Best Religious/Nonreligious Debate Ever

[_Tarski]

Tarski

Ok for now I want to skip Stak's talk on induction,form and validity which in my opinion Stak was wrong, but if we deal with that, perhaps later.

I want to unpack this:

Stak writes:

Dawkin's own argument is a simple modus ponens.

A --> -G, A, .:. -G

If the ARGUMENT of this chapter is accepted, the factual premise of religion- the GOD HYPOTHESIS- is untenable (that means NEGATION).

Do you agree with this Tarski..that this is Dawkins' deductive argument?

Marg, I still haven't read the book.

The sentence is an "if then statement".
However I don't think it is best interpreted as a modus ponens for several reasons. For one thing "A" is not a truth functional statement (or a predicate). Is is the word "argument" that refers to a whole promised line or reasoning and rhetoric. The sense of the word is not specified. That is, is it to be a formal argument of the sort that could be reflected in a formal language or deductive system? I think not but for this little issue of whether I see a modus ponens, it doesn't matter. I don't think there is a modus ponens in that sentence (maybe such an interpretation could be forced but I don't see how or why once would want to).
By the way, I don't think that "untenable" is just a simple logical negation anyway.

I would say that this is just a stylized or semi-idiomatic form of speech that amounts to the promise to convince. If one takes it too seriously we get something like the absurd idea that whether a belief is untenable (difficult or impossible to defend) or not depends on whether some unspecified person or persons accepts an argument (acceptance being a psychological state).

He doesn't really mean that the conclusions of his argument follow from the mere fact that he can get some humans to accept the argument.

.............................................silliness.............................
Suppose that the argument A were an instance of affirming the consequent (a fallacy):
Then I suppose we could encode the argument in a statement (A1 below).

A1: ((P--->Q) and Q)--->P
A2: B(A1)
_____
P

where B(x) means x is accepted by person B

WTF is that??
Ok this is admittedly silly.
....................................................end silliness.......................

But, see, I haven't read the book.

I can guess that he will attempt to undermine the usual motivations for positing a God in the first place and then augment that by pointing out the lack of evidence for supernatural events and also bring up other things such as scriptural absurdities and other unpleasantness that seem to almost always be part of the theistic package.
So his book is best viewed as rhetoric maybe. (??)

But I haven't read the book so I don't know how formal his arguments are supposed to be and whether he succeeded in doing what was promised. If he is really only promising to convince then perhaps we should be thinking more that he is doing what scientists do when they try to convince each other of big ideas. If there is anything to Khun's ideas, then we shouldn't expect "formulas" or fully articulated methods to arrive at consensus. As an example, is Occam's razor a principle of deduction or formal princple? No. Is it even a sharply defined principle that can be mechanically applied even in principle? No. (Need examples?)


We know that Dawkins is not claiming to prove that God does not exist because he says that he knows of no such proof. (In fact, he mistakenly thinks it is because one cannot prove a negative)
So what could it mean that he will make the God hypothesis untenable? He probably means something closer to making it unlikely or seem unlikey (is there a distinction if we take the subjectivist stance on probability? That is a whole other discussion.)

In what sense could he do this?

OK, well, let us consider a toy example. This is something logicians, mathematicians and philosphers do all the time. The toy example I have in mind is Russell's teapot but considered differently.

Why do we say that the existence of such a teapot is unlikely? It is after all, far from impossible. We do not apply a formal Bayesian argument or at least there should be no need to do so. We go directly to those kind of intuitions that formal probability was designed to mirror but can never fully found.
Basically, because our probabilistic intuitions tell us that if we pick a statement at random (in the informal sense of random) and don't recognize any rational or evidential reason for it to be true then it is unlikely to be true since most such statements are false. (For example, the statement that there is an ice mountain range on one of Jupiter's moons that is recognizably the Coca Cola logo when viewed from a certain position in space. Or, so as to minimize worries about specified complexity, consider the statement "a comet just crashed into the star nearest to our sun.) There is just no reason or motivation, other than maybe wishing, to believe such things.
Do we need to formalize this instance of rationality? I think Hilary Putnam for one would say not.

But, the position some readers will start in will be that the notion of God must be taken seriously because it is thought that there are reasons to believe. And, after all can we really dismiss such a ubiquitous idea so quickly? God is not the Teapot because we are not all on the same page when it comes to evidences and motivations for God but we probably are on same page with the teapot (who would believe such a thing?).

So Dawkins wants to change that by dealing with supposed motivations, reasons, and evidences for belief. Thus making the God hypothesis more like the Teapot hypothesis.
His main target would likely be questions of complexity and design (Paley type arguments). (Oh, remember, I'm guessing)
I say "more like" the teapot since the difference will remain that God is a hopeful idea meeting human needs and may remain so while the orbiting teapot is not and never will be.

So if one can remove or reduce to a minimum all the rational motivations for believing in God and convince the reader that there is no credible evidence for God, then like the teacup it becomes "unlikely". Could this be all he is doing? And why not? The question is then how well he convinced the intelligent and open minded reader.
I also accept the idea that Dawkins is not addressing, and is under no obligation to address, any Karen Armstrong-ish notion of God that is highly abstract and/or removed from traditional notions of a creator God or personal God of salvation. Saying that to me, or whoever, "God" is just a word for the laws of physics is or just a word for "love" is hardly a comeback that will matter to Dawkins' project.

But asking me to offer my opinion at this point is unfair since I haven't read the book.
I wonder why I went on and on about it.

[_marg]

Thanks Tarski..by the way I agree with everything you've said in the first half of your post, and you helped to clarify and confirm my thoughts. For now I'll skip comment on it give you some information because you mention you haven't read the book.

I think Dawkins is offering more than what you've speculated. His argument is laid out in chapter 4 ..with the main important sections in the last half in "The Anthropic Principle: Planetary Version" plus the later "Cosmological Version". I believe Stak thinks that Dawkins needs to argue against arguments for God's existence..but I asked Stak as did you with a similar question, in the the other thread to give what argument for God is strong that Dawkins' failed to consider or considered poorly and to date to my knowledge there's been no response to that by Stak.

So in my opinion chap 4..last half is the main argument in Dawkin's book and I'll try to pull out key points for you. And by the way Stak is arguing against Dawkin's 6 point argument and summary.

I'm using a pocketbook version..don't know where my hard cover is.

Quotes from God Delusion (my words in brown):

God Hypothesis defined and concise explanation of what he is arguing
Page52
Instead I shall define the God Hypothesis more defensibly: there exists a superhuman, supernatural intelligence who deliberately designed and created the universe and everything in it, including us. This book will advocate an alternative view: any creative intelligence, of sufficient complexity to design anything, comes into existence only as the end product of an extended process of gradual evolution. Creative intelligences, being evolved, necessarily arrive late in the universe, and therefore cannot be responsible for designing it. God in the sense defined, is a delusion: and as later chapters will show a pernicious delusion.


Point form summary of his main argument..essentially laid out in Chapter 4
p 187- 189


This chapter has contained the central argument of my book, and so, at the risk of sounding repetitive, I shall summarize it as a series of six numbered points.

1. One of the greatest challenges to the human intellect, over the centuries, has been to explain how the complex, improbable appearance of design in the universe arises.

2. The natural temptation is to attribute the appearance of design to actual design itself. in the case of a man made artifact such as a watch, the designer really was an intelligent engineer. It is tempting to apply the same logic to an eye or wing, a spider or a person.

3. The temptation is a false one, because the designer hypothesis immediately raises the larger problem of who designed the designer. The whole problem we started out with was the problem of explaining statistical improbability. It is obviously no solution to postulate something even more improbable. We need a 'crane', not a 'skyhook', for only a crane can do the business of working up gradually plausibly from simplicity to otherwise improbable complexity.

4. The most ingenious and powerful crane so far discovered is
Darwinian evolution by natural selection. Darwin and his successors have shown how living creatures with their spectacular statistical improbability and appearance of design, have envolved by slow, gradual degrees from simple beginnings. We can now safely say that the illusion of design in living creatures is just that –an illusion.

5. We don’t yet have an equivalent crane for physics. Some kind of multiverse theory could in principle do for physics the same explanatory work as Darwinism does for biology. This kind of explanation is superficially less satisfying then the biological version of Darwinism, because it makes heavier demands on luck. But the anthropic principle entitles us to postulate far more luck than our limited human intuition is comfortable with.

6. We should not give up hope of a better crane arising in physics, something as powerful as Darwinism is for biology. But even in the absence of a strongly satisfying crane to match the biological one, the relatively weak cranes we have at present are, when abetted by the anthropic principle, self evidently better than the self-defeating skyhook hypothesis of an intelligent designer.

His concluding remark:

If the argument of this chapter is accepted, the factual premise of religion–the God hypothesis–is untenable. God almost certainly does not exist. This is the main conclusion of the book so far. Various questions now follow. Even if we accept that God doesn't exist, doesn't religion still have a lot going for it? Isn't it consoling? Doesn't it motivate people to do good? If it weren't for religion, how would we know what is good? Why, in any case, be so hostile? Why, if it is false, does every culture in the world have religion? True or false, religion is ubiquitous so where does it come from? It is to this last question that we turn next.
------------
Some quotes discussing anthropic priniciple
Page 164
The anthropic principle, like natural selection, is an alternative to the design hypothesis. It provides a rational design free explanation for the fact that we find ourselves in a situation propitious to our existence.

page 165
Just as we did with the Goldilocks orbits, we can make the point, that however improbable the origin of life might be, we know it happened on earth because we are here. Again as with temperature, there are 2 hypothesis to explain what happened–the design hypothesis and the scientific or anthropic hypothesis. The design approach postulates a God who wrought a deliberate miracle, struck the prebiotic soup with divine fire and launched DNA or something equivalent on its momentous career.

Again as with Goldilocks, the anthropic alternative to the design hypothesis is statistical. Scientists invoke the magic of large numbers. It is been estimated that there are between 1 billion and 30 billion planets in our galaxy, and about 100 billion galaxies in the universe. Knocking a few noughts off for reasons of ordinary prudence, 1 billion billion is a conservative estimate of the number of available planets in the universe. Now, suppose the origin of life, the spontaneous arising of something equivalent to DNA, really was a quite staggeringly improbable event. Suppose it was so improbable as to occur on only one in 1 billion planets. A grant giving body would laugh at any chemist who admitted that the chance of his proposed research succeeding was only one in 100. But here we are talking about odds of 1 in 1 billion. And yet… Even such absurdly long odds, life will still have arisen on 1 billion planets of which Earth, of course is one.

This conclusion is so surprising, I'll say it again. If the odds of life originating spontaneously on the planet were 1 billion to one against nevertheless that stupefyingly improbable event would still happen on 1 billion planets. The chance of finding any one of those billion life bearing planets recalls the proverbial needle in a haystack. But we don't have to go out of the way to find a needle because [back to the anthropic principle] any beings capable of looking must necessarily be sitting on one of these prodigiously rare needles before they even start the search.

Any probability statement is made in the context of a certain level of ignorance. If we know nothing about the planet, we may postulate the odds of life's arising on it as say, one in 1 billion. But if we now import some new assumptions into our estimate, things change. A particular planet may have some peculiar properties, perhaps a special profile of element abundance says in its rocks, which shift the odds in favor of life's emerging. Some planets in other words are more “Earth-like” than others. Earth itself, of course is especially Earth-like! This should give encouragement to our chemists trying to re-create the event in the lab, for it could shorten the odds against their success. But my earlier calculation demonstrated that even a chemical model with odds of success as low as one in 1 billion would still predict that life would arise on 1 billion planets in the universe. And the beauty of the anthropic principle is that it tells us against all intuition, that a chemical model need only predict that life will arise on one planet in 1 billion billion to give us a good and entirely satisfying explanation for the presence of life here. I do not for a moment believe the origin of life was anywhere near so improbable in practice. I think it is definitely worth spending money on trying to duplicate the event in the lab and
– by the same token, on SETI, because I think it is likely that there is intelligent life elsewhere.

Even accepting the most pessimistic estimate of the probability that life might spontaneously originate, this statistical argument completely demolishes any suggestion that we should postulate designed to fill the gap. Of all the apparent gaps in the evolutionary story the origin of life can seem unbridgeable to brains calibrated to assess likelihood and risk on an everyday scale: the scale on which grant giving bodies assess research proposals submitted by chemists. Yet even so big a gap as this is easily filled by statistically informed science, while the very same statistical science rules out a divine creator on the “Ultimate 747" grounds we met earlier.


The Anthropic Principle: Cosmological Version

Page 171


I won't go through the rest of recent 6 numbers. The bottom line for each of them is the same. The actual number sits in a Goldilocks band of values outside which life would not have been possible. How should we respond to this? Yet again, we have the theists answer on the one hand, and the anthropic answer on the other. The theist says that God when setting up the universe, tuned the fundamental constants of the universe so that each one lay in its Goldilocks zone for the production of life. It is as though God had 6 knobs that he could twiddle, and he carefully tuned each knob to its Goldilocks value. As ever, the theists answer is deeply unsatisfying, because it leaves the existence of God unexplained. A God capable of calculating the Goldilocks values for the 6 numbers would have to be at least as improbable as the finely tuned combination of numbers itself, and that's very improbable indeed. This is exactly the premise of the whole discussion we are having. It follows that the theists answer has utterly failed to make any headway towards solving the problem at hand. I see no alternative but to dismiss it, while at the same time marveling at the number of people who can't see the problem and seemed genuinely satisfied by the “Divine Knob Twiddler” argument.

Maybe the psychological reason for this amazing blindness has something to do with the fact that many people have not had their consciousness raised, as biologists have, by natural selection and its power to tame improbability.

Page 172
Biologists, with their raised consciousness of the power of natural selection to explain the rise of improbable things, are unlikely to be satisfied with any theory that evades the problem of improbability altogether. And the theistic response to the riddle of improbability is an envasion of stupendous proportions. It is more than a restatement of the problem, it is a grotesque amplification of it. Let's turn, then, to the anthropic alternative. The anthropic answer, in its most general form is that we could only be discussing the question in the kind of universe that was capable of producing us. Our existence therefore determines that the fundamental constants of physics had to be in their respective Goldilocks zones. Different physicists espouse different kinds of anthropic solutions to the riddle of our existence.

Page 175
It is tempting to think [and many have succumbed] that to postulate a plethora of universes is a profligate luxury which should not be allowed. If we're going to permit the extravagance of a multi-verse, so the argument runs, we might as well be hung for sheep as a lamb and allow God. Aren't they both equally un-parsimonious ad hoc hypothesis, and equally unsatisfactory? People who think that have not had their consciousness raised by natural selection. The key difference between the genuinely extravagant God hypothesis and the apparently extravagant multiverse hypothesis is one of statistical improbability. The multiverse, for all that it is extravagant is simple. God, or any intelligent, decision taking calculating agent, would have to be highly improbable in the very same statistical sense as the entities he is supposed to explain. The multi-verse may seem extravagant in sheer number of universes but each one of those universes is simple in its fundamental laws, we are still not postulating anything highly improbable. The very opposite has to be said of any kind of intelligence.

With regards to Darwins' use of terminology of 'cranes and skyhooks"

Page 139
A deep understanding of Darwinism teaches us to be wary of the easy assumption that design is the only alternative to chance, and teaches us to seek out graded ramps of slowly increasing complexity.

Page 98
Entities that are complex enough to be intelligent are products of an evolutionary process. No matter how Godlike they may seem when we encounter them, they didn't start that way. Science fiction authors such as Daniel F Galouye in Counterfeit World have even suggested [and I cannot think how to disprove it] that we live in a computer simulation, set up by some vastly superior civilization. But the simulators themselves with have to come from somewhere. The laws of probability forbid all notions of their spontaneously appearing without simpler antecedents. They probably owe their existence to a [perhaps unfamiliar] version of Darwinian evolution: some sort of cumulatively d ratcheting 'crane' as opposed to 'skyhook', to use Daniel Dennett's terminology. Sky hooks–including all gods are magic spells. They do no bona fide explanatory work and demand more explanation than they provide. Cranes are explanatory devices that actually do explain. Natural selection is the champion crane of all time. It has lifted life from primeval simplicity to the dizzying heights of complexity, beauty and apparent design that dazzle us today.

[_MrStakhanovite]

So who am I responding to?

[_MrStakhanovite]

I believe Stak thinks that Dawkins needs to argue against arguments for God's existence..

Not in chapter 4, he deals with arguments for God in chapter 3.

but I asked Stak as did you with a similar question, in the the other thread to give what argument for God is strong that Dawkins' failed to consider or considered poorly and to date to my knowledge there's been no response to that by Stak.

I moved that discussion to a separate thread, here was my answer:

I like Ontological arguments, but I use them for building possible metaphysical systems for a Naturalist worldview. It’s a good place for a Theist to start, but there is a lot of work to be done after that argument. There are two broad strategies that I have respect for:

Reformed Epistemology: I think the project launched by Wolterstorff and Plantinga has promise, probably because I like the route they take to try and ground beliefs contra evidentialism, but I don’t think either of them have come to close to establishing what they’ve set out to do.

Neo-Classical: Another strategy I think is on the right track is Swineburne’s original idea to take all the classical deductive arguments from history, and turn them into inductive arguments and constructs a cumulative argument for the probability of God.

I don’t think there is going to ever be a silver bullet type argument that can achieve what Theists want, so I don’t think there is a strong argument for the existence of God out there (nor do I think any good Theistic Philosophers think that either), the most profitable way seems to be building a slow case that accumulates strength over time, and the only two projects I see doing that now is Reformed Epistemology and Classical arguments construed inductively.

[_Tarski]

So who am I responding to?

Let's stick to the other thread and stick with foundations of logic and the status of mathematical induction--at least until I have read the Dawkins book.

I will say this much though, Dawkins seems to be using quite of bit of the ideas of Daniel Dennet found in the book Darwin's Dangerous Idea. Dennett probably does a better job of it from the point of view of philosophy because he is going into more detail and speaking to a more philosophically sophisticated audience.

On the other hand, Dennett does not strike me as a guy who believes that rational thinking about empirical matters amounts to formal maneuvers well reflected in some deductive system somewhere. He seems unimpressed by ontological arguments for example. Must we always be convinced by an argument that followed formal rules? The formal rules we find in predicate calculus, sets theory, recursion theory and even modal logic are supposed to mirror and model rational thought, not define it outright. In fact, deontic logic has problems reflecting rational thought about morality.

I have several examples that suggest that formal logic of any kind can produce absurdities when applied to real world categories such as thoughts, chickens, ideologies, atoms and gods. None of these are completely without vagueness.

A toy example:

A parent of a chicken is a chicken. Now inductively, the ancestors of chickens must have all been chickens --contradicting evolution. The concept of "chicken" just isn't well defined when viewed over geological time scales.
But we can still reason as if there were no vagueness when the vagueness is insignificant:

Bill likes all birds. (assumption)
A chicken is a bird.
Therefore, Bill likes chickens.

(But even here, is a dead and rotting chicken a chicken? )

So one can push logic to a breaking point in real life and there exist much more subtle examples.
See the discussion of deontic logic in the wikipedia entry on modal logic.


Personally, when I read Godel's ontologically argument I have no confidence that this is not what is happening. Things are formally crisp (as symbols with rules of manipulations) but what do the formalities map onto in the "real" world, what is the interpretation?? The notion of an interpretation is a tricky one.
We are attempting the most extreme application of formal logic possible (arguing about "God").

[_MrStakhanovite]

Let's stick to the other thread and stick with foundations of logic and the status of mathematical induction--at least until I have read the Dawkins book.

Yes, I consider mathematical induction a totally separate topic.

I will say this much though, Dawkins seems to be using quite of bit of the ideas of Daniel Dennet found in the book Darwin's Dangerous Idea. Dennett probably does a better job of it from the point of view of philosophy because he is going into more detail and speaking to a more philosophically sophisticated audience.

This is actually a rabbit trail I went down. Dawkins cites Dennett’s Dangerous Idea book, which in turn was talking about a citation from Dawkins’ The Blind Watch Maker. This is in part what lead me to conclude Dawkins argument was flawed.

On the other hand, Dennett does not strike me as a guy who believes that rational thinking about empirical matters amounts to formal maneuvers well reflected in some deductive system somewhere.

This is part of the conversation you missed, but I’m not saying Dawkins argument is a strict deductive argument. The short of it is, is that there are generally three types of inductive reasoning in science: Inductive Generalization, Hypothetical Induction, and Probabilistic Induction, and I think the best way (and strongest possible way) to read Dawkins is as a type of hypothetical induction, or a demonstrative induction. That means this type of induction isn’t considered an ampliative inference, but an inference that allows a conclusion to follow from what scientists know to be true.

What I wanted Marg to do is pick some way of assessing Dawkins’s 747 gambit, so I could demonstrate it doesn’t follow. A number of things could work here, such as a natural deductive system that has only rules of inference, and no axioms, or we could construe Dawkins’ argument as a probability.

I have several examples that suggest that formal logic of any kind can produce absurdities when applied to real world categories such as thoughts

Of course, logic isn’t the end all be all, but I think to asses Dawkins’ 747 argument, we need some kind of rules to do so, rather than just literary quality.

[Guest]

The sentence is an "if then statement".
However I don't think it is best interpreted as a modus ponens for several reasons.

This really confused me, and this is why I hesitated to respond because I think you are at a disadvantage for not closely following the entire thread, and not having read the chapters being discussed. I think Marg did you a disservice by providing no context and just a snippet for you to evaluate

For one thing "A" is not a truth functional statement (or a predicate).

Yes it is, it has to be. In this post I’m talking to Marg about basic sentential logic, translating English into a propositional language so it can be evaluated. It is entirely based on truth functioning. All she showed you was just a snippet of this post.

Is is the word "argument" that refers to a whole promised line or reasoning and rhetoric. The sense of the word is not specified.

It is specified in the Dawkins text, allow me to quote Marg:

If the argument of this chapter is accepted, the factual premise of religion–the God hypothesis–is untenable. God almost certainly does not exist. This is the main conclusion of the book so far.

He calls it an argument, breaks down all his main points into 6 bullets, and says that if you accept all 6 bullets, then the God hypothesis is untenable and that God almost certainly does not exist.

That is, is it to be a formal argument of the sort that could be reflected in a formal language or deductive system?

Absolutely. Any argument made can be reflected in a formal language.

[_MrStakhanovite]

This entire argument I’ve had with marg is based on this exchange:

Deduction is about logical validity and form ..not induction

Look at what you just wrote. You just told me, that induction is not about validity and form. You are telling me, that when someone makes an inductive argument, they don't have to offer a proof to show it's valid. Do I have to explain why this is patently absurd and borderline stupid?

Yes you will have to explain why this is patently absurd and borderline stupid...if you don't mind

SAUCE

This is the point I lost respect for marg. She was insisting that inductive arguments need not follow a form. You can’t even have an argument without following some kind of pattern, form, some steps to follow. This is the point where mathematical induction got introduced by me.

[_marg]

Well Stak, I hope Tarski weighs in here because we definitely need a mediator.

And by the way thank you for linking to that post..as you can see I'm making a similar point to Tarski asking how can you have a -G..in this situation... but I won't deal with that now.

This is my take..induction requires a leap in reasoning from premises to conclusion. That leap in reasoning is why the conclusion is not conclusive. Deductive reasoning is when there is a conclusive conclusion. So it's essentially mathematical, with different recognized forms..and symbols can be used interchangable within the forms for different variables. When an argument is presented in deductive form..it's considered in valid form. To my knowledge there is no valid form in inductive reasoning. In inductive reasoning it's called cogent when the argument is strong.

Now the mathematical induction examples are within the game of math. For math induction equations..the equations hold true up to infinity because there is no reason given the equation that the variable won't hold true for all natural numbers to infinity. (At this point I don't recall the actual equation I looked at..I'd have to review). So there is a bit of a leap in reasoning, but because it's within constructed equation..it can be determined that the conclusion is conclusive up to infinity. This is unlike an argument representing the experiential world in which the conclusion is dependent on variables one doesn't know with certainty or can predict. So the actual mathematical induction equations are deductive reasoning.

Now Dawkins is arguing against the argument from design for God in that list of 6 points to the conclusion. He's not making an affirmative claim of something existing. He's countering the argument from design ..an affirmative claim for God's existence and saying that there are other arguments for how life came about with actual probability estimates...whereas there is no probability estimate from the design for god argument. Therefore those arguments have greater justification that the Design argument. He's not making the extraordinary claim, he's giving reasoning why it's justified to reject the extraordinary claim for God based that is based on the argument from design. He's making a leap in reasoning or inductive reasoning ..even though he's arguing that with "almost certainty"....his reasoning leads to rejection of the Design argument for God.

Stak you turned his argument into a deductive argument because I believe you took "almost certainty" as being so close to a conclusive conclusion..so therefore assume it is conclusive. But let's say we look at the claims hat Santa exists...and someone argues for it. If someone argues that with almost certainty Santa does not exist because the affirmative claim lack evidence and reasoning...that doesn't mean to reject the affirmative claim...the rejection conclusion is conclusive. It is still an inductive argument ..but because it's a rejection of an extraordinary claim which has little warrant for it...it's justified in stating ..with "almost certainty" that Santa doesn't exist...because the warrants for the argument or the affirmative claim for Santa are poor. To reject an extraordinary claim of the existence of something..doesn't require much reasoning evidence. Whereas to make an affirmative claim for the existence of something does require evidence which commensurates with the claim.

[_Tarski]

For one thing "A" is not a truth functional statement (or a predicate).

Yes it is, it has to be.

Does "A" refer to an argument or a statement about an argument? An argument is not a statement. In modus ponens, the letters refer to statements--statements that can be true or false. Arguments are valid or invalid.

Anyway, suppose I make a long argument in a book. Suppose it is even deductive.

Maybe it has the form

F1
F2
.
.
.
Fn
___________
C

where the F's are possibly complex compound statements etc.
Maybe it takes pages.

Can I now say that my argument is a modus ponens by letting A stand for the whole argument above and writing the following.

If A then C
A
therefore C

No, because A is not a statement but an argument ( a series of statements ).

But we can try to fix that by letting A1 stand for the statement
"The reader accepts the argument A"

Then we can try

If A1 then C
A1
therefore C

This still doesn't work as a sound argument (even if it is trivially valid) since it is certainly not true that C follows from A1. The acceptance of an argument by a person is not what logically forces the conclusion.


What if I simply said that if the reader accepts my argument then they must accept my conclusion. (A needless sentence for sure)



Would a reader then be justified in saying my whole argument was a simple modus ponens?

Of course not.

Here is another silly "reduction" to modus ponens.

If my argument leading to conclusion C is sound then C
My argument leading to conclusion C is sound.
Therefore C.

I could do this no matter what argument I have in mind.
By the way, can you see why I said sound instead of valid?

Absolutely. Any argument made can be reflected in a formal language.

In more than a trivial sense? Is this supposed to be obvious?
I wonder if you could argue to that conclusion and then represent the argument as a valid inference in a formal system.