The Roles of Logic and Science in Questions of Theology

[_JAK]

The definition as quoted by CC reads:
“Definition 1: x is God-like iff x has as essential properties those and only those properties which are positive”

Regardless of any debate over “properties” vs. “essential properties” and regardless of consensus or lack thereof on “positive,” the definition itself makes assumption. That assumption is repeated in “Axiom 3,” “Corollary 1,” “Theorem 2,” and “Theorem 3.”

You need to explain this better. How does merely making a technical definition amount to assuming the outcome of the argument??

For example, suppose I make the following definition.

Definition: A Riemannian manifold is ghost-like if it is geodesically complete but not metrically complete.

Now if I make an argument showing that ghost-like manifolds exist, then I will have certainly made a mistake, because in fact, it can be proved that all geodesically complete manifolds are metrically complete. So ghost-like manifolds do not exist. But the definition is OK as it stands until the existential question is settled rendering it empty (and it is settled in this case; they don't exist).

I have not made a mistake in the very definition have I? I can define whatever I want as long as the definition is clear and refers to only understood ideas and entities.
If Godel makes a mistake here, it is either in that the definition is not clear (referring to unclear notions of positive etc). Otherwise the mistake comes later in the argument.

Notice that the argument would be the same even if he used the word G-like or even H-like or Q-like in the definition.

To my eye, definition 3 looks suspicious. What word or concept is being defined? exists?
On the face of it 3 looks more like a claim than a definition.

I suspect that it boils down to the usual issue over whether existence (or necessary existence) is a property (or in this case a positive property-whatever that is!).

Now you also see the word "God" in axiom 3 and so you seem to conclude that God's existence is assumed there. But again this can't be the problem.
The axiom reads "Axiom 3: The property of being God-like is positive". This doesn't assume the existence of a God-like being and God-like is still so far just coinage for what is defined in definition 1 (we didn't need to use the word "God" at all).

The question for axioms is whether they are clear and whether they can usefully be regarded as true. Well, is Axiom 3 true and clear?
Not to me. First, I am unclear on the term "positive". Where is it defined?
Second, even after having settled on a sense for the word positive it still seems unlikely that I would consider the axiom to be obviously true.

Response to Tarski Sat Sep 01, 2007 7:27 am
That post is far back from where this response appears.

1. What is the topic under discussion?
It is:

The Roles of Logic and Science in Questions of Theology

2. Following that title, we have discussion in which an ever-present term “God” in Theology is used.

3. Assuming the quote from CC is accurate, the fuzzy construction lies there. That is where the explanation needs clarification.

Tarski stated:
You need to explain this better. How does merely making a technical definition amount to assuming the outcome of the argument??

What’s your basis for concluding we have in definition 1 “merely making a technical definition”? It is not stipulated on the page CC gave. If it’s stipulated elsewhere -- where? And we have at hand the topic The Roles of Logic and Science in Questions of Theology.

Even if stipulated, terms used in a definition which lack clear, unambiguous meaning make for a weak definition.

The use of “God-like” refers to what? Since it follows a linking verb, it’s a noun or a predicate adjective (grammatically). The definition appears to lack clarity and the author of that “need(s) to explain better.” Neither you nor I have the burden of responsibility for the clarity of someone else’s definition.

We then require disambiguation. But, we don’t get it. Instead, we get even more ambiguity.

“Definition 1: x is God-like iff x has as essential properties those and only those properties which are positive” is ambiguous with “iff” (if and only if) followed by terms which lack clarity.

I think it reasonable for us to demand the highest standards of clarity and precision. If this construction (as represented by CC) were specified as “merely a technical definition,” that might be an improvement. It wasn’t. Worse, God in any time of the past many centuries has cultural connotations as does “God-like.” Why use it if the intent were as you claim?

If the intent mathematically were to “merely” as Tarski speculates, some clearly meaningless, nonsense phrase or group of letters would have been superior to “God-like.” So why was “God-like” used?

Why not 791 in place of “God-like”? I remain skeptical of your claim that this entire construction was “merely making a technical definition...” Had that been the case, “God-like” would not have been used.

Add to that the use of ambiguous but emotionally ameliorative words: “properties which are positive,” and the circular construction in Axiom 2 “a positive property is positive” and Axiom 3 “The property of being God-like is positive.” If we had 791 rather than “God-like,” you would have a better argument for “merely making a technical definition...” But we don’t have that. We have “God-like.” Again, why?

Now, it’s an even greater stretch to defend that the author is: “merely making a technical definition...”

Tarski stated:
To my eye, definition 3 looks suspicious. What word or concept is being defined? exists? On the face of it 3 looks more like a claim than a definition.

Definition 1: x is God-like iff x has as essential properties those and only those properties which are positive

Definition 2: A is an essence of x iff for every property B, x has B necessarily iff A entails B

Definition 3: x necessarily exists iff every essence of x is necessarily exemplified

Yes, I can see your point in the context of your previous statements.

You then suggest that what is presented as “definition” is (or may be) claim that x exists. However, we still have the same kind of construction as in 1 and 2. What makes (or would make) it (3) a definition?

In Definition: 1 “x is God-like...”

In Definition: 3 “x exists”

Both are claims regardless of the subordinate clause which follows.

In Definition 2: “A is an essence of x”

One of the critic which I previously cited observed that we have “fuzzy” definitions. Another that {“Modal logic” is frequently obsessed with metaphysics, temporal reasoning, epistemics, the analysis of action and processes, and ethical reasoning.}

Tarski stated:
Now you also see the word "God" in axiom 3 and so you seem to conclude that God's existence is assumed there. But again this can't be the problem.

There are multiple problems as my analysis has shown. The use of “God-like” from the beginning presents a problem. A critic observed that we have “a sleight of hand” and a “ruse” of words in this construction.

Keep in mind the context of the language and the topic under discussion: The Roles of Logic and Science in Questions of Theology

Your defense is: “merely making a technical definition...” “a coinage.”

Tarski stated:
The axiom reads "Axiom 3: The property of being God-like is positive". This doesn't assume the existence of a God-like being and God-like is still so far just coinage for what is defined in definition 1 (we didn't need to use the word "God" at all).

This begs the question: Why was God used? beginning with Definition 1. Your claim that “God-like” is “just coinage” is not supported beyond your claim here. Only you have made that claim. It was not in the post which CC made. So the question remains: Why use “God-like” and not some other “coinage” which would have no generally recognized theological link?

You stated:
Notice that the argument would be the same even if he used the word G-like or even H-like or Q-like in the definition.

Do words have meaning? Do those who read words see them in context?
The answer to both questions is affirmative. So the criticisms “ruse” of words and “fuzzy” definitions applies.

Why was one of your words or my “791” not used? To pretend that “God-like” has no connotation and that we are “merely” discussing an argument form is misleading. Why was it done?

Previously, I stated: “I think it reasonable for us to demand the highest standards of clarity and precision.” Conspicuously, this was not done. Moreover, in the title for this discussion was used the word Theology. In theology “God-like” and “God” are not used as “coinage” or “merely making a technical definition...”

You stated:
The question for axioms is whether they are clear and whether they can usefully be regarded as true. Well, is Axiom 3 true and clear?

The question for definitions “...is whether they are clear...” And in the stated construction, definitions are ambiguous. “God-like” is ambiguous as a predicate nominative or predicate adjective in Definition 1.

Reasoning and evidence which fuels that reasoning is subject to clarity and whether they can be regarded as true. Language which is fuzzy is not clear.

I submit the construction was an assumed God. Had this been “merely” or “just coinage,” another neutral term (or phrase) would have been used. “God-like” is not a neutral term.

Argument is not devoid of context. It requires words and wording. And “God-like” and “God” have context. Your suggestions (if the intent was “merely” or “coinage”) as well as my “791” would have been superior. Even so, it would not have eliminated the ambiguity inherent in the referenced post of CC.

JAK

[_Tarski]

Response to Tarski Sat Sep 01, 2007 7:27 am
That post is far back from where this response appears.

1. What is the topic under discussion?
It is:

The Roles of Logic and Science in Questions of Theology

2. Following that title, we have discussion in which an ever-present term “God” in Theology is used.

3. Assuming the quote from CC is accurate, the fuzzy construction lies there. That is where the explanation needs clarification.

Tarski stated:
You need to explain this better. How does merely making a technical definition amount to assuming the outcome of the argument??

What’s your basis for concluding we have in definition 1 “merely making a technical definition”? It is not stipulated on the page CC gave. If it’s stipulated elsewhere -- where? And we have at hand the topic The Roles of Logic and Science in Questions of Theology.

He is defining a term. That’s a coinage. We do it all the time in math and logic. The definition of the word “smooth” is technical too despite the connotation. One cannot use anything that follows from the connotation in proofs but once one understands smoothness in its technical sense one also sees why the word smooth was chosen.

Even if stipulated, terms used in a definition which lack clear, unambiguous meaning make for a weak definition.

Indeed, but making an insufficiently clear definition is not the same thing as simply begging an existential question. I do not claim that Gödel’s proof is successful JAK. I do claim that Definition 1, despite being unclear by virtue of reference to an undefined notion of positive, nevertheless does not assume the existence of God. You are simply mistaken on this point.

The use of “God-like” refers to what?

JAK! It refers to nothing until defined. He is making the very definition so it refers to what is defined.

Answer me this: To what does the word “manifold” refer to in the following definition?

Definition: A manifold is a topological space that is locally Euclidean.

The definition appears to lack clarity and the author of that “need(s) to explain better.” Neither you nor I have the burden of responsibility for the clarity of someone else’s definition.

No but we do have the responsibility of getting our criticisms correct. He does not beg the existential question in definition 1.

We then require disambiguation. But, we don’t get it. Instead, we get even more ambiguity.

Perhaps the definition of manifold given above is ambiguous to you. Are you sure you have the background needed to make such judgments?

“Definition 1: x is God-like iff x has as essential properties those and only those properties which are positive” is ambiguous with “iff” (if and only if) followed by terms which lack clarity. I think it reasonable for us to demand the highest standards of clarity and precision. If this construction (as represented by CC) were specified as “merely a technical definition,” that might be an improvement. It wasn’t. Worse, God in any time of the past many centuries has cultural connotations as does “God-like.” Why use it if the intent were as you claim?

Why use the word “smooth” to describe infinitely differentiable? That word has connotations too. One may not use such connotations in any proof but once one gets a feel for the concept one sees why the word choice was made.

If the intent mathematically were to “merely” as Tarski speculates, some clearly meaningless, nonsense phrase or group of letters would have been superior to “God-like.” So why was “God-like” used?

I am not speculating and I explained that above.

Why not 791 in place of “God-like”? I remain skeptical of your claim that this entire construction was “merely making a technical definition...” Had that been the case, “God-like” would not have been used.

Perhaps you would prefer the following formulation:
http://upload.wikimedia.org/math/3/2/3/ ... 788b38.png

Now, it’s an even greater stretch to defend that the author is: “merely making a technical definition...”

Far from being a stretch, it is obvious. I deal with these kinds of definitions everyday and have done so professionally for 30 years. Perhaps you are confused by what Imean by technical definition. He is defining a new word. It's coinage and has only the meaning given in the definition.

Do words have meaning?

Yes and in Godel’s argument God-like has the meaning he gave it. It’s a freaking definition.

Do those who read words see them in context?

Well, in this case you do not seem to see them in context. The context is a formal proof where a formal definition is given and where the connotations one may bring are only relevant if Godel somewhere equivocates between the definition he gave and some other definition which derives from the ordinary use of the word God. You haven’t shown where he does that. I don’t think he does, and that is not the problem with the argument.

Why was one of your words or my “791” not used? To pretend that “God-like” has no connotation and that we are “merely” discussing an argument form is misleading. Why was it done?

I already explained that. There are many more examples from math. The meaning of irreducible in ring theory does not appeal to any preexisting connotations and no one ever imports those connotations. However, again, when you see the definition and its consequences, you also see that those connotations are at least apropos.

[_marg]

Well, you should be. The point is quite simple. We do this in logic and math all the time.
Another example.

But giving examples of math is no good Tarski. Math is completely conceptual. I appreciate it can be applied to the actual world. Negatives do exist in math. But when we are talking about things existing in the actual world, it's not just conceptual, if that thing exists. As I said before one can imagine an infinite (literally) number of things. To talk with any substance, as if a thing exists in the actual world, there has to be a link to the actual world. Where is Godel's link? As you said he could have used the term G-Like instead of God-like and I agree. At this point, I'm not even discussing that the def'n he gave either doesn't make sense or I'm not understanding the sense it's supposed to make. So please, if you are going to give examples don't use math. It's not the same thing.

previously:Why on earth for example would one ever present a definition of a thing actually existing without any justification or link to the actual world for that thing?

Tarski: Come on! How can one ask a question about something that has no definition?

If I ask you if you believe that infinite cardinals exist would you first want a definition? If I then give the definition would you accuse me of assume the existence of infinite ordinals in the first place? What a silly catch-22 I would be in.

I'm not following you Tarski. I didn't say one shouldn't give definitions, I said why would one do so, without any link to the actual world. And I'm talking about things which exist as actualities or potentially could exist as actualities. One doesn't first create def'ns of things existing and go looking for them, without any justification.

Let's say scientists expect to see intermediary stages of bone structure between one species and another, so if they go looking for them or have expectations of finding them...there is rational justification for doing so. Or let's say people have claimed to have seen giant octopus 40 feet long, and there were a number of sightings at different times, so scientists might go looking. Or a phenomenon is not explained well and something else is expected, because that explanation doesn't quite suffice, they might go looking, with an idea of what to find. But they can not go looking for every thing that man can possibly create by definition alone. It's a physicial impossibility. What link does Godel make to the actual world?

So when someone let's say a scientist sets up a definition of a thing and then gives that thing a label they are in effect presenting an assumption that that labeled thing exists.

How do you even come to the opinion that there is no God without having a definition to give when push comes to shove? Perhaps you mean sothing different than Godel or me or Mr. Tanaka. So if someone offers a definition of God for purposes of precision do you then accuse them of having assumed a priori that such a God exists?

No it is you that are working backwards.

First of all Tarski, no one would presume "no God" without first the notion of the positive "a God" The positive notion of something has to come first before any negative of non existence can logically be made. So to set up an argument which is about the existence of a thing and that thing is defined in Godel's case God ..that thing being defined is assumed to exist. That's what the argument is about.

As for you not being convinced I guess there is not much more I can say. Suppose I give you the standard proof that there exists an infinite number of primes and you say you are not convinced? I can try to explain but you are free to not be convince. At some point I should give up I guess.

You can have negative numbers, you can not have negative things. There is a Tarski..if Tarski was never born, there is no "negative Tarski". And if you weren't born there would be no reason for anyone to look for you.

All I can say more is that I have been working with definitions, axioms and theorems for more than 30 years and have published in top journals. This doesn't prove anything but it should give you pause.

I know it can be very frustrating.

I ran this by another friend (also an atheist and a logician). I asked if he thought that definition 1 simply assumes the existence of God.
He looked at me like I was kidding so I had to say, "just humor me". He said "Of course not. It's just a definition".

If I am presenting an argument to you about the existence of something and I say : x is pox-like if an only if it is red and slimy. Don't you think in that definition there is the assumption that a pox exists? It's possible it could exists as a conception only, but that's not what I'm attempting to present in my argument. I'm presenting you with an argument in which I am attempting to prove the existence of an actuality, something which really exists out there. By using ther words pox-like there is the implied assumption of a pox existing.

A deductive proof of the type we see here could never prove the existence of a material object of course. You seem to think Godel and anyone else must treat God as an (imaginary) material object. Godel does not view God in this way--Mormons basically do. Godel does you the service of defining what he means by his words to be clear, and you object that, by this kindness, he has already begged any and all questions about God. That's weird.

No I'm not assuming Godel's God has to be material. Frankly I don't know what Godel's god is, I've asked the question and didn't receive a response, from either CC or Gad. I had a few questions which I'd have to go back and find. Can you tell me what Godel's god is? But the use of the word God(-like) in the definition assumes that God (whatever it is) exists just like the use of the word pox (-like) which I used previously assumes a pox exists (whatever it is).

[_Tarski]

Well, you should be. The point is quite simple. We do this in logic and math all the time.
Another example.

But giving examples of math is no good Tarski. Math is completely conceptual. I appreciate it can be applied to the actual world.

I am starting to wonder what you mean by "actual world". Can you give an example of something actual that isn't physical?
If not then I think I am right when I say that for you only material things are actual?
What is the difference between a thought that I actually have at time time and one that I could have had (and might have later) given the structure and capabilities of my brain. That is, what is the difference between an actual thought and a merely possible thought?

Negatives do exist in math.

Huh?

But when we are talking about things existing in the actual world, it's not just conceptual, if that thing exists.

Not if that thing is a concept! LOL
What counts as a thing for you? Must it be physical?
Is a force a thing? Is energy a thing? Is mass a thing? Momentum? A wave? A pattern?

Can a pattern be actual?

As I said before one can imagine an infinite (literally) number of things. To talk with any substance, as if a thing exists in the actual world, there has to be a link to the actual world. Where is Godel's link?

that's a fair question. But this has no bearing on whether definition 1 assumes the existence of God. Lets keep on point and not shift to other claims (which I my already agree with).
Godel hopes that there is an actual notion of positive in the real world that satisfies his axioms. I don't think there is but if there were Godel would be well on his way to a proof of something that would have a bearing on the real world.
But the problem is that Godel (and quite a few other bright people) hold to a kind of neoplatonism wherein mathematical entities such as numbers have a reality (albeit nonphysical). One can argue that but then we have changed subject again.

As you said he could have used the term G-Like instead of God-like and I agree. At this point, I'm not even discussing that the def'n he gave either doesn't make sense or I'm not understanding the sense it's supposed to make.

Then do we no agree that the problem in definition 1 is not that it assumes the existence of God?
if not definition 1 then what would you like to discuss?

previously:Why on earth for example would one ever present a definition of a thing actually existing without any justification or link to the actual world for that thing?

Tarski: Come on! How can one ask a question about something that has no definition?

If I ask you if you believe that infinite cardinals exist would you first want a definition? If I then give the definition would you accuse me of assume the existence of infinite ordinals in the first place? What a silly catch-22 I would be in.

I'm not following you Tarski. I didn't say one shouldn't give definitions, I said why would one do so, without any link to the actual world.

Perhaps because one intends to argue that there is a link. The argument is not contained in the definition.
Also, since you think that numbers aren't connected to the actual world, why would one ever define a prime number?

And I'm talking about things which exist as actualities or potentially could exist as actualities. One doesn't first create def'ns of things existing and go looking for them, without any justification.

if one wants to ask if there is a God doesn't it make sense to define what one means by god before searching? Otherwise there are no constraints. I might say "here he is" and hold up a shinny rock.

Let's say scientists expect to see intermediary stages of bone structure between one species and another, so if they go looking for them or have expectations of finding them...there is rational justification for doing so. Or let's say people have claimed to have seen giant octopus 40 feet long, and there were a number of sightings at different times, so scientists might go looking.

What if Godel claims to have perceived God instead of an octopus? Then can we look for God? What if Godel claims that God is not a physical entity? Shouldn't we ask him what kind of being he has in mind and the let him make the definition? Who shall stipulate the limits of our expectations and curiosities?

Or a phenomenon is not explained well and something else is expected, because that explanation doesn't quite suffice, they might go looking, with an idea of what to find. But they can not go looking for every thing that man can possibly create by definition alone. It's a physicial impossibility. What link does Godel make to the actual world?

Godel thinks the physical world is structured by the idea platonic world. That is where he should be attacked.
You seem to assume only physical existence is any kind of existence. Do you have proof of this? Godel assumes that there is something deeper than physical existence (not spiritualistic mind you, that's just a variation on a substance ontology).
I do not claim he is right. I only want to focus and where the real problems lie (not in definition 1).

So when someone let's say a scientist sets up a definition of a thing and then gives that thing a label they are in effect presenting an assumption that that labeled thing exists.

No, I have already shown that is wrong. They may have merely a hypothesis that the thing exists. But again, you miss the thrust of the Platonic viewpoint. Prime numbers are real in that view. In idealism only mind is real. In other views only material substance is real (how is that defined by the way? LOL)

How do you even come to the opinion that there is no God without having a definition to give when push comes to shove? Perhaps you mean something different than Godel or me or Mr. Tanaka. So if someone offers a definition of God for purposes of precision do you then accuse them of having assumed a priori that such a God exists?

No it is you that are working backwards.

First of all Tarski, no one would presume "no God" without first the notion of the positive "a God" The positive notion of something has to come first before any negative of non existence can logically be made. So to set up an argument which is about the existence of a thing and that thing is defined in Godel's case God ..that thing being defined is assumed to exist. That's what the argument is about.

The notion comes first not the assumption of existence. Are you now actually promoting as correct, the idea of assuming the existence first?

As for you not being convinced I guess there is not much more I can say. Suppose I give you the standard proof that there exists an infinite number of primes and you say you are not convinced? I can try to explain but you are free to not be convince. At some point I should give up I guess.

You can have negative numbers, you can not have negative things. There is a Tarski..if Tarski was never born, there is no "negative Tarski". And if you weren't born there would be no reason for anyone to look for you.

??
I have no idea what you are saying. The meaning of negative is contingient on the context. Electrons are real and they have negative charge. Temperature can be negative on a certain scale too. What do you make of negative energy in black hole theory?

All I can say more is that I have been working with definitions, axioms and theorems for more than 30 years and have published in top journals. This doesn't prove anything but it should give you pause.

I know it can be very frustrating.

I ran this by another friend (also an atheist and a logician). I asked if he thought that definition 1 simply assumes the existence of God.
He looked at me like I was kidding so I had to say, "just humor me". He said "Of course not. It's just a definition".

If I am presenting an argument to you about the existence of something and I say : x is pox-like if an only if it is red and slimy. Don't you think in that definition there is the assumption that a pox exists?

No
We do expect to find read and slimy things but the definition does not assume it as such. By the way, by your definition a red rubber ball covered with slim is pox-like by definition. It still a fine definition logically to the extent that slimy is well defined.

If I hold up a slimy red rubber ball then I have demonstrated the existence of a pox-like being.

On the other hand, Godel's definition of God-like is a bit more interesting and should he have ever succeeded in making it clear that his notion of positive answers to something in real life he would be on his way to showing that a god-like being (in his definition) exist. We then go back and look at his definition and ask OK so what? Is this something would should like to consider God? What is it about his God-like being that we should find impressive of God-like in the ordinary nontechnical sense. If there is nothing then he would be in the position of someone having shown that there exist pox-like beings such as slimy red balls (so what? we should ask)

[_Calculus Crusader]

JAK and marg:

You should quit while you're behind.

[_marg]

Well, you should be. The point is quite simple. We do this in logic and math all the time.
Another example.

But giving examples of math is no good Tarski. Math is completely conceptual. I appreciate it can be applied to the actual world.

I am starting to wonder what you mean by "actual world". Can you give an example of something actual that isn't physical?
If not then I think I am right when I say that for you only material things are actual?
What is the difference between a thought that I actually have at time time and one that I could have had (and might have later) given the structure and capabilities of my brain. That is, what is the difference between an actual thought and a merely possible thought?

As I mentioned previously I didn't make up the concept of scientific actualities. When I talk about the actual world that is what I'm referring to.

So let me use the notes to a course which discusses this concept, where I first heard it. The notes are not a transcription of the course, but they are the notes officially put out by the course called Science Wars: What Scientists know and how the know it. by prof. Steven Goldman. in Chap 24 "Truth History and Citizenship"


II) John Dewey's conception of experience suggests why science is ambivalent about knowledge and points a way to overcoming it.

A. A stumbling block in attempting to understand science as a process of inquiry and as knowledge, in the strict sense, is the defensiveness of scientists on the subject of the relationship of science to reality.

1) The term reality is so freighted with connotations and values that it is preferable to say that the object of scientific knowledge is neither experience nor reality but actualities - scientific objects, such as the Sun, the Earth, atoms, genes, black holes - all inductively inferred from experience

2) Scientific theories can be understood as mapping, not onto some ultimate and inexperienceable Reality, but onto such actualities which are rooted in emperical experiences, current or potential, directly or indirectly, via instruments, all defined by the scientific community.

3) The mapping criteria always link actualities to experience and allow us to check the correspondence of claims about the behavior and properties of actualities with experience.

4) Note that instruments used to produce experiences that validate actualities are themselves the products of the thinking associated with the actualities

B. Actualities invariably re-describe and displace ordinary experience

1) Copernican astronomical theory is a case in point, as is expanding Universe theory, the atomic theory of matter and quantum field theory

2) Ask a scientist what is real and the answer will be particles and fields, forces and structures (mathematical and physical), genes and molecular assembly plants, that is actualities defined by science

3) Redefining actualities is less threatening than redefining Reality and the check of correspondence with new experiences reinforces our conviction that these objects defined by the scientific community are "real" in a sense we can justify pragmatically.

So before I go onto to addressing your post perhaps you could contemplate...the concept of a scientific actuality..because that is what I'm talking about when I say the actual world.

[_marg]

JAK and marg:

You should quit while you're behind.

I don't treat discussion as a game to win. I want to learn from others but I need to understand their point before acceptance. I asked you questions and you chose not to answer. Perhaps you wanted to win.

[_Tarski]

[color=darkblue]
II) John Dewey's conception of experience suggests why science is ambivalent about knowledge and points a way to overcoming it.

A. A stumbling block in attempting to understand science as a process of inquiry and as knowledge, in the strict sense, is the defensiveness of scientists on the subject of the relationship of science to reality.

Yes there are many approaches to handling the thorny issues about "reality" as it relates to scientific inquiry. I see you have read up on at least one of them. So far, I haven't seen something that answers everyone's concerns regarding the status of science and it's relation to ontology and epistemology.

The notion of "scientific actuality" is not a standard notion. A quick google search for "scientific actuality" give only 609 hits! Where as "scientific reality" gives 90,700 and "mathematical reality" gives 27,300.

Anyway, I have had a few courses and read a few books on these matters and don't recall seeing quite that phrase before.

1) The term reality is so freighted with connotations and values that it is preferable to say that the object of scientific knowledge is neither experience nor reality but actualities - scientific objects, such as the Sun, the Earth, atoms, genes, black holes - all inductively inferred from experience

This is nice but not quite a clear definition is it? We only have a list of examples. Since we don't have a definition or even a clear criteria we don't know how far to take it. Below, your quote mentions forces and structures as somehow scientifically real.
So can we extend the list? How far?

the Sun, the Earth, atoms, genes, black holes, quarks, strings, structures, branes, [parallel universes, interactions, patterns, information, computations, software, thoughts, beliefs, behaviors, space, time, spacetime, number, set, quale, notion.....?

What kinds of experiences shall be allowed? Experience with numbers, sets and topologies? (Kitcher believes that mathematics is empirical!!),
spiritual experience with gods and devils (oh please no!)?

2) Scientific theories can be understood as mapping, not onto some ultimate and inexperienceable Reality, but onto such actualities which are rooted in emperical [sic] experiences, current or potential, directly or indirectly, via instruments, all defined by the scientific community.

"inexperienceable Reality"? Is this like Kant's noumena? There are deep and troubling waters in that direction.

Suppose one sets up a solid criteria for what counts as a "scientific actuality". Then that encompasses some things that fit and others that don't but how does one then leap to the notion that anything that doesn't fit the criteria cannot be real in any way at all? In other words, how does one argue that the complement of the class of scientific actualities is empty or at least devoid of anything but the imaginary?

I am glad that you seem to have a loyalty to the scientific outlook. However, I encourage you to check out some perspectives beyond Chapter 24 of Steven Goldman book.

Perhaps
"Philosophy of Science A Contemporary Introduction" by Alex Rosenberg

and for ontological question regarding mathematical objects:

Thinking about Mathematics: The Philosophy of Mathematics by Stewart Shapiro
and
Platonism and Anti-Platonism in Mathematics by Mark Balaguer

To be fair, I will take a look at the book you mention.

[_marg]

Let me see if I understand you Tarski,

You are saying it is a valid argument to argue that anything which can be conceived can possibly exist..and then one can proceed to define their conceived thing. And it is irrelevant whether or not that thing actually exists. It may turn up down the road or it may never turn up but just the same it may possibly exist.

And what I'm saying Tarski is there is an implied assumption when one creates an argument for the existence of something which could exist as an actuality. The argument assumes there is justification to assume the actual thing in the first place. As was pointed out in my previous post..the concept of scientific actualities is that they are all all inductively inferred from experience. There is a link to the actual world. So gravity for example is an actuality. We can not see gravity but a rational argument can be made for its actual existence. And the concept gravity can be explored. First the observations were made, described and the word gravity applied to it.

Now I have not looked closely at Godel's argument. I was hoping those who have claimed to have studied it, would have explained to me, what is Godel's god and how does it link to the actual world. Because otherwise if it doesn't I can not see the value in it. One can claim an infinite number of possibilities could exist, but of what value is that, if there is no pragmatic purpose and no link to justify it?

Now I know you are saying Godel's first def'n doesn't assume a God, but the first def'n is within the context of the whole argument, the purpose being to establish a conclusion that some sort of a god could possibly exist. Of course it is obvious that any sort of god could possibly be conceived, one doesn't require an argument for that. Just because something is conceived does not mean it can possibly exist as an actuality or that it is likely to exist or that it does exist.

[_Tarski]

Let me see if I understand you Tarski,

You are saying it is a valid argument to argue that anything which can be conceived can possibly exist..and then one can proceed to define their conceived thing. And it is irrelevant whether or not that thing actually exists. It may turn up down the road or it may never turn up but just the same it may possibly exist.

No, I am saying that it is possible to make a clear and valid definition of a entity or type of entity without thereby assuming a priori that there exist any such entities.

I can come up with a definition of unicorn precise enough for you to properly tell me that there is no evidence for the existence of any such animal.

I can also define a new term that makes perfect sense without assuming anything as to existence. For example, let me make such a definition now.

Definition: By "Supertall" we shall mean a hominid that is taller than 25 feet.

Now I may go on to ask if there exist any supertalls or not. (I think not!)

There have been instances in mathematics where a valid definition was made and later it was proved by hard work that no such mathematical object could exist.

In science we had phlogiston and elan vital etc.