc. where in order to figure out whether the predication is being made, predication of mortality to humans, predication of white and black to swans, in order to figure that out involves field work. The proposition puts together or synthesizes new information. Proposition says more than what it included in the very def’n of it’s subject term.
Being either white or black, being mortal is not part of the def’n of swan, the def’n of human being necessarily.

Suppose I said a bachelor is an unmarried male of marriageable age or all bachelors are unmarried. Well if def’n of bachelor is unmarried male of marriable age, then the statement all bachelors are unmarried is analytic. That is you may discover the truth of the predicate by simple analysis of the meaning of the subject.

Analytic you can discover the truth by analysis alone.

So far there isn't much to disagree with here even if it is a bit simplistic.

Consensus in 20th century is that any statement that can be known a priori, independent of experience must've necessity be analytic.

Lets grant that is true in some appropriate sense. Then what? Does experience with the universe of possible analytic statement count as experience? LOL

That is we must be able to discover its truth by analysis of the subject term.

THE subject term?

Now see a bit of a problem. There may be hundreds of subject terms in the background of an analytic argument. The network of defintions may span a library full of usefull definitions about number, set, class, functions etc.
To say that when, by a long analysis than may span decades and involve the best minds of logic and math we end up with no new information is quite absurd. if you are representing him correctly, Prof J. Hall just fails to understand how much goes on in an exact science such as mathematics. Some have even argued that because we must explore the analytic world we are really doing something broadly empirical! We do fieldswork in the abstract world as it were!

That any statement that is synthetic, any statement that delivers new information is of necessity a posteriori.

Except that what we might be exploring when we gain experience is the universe of anylytic truths that extend far beyond our ken.

It’s going to use reason with the fuel working with raw material provided by experience.

Does expereince with analytic entities such as number count as experience. If I had Prof. Hall in my office I would ask him this.

Point: If the ontological argument is a priori and if truth of conclusion is discovered by analysis of what is contained in subject term alone, what we have here is a circular or question begging argument. It presumes the very thing it sets out to prove."

Again, this only seems to apply to the simplest and most trivial of syllogisms where there may only be one subject and even Dr. Hill can determine if the statement is true analytically. But what if he can't? What if the best minds can't and yet want to know badly?
If they ever find out will we say they have discovered no new truth but only trivial tautology?

Picture this: Numbers can be defined analytically.
Now Fermat's last theorem is a statment about numbers that is quite simple to state. Yet, it took 200 years of complex hard work in advanced mathematics before it was proven to be true. Before that, we didn't know. Now we do know! Are you telling me, is Mr. Hall telling me, that we have gain no new information??????

That's absurd.

I am afraid that a deeper knowledge of mathematics (the premier analytic discipline) would do Dr. Hall some good (unless you are just misrepresenting him).

Those of us in mathematics and similar subjects are continually having to combat such simplistic thinking coming from Professors outside the field such as those in the English departments or even those in the philosophy department who do not specialize in logic or who do not know any deep mathematics.

previously: Does math always allow for the nul or the non existence of things? Is it possible that conceptually the same problem doesn't exist for numbers as for conceptual things?

What I am saying Tarski is numbers don't care whether things exist or not. But sentences with subject and predicate assume the subject exists conceptually.

You are equivocating between exists and exists conceptually I guess.

What do make of this sentence.

"Round squares do not exist"

or

"A a final prime does not exist".

In what sense do we assume that a "final prime" exists just because it is the subject of a sentence???
Tricky question rigth?

Correct math can address the empty set but that wasn't an option given in the def'n by Godel, no empty set was allowed as part of the def'n, to replace the God in God-like..

??
Too conceptually muddled to even comment on.

By the way, if history had been just a bit different we might be calling this the "vacuous set" instead of the "empty set". Then we would have to say that the vacuous set exists. I'm am sure that would irk you to no end.

Why would I be irked? I don't understand your point.

I guess I shouldn't be surprised.

Let's answer just this one question:

Did humanity gain new information when Andrew Wiles et. al. proved Fermat's famous last theorem in the 1990s?? Was a discovery made and did science progress?

Yes or no? Recall that we wanted to know whether it was true or not and have struggled to find out for 200 years!!

Ask the same question of Prof. Hill if you can.

Note that the theorem of Fermat is but one example. many more theorems took a long time and many are used in physics!!

Also, note that Hill's opinion is in direct and violent opposition to Godel himself and also to many other great thinkers such as Penrose.

Here is another example for you (and Prof. Hall).

The Mandelbrot set is a completely analytically defined mathematical object. Yet we are continually exploring it and are profoundly surprised by what it has to offer. Exploring it is like exploring a galaxy.

Read up on the Mandelbrot set and tell me if you think that there can be no new information discovered about this purely analytic object???

It has been suggested by some thinkers that the entire universe is ultimately mathematical in nature-- a vast tautology to an omniscient being (who does't exist anyway).

it is also true that we sometimes use computers to do experimental mathematics and sometimes thereby learn of analytic truths which e then try to prove by purely deductive means! What do you and Mr. Hill have to say about that?

You sure put a lot of stock in this one course.

[_marg]

Of historic interest concerning JAK's opening words and accusations.

Within 1 hour of CC posting on Godel, JAK had made his first accusation of assuming conclusions. But that accusation was merely 7 minutes after his analysis of Armstrong. Is it reasonable that JAK familiarized himself with Godel in one hour -- but most likely 7 minutes?

As some of the lurkers may be curious, note JAK's instructive paragraph:

To accept the ontological arguments of Gödel, requires an irrational leap. His ontological argument has often been said to ascertain God's existence by a philosophical sleight of hand or a ruse of words. Gödel’s arguments are flawed, if by nothing else, his assumptions absent evidence. The minutia of his arguments tends to be intimidating. In any case, they are not transparent and philosophers today do not accept (universally) his assumptions and application of those assumptions to agree with Gödel’s conclusion.

Gad in my opinion there is a large difference between the symbolic form of Godel's argument versus the word format. If you unravel the symbolic form and include in that the conception of universal truths, of course one can conclude a universal truth must exist and it's better to exist than not so it is a positive.

But that is not what CC presented. CC presented an argument by I don't know who, whether it was Godel or not, who used a valued laden word God. According to Prof. Hall and I agree with him, all arguments which are analytic a priori are question begging and presume the subject being argued for. I reread the entire thread last night and other for the minor disagreement over whether a def'n presumes the existence of the subject in question, everything JAK said was in agreement with Prof. Hall.

Prof Hall explains the basic of modal logic and points out that he's no expert but the experts disagree with one another. And iIn particular he mentions a theist philosopher/logician Peter Geach who says that model argument for the existence of God are absurd.

I ask CC what he meant by God and what he thought the argument meant ..and no response from him.

Godel's argument in essence has nothing to do with theology unless one wants to lift the logic from there with it's conclusion and apply it their own assertions of whatever God they believe in. But that does not mean that theology and the existence of a God is logically based, by doing that. Where is the logic of lifting that argument onto a theological God?

When rereading the thread last night, I appreciated even more than previously how brilliant JAK is. He doesn't have to know model logic, to appreciate that when using a value laden word such as god into an analytic a priori argument, it presumes God and is a question begging argument. An ultimate platonic reality is not equivalent to the conception of a God which exists.

Your fixation on JAK throughout this entire argument is strange and petty. The argument which you should be focussing on is ..is theology logically supported or based. JAK is not the focus. Yet you want the entire focus to be on him.

There is absolutely no comparision to the numerous logical rational statements JAK has presented in this thread versus the anemic arguments you have presented which were laden with baggage of hostility.

Get with the program Gad, a discussion is about issues.

Note the bold is plaigerized from here:

http://www.apollos.ws/ontological-argument/

But also note that the "HIS" reads from the article "THE". JAK's original misuse of copyrighted material also betrays that he thinks "the ontological argument" had its origin in Godel. How funny.

I have to say so what? JAK presented much more than that one quote which illustrated his appreciation of logic. You are looking for things to criticize. And perhaps he did think the ontological argument had its origin in Godel. I don't know. But it makes no difference to the thrust of the points of his argument. So it's not relevant to the issue. The only thing relevant is whether his reasoning was valid. And it was.

The argument in word format is a question begging argument. It is an analytic a priori one. Now we can add the twist that it's a modal argument , but that certainly in my opinion was not presented by the word format . Had it said x is a god- like platonic conception then I'd agree that , that concept necessarily exists.

As I said though rereading last night the thread and JAK's post again, made me appreciate just how brilliant he is.

[_Tarski]

As I said though rereading last night the thread and JAK's post again, made me appreciate just how brilliant he is.

You've been bamboozled.

by the way, here is where you can read about the mandelbot set.
http://www.ipod.org.uk/reality/reality_ ... iverse.asp

Tell me if you think no new information can be discovered about it since it is a purely analytically defined object?
Hint: We discover profound things about this set all the time. Knowledge is gained.

[_marg]

I'm sorry Tarski I won't be able to address your post today.

I skimmed it though. You say

['m it is also true that we sometimes use computers to do experimental mathematics and sometimes thereby learn of analytic truths which e then try to prove by purely deductive means! What do you and Mr. Hill have to say about that?

Well he explains using the Euclidean analytic a priori argument.

So what I'll do is eventually post that for you.

You sure put a lot of stock in this one course.

Well I put a lot of stock into things that make sense to me from people who have garnered respect. I try to understand things conceptually. So I often don't know details, I'm not a scientist, no philosopher, no mathematician but if someone has expertise and they present it such that it I can get a hangle on it conceptually that's what I'm interested in.

Someone like this professor is pulling information from many sources. He will bring in Kant and explain Kant's perspective on why ontological arguments fail, and hence I don't have to read every philosopher and determine which one has an argument against Ontological argument and what they say...that's done for me. We live in an age of specialization and to some extent have to rely on others, but I critically judge the source as well as what they say. You have a valid point that you teach logic and math but I critically judge your perspective of always it seems equating what goes on in math to what to goes on in the world conceptually or not. It seems to me that when symbols are put into word format, some slight of hand, word magic, can happen without being appreciated.