Because it can be reworded into a tautology, which makes it necessarily true.

[(p > q).p] > q

Here's the truth table for modus ponens (your argument form):

So it goes right back to basic metaphysics, and the axiom of identity, which itself is defended through retortion. I.e. to exist is to exist as something, to have a non contradictory nature.

The only basic metaphysic required is the existence of sentient brains.

Now, you tell me: how can you justify your claim through appeal to the supernatural?

That's funny, you don't say why.

I answered your question by showing that modus ponens is a necessary truth. That's precisely why modus ponens works.

Perhaps you have a question concerning cosmology or basic metaphysics? I.e. why there is a universe in the first place? Why it exists as it does? Is your question really ontic in nature?

If so, it's unrelated to the question of how we justify any a priori system. It's a question of cosmology or metaphysics/ontology.

Now, I'll ask a second time: can you show me how you can 'justify' 'logic' through an appeal to the supernatural?

Glad you are hanging in there.

You word that as if it's problematic for my case, yet you don't specify why. The fact that modus ponens works is because it is a tautology. Tautologies are necessarily true. Where's the problem in my account?

I provided you with an explanation as to how we (any logician, theist or atheist) justifies modus ponens, without making any appeals to the supernatural. I think what you are really after is a question related to metaphysics, or even cosmology. I.e. why is nature uniform?

Isn't that really your goal here? 

First, atheism is merely a lack of belief in god. It's not a worldview, nor an epistemology nor a grounds for 'logic'. I think you want to ask: "How can a naturalist, or how can a materialist account for modus ponens?"

Second, I must ask you again: what do you mean by 'can't justify these tautologies? They exist necessarily, given the existence of sentient brains, so your question cannot be a question pertaining to justifying deductive logic, it must in fact be a question related to metaphysics "Why does A=A? How do we know that?" or even cosmology "Why is there a universe"?

These questions are outside of matters of logic. They relate to metaphysics or even physics. Not logic. Once we have a sentient brain, modus ponens is a necessary truth, so you're question seems more related to "Why do we have sentient brains" Why does A=A? I.e. the usual uniformity questions of presuppers.

Yes.

What sense is that? In what sense isn't it true? Can you show me how modus ponens can be false? 

The axiom of identity is not so much 'true' - truth and falsity are properties we apply to propostions - as much as it is simply necessary. How can it be unnecessary? How can it be false?

Why? You would expect that it would be false for A to equal A?

Why? Can you show me why it seems this way to you?

Why not? You don't say why. I've shown you why modus ponens must work, without making any reference to the supernatural. You seem to want to ask a question outside the purview of logic altogether.

Why?  Appealing to a "Uniformity of God" - if this is what you are doing, is a non solution, as is any appeal to uniformity*

Let me show you why: 

The Christian "solution" to the supposed problem of logic or induction (usually this argument is used contra Induction, Presupp) usually is an appeal to revelation: "God told me (via the biblical revelation) that he promises to uphold the general uniformity and intelligibility of nature"

But, even accepting this as true for the sake of argument, this assertion does not solve the 'problem' The problem has just been pushed under the rug. Simply predicating a uniformity of nature on a Uniformity of "god" (who will purportedly uphold the uniformity of nature) does not change the problem. We can ask the same question of the presuppositonalist about the foundation for their belief in the uniformity of God as they ask about the assumption of a uniformity of nature: Leaving aside, for a moment, the insurmountable ontological problems with the 'god' term, on what non-question-begging grounds can you justify your expectation that God will keep his promise, or that God will be as he is tomorrow as he was yesterday?" You run into the same meta-problems that follow from using the uniformity of nature argument.

In addition, simply appealing to "revelation" as some form of knowledge distinct from empirical, sense-based inference doesn't work, because the "problem of induction or deduction" is one of logic and reason - not one restricted to inferences based upon materialistic sense-input. And revelation is just one more form of experience. Whether the Christian encountered God's "revealed" claims in an old book, or whether he even wishes to claim God beamed an experience of revelation right into his mind...the same question is begged: "On what grounds do you have the expectation of uniformity, that your experience of God means that God will be the same tomorrow as it was today?"

If one simply retreats to "Well, part of my presupposition is that God is immutable", then one has still failed to justify or solve the problem - one has just "presupposed" it away. You have offered no more rational justification than anyone else who holds the mere expectation that nature will remain uniform - the very expectation he says secularism supposedly fails to justify! And since the Christian's God claim does absolutely no more epistemological duty than the mere presupposition that nature is uniform, one can hardly claim it's necessity. And we all tend to (as a matter of habit) presume nature will remain uniform anyway.

I apologize if your argument uses a different engine.

How is that an answer?

What is 'god'?

And how, precisely, does 'god' ensure that modus ponens works?

Just asserting "god" does not work. You must go through the trouble of explaining how 'god' justifies modus ponens. You must show what he 'adds' that is 'missing.' I've shown you how any naturalist does it. Can you give the supernatural account?

* As Howson & Urbach point out, assuming a uniformity of nature is a nonsolution, since it's a fairly empty assumption. For how is nature uniform? And what, really, are we talking about. What would really be needed are millions upon millions of uniformity assumptions for each item under discussion. We'd need one for the melting temperature of water, of iron, of nickel, etc, etc. For example "block of ice x will melt at 0 Celsius;" for these types of assumptions actually say something. Furthermore, the uniformity of nature assumptions fall prey to meta-uniformity issues - for how are we to know that nature will always be uniform? Well, we have to assume that too. And how do we know that the uniformity of nature is uniform? Ad infinitum. So, to "solve" a problem in logicn by uniformity of nature solutions doesn't really work.  The assumption of a uniformity of nature is a necessary, but insufficient condition for justifying logic.

Todangst has answerred your objections more than handily. Your refusal to accept the answers has no bearing on their veracity. As for the below portion, what is it exactly that you think you have said?

One expects a natural thing to exhibit order.

Surely you see the problem with this unfounded assertion, especially in light of the fact that you come here questioning the basis by which one can expect anything. Doesn't that timber in your eye hurt?

Even beyond the glaring emptiness of  your 'solution, on what basis do you know 'order'? Where do you get this concept of not ordered by which you can determine that created things exhibit order?

Why? You say it does but you give no reason. How in the holy hell can anyone come into a forum questioning the means by which we can claim to know things and then simply assert that they can fix the problem with an empty and broken supernatural claim. Surely you don't think people here are stupid and gullible enough to fall for your term (god) as a soution to anything simply because you make empty claims. 

Because it's a necessary truth. (It's true in any possible world.)

Because it's defended through retortion. (Attempts to refute the axioms of existence, identity, ect. require an argument that relies on them.)

So there literally is no possible way to doubt these axioms... in fact, to doubt them is to verify them! This was the discovery of Descartes.

You present a false dilemma. No one needs to use logical argument to defend an axiom in the first place. The axiom of identity is gleaned, a priori. It is defended through retortion. One cannot use classical logic without relying upon it in the first place. One cannot reason at all without the axioms of existence and idenity being affirmed.

How can anything exist, without existing? How can anything exist without existing as something, i.e. without having identity? Unless you can answer these questions, it should be apparent to you why we can have a 'conviction' about the axioms of existence and identity! The very nature of any existent is that it exists as something, ergo existence and identity are unavoidable.

Right. Necessity. It's necessarily true. You seem to skip over this without actually considering it. If it is necessarily true, in all possible worlds, then the matter ought to be clear: this is precisely how we justify our use of axioms: we rely on them, hence they are defended through retortion. Any attempt to refute them leads to a stolen fallacy concept.

Right.

It's not a leap.... quite the contrary... its unavoidable in the case of the axioms of existence, identity and consciousness for a human. In fact, one cannot reason without them, they are part of the nature of reason!

How can you reason without existing?

How can you exist without existing as something?

How can you be aware of these axioms without being conscious?

Also, I must comment on another issue: You use the term "logic" as if all logic is the same, or that all logic relies on the same axioms, and imply that logic necessarily relies on axioms. None of this is exactly true.

Yes, Aristotelean/Syllogistic logic relies on the axiom of identity:

The Law of Identity: For things, this law asserts that "A is A" or "anything is itself." For propositions: "If a proposition is true, then it is true."

The Law of Excluded Middle: For things, "anything is either A or not A." For propositions: "A proposition, such as P, is either true or false." We also refer to such statements as "tautologies"

The Law of noncontradiction: For things: "Nothing can be both A and not-A." For propositions: "A proposition, P, can not be both true and false."

But, while reason itself relies on basic axioms, not all logics themselves require these axioms. For example, the set of axioms for the sentential, or propositional, logic is {} - the empty set!

So how does such a system "get off the ground"?

It creates a set of rules, defined within the system:

Let the set of English capital letters be well-formed formular (WFFs), which may be appended by zero to an infinite amount of primes to indicate different WFFs
If A and B are WFFs, then (A v B) is a WFF
If A and B are WFFs, then (A & B) is a WFF
If A is a WFF, then (~A) is a WFF
If A and B are WFFs, then define (A -> B) to be ((~A) v B)
If A and B are WFFs, then define (A <-> B) to be ((A -> B) & (B ->A))
No other strings are WFFs

It's not inexplicable seeing as I've explained precisely how it works!

How is it inexplicable that something that exists, exists?! Where's the mystery here? Help me out.

How is it inexplicable that something that exists, exists as something (identity) and not its antithesis?

Again, in the case of the axioms of existence, identity, consciousness, they are part of the very nature of reason. You might as well state that it's inexplicable why all squares have four sides.... Its unavoidable as its part of its nature.

How on earth is this true?!

To know anything one must have an implicit knowledge that something exists, that it exists in some fashion. That everything has a non contradictory identity. How can one even know anything unless one begins with these basic axioms? The very nature of reason itself is an actualization of the implicit awareness of these axioms. Reason itself exists and exists as something!

Can you explain how there could be reason without the axioms of existence and identity? You hold that we come to these axioms, at least implicitly, and that this is in 'defiance' with how we come to conclusions. Explain how anyone could come to any conclusion without these axioms being a basic foundation to any conclusion. How is our gleaning of the the law of identity a priori, which is implicit in every statement, in defiance of how we reach well founded conclusions?

We can't even hold that 1+1=2 without already knowing, a priori, that A=A. There is nothing about the gleaning of the law of identity that defies how we arrive at well founded conclusions. In fact, the opposite is true: it is the very basis of how we are able to come to any conclusion at all.

You presume this is a problem when it is not. Reason itself has a nature, and this nature is required in order to use logic. Axioms are a matter of pure reason - i.e. a self exploration of what reason itself is - reason itself is an existent, it has an identity, hence it is unavoidable that pure reasoning will reveal the axioms of existence and identity (and thereby, consciousness)

You keep running about looking for why this is so, and you leave out looking at the nature of reason itself: Once we exist,existence is axiomatic. Once we exist, identity is axiomatic.

As for logic...

Logic (Greek logos, "word," "speech," "reason&quot is the science that evaluates valid reasoning within arguments. That's it. Surprised? Many people think logic refers to a lot more than just that. But logic is not a set of laws that governs the universe - that's physics. Logic is not a set of laws that governs human behavior - that's psychology. Logic is no a method for 'studying the world', that's science. Logic is not the method for assessing axioms, that's a matter of pure reason. Logic is not a way of evaluating 'truth' - that's philosophy. Logic is not transcendent or immaterial - that's incoherent, as these terms have no ontological status (i.e. no positive way of identifying them.) Logic is simply a set of rules, created by sentient brains, to tell us when an argument works - when an argument supports the conclusion the arguer wants to make. In short, a logical argument will crank out a true conclusion, if we feed true premises into it! That's it!

This is simply nonsense for the two reasons I have already outlined.

You're just not paying attention at this point. You're just spitting out your presupper script.

Another false dilemma. There's no need to invoke "transcedence", and the term is incoherent to boot.

Axioms, are abstractions that exist in a brain. The reason we see the 'same axiom' in different brains (i.e. the reason they are universals) is because the same idea can be represented in mulitple copies - the same firing of neurons in my brain as someone else's (more or less), which then become emergent phenomenon such as "abstract concepts" to our consciousnesses. Similar brains working within the same, exact universe, will come to the same inescapable conclusions, if they are necessary concepts.

For more on this, see: http://www.rationalresponders.com/a_materialist_account_for_abstractions_or_how_theists_misplace_the_universe

There's no need to refer to a 'nether' world beyond our world. And, references to 'transcedence" or immateriality are incoherent:

http://www.rationalresponders.com/supernatural_and_immaterial_are_broken_concepts

Again, you simply don't grasp that axioms of existence and identity can be gleaned from pure reason because the very nature of reason itself relies on it. You can call this 'logic surpassing' as if anything 'prior' to logic must be miraculous and supernatural, but this is merely an expression of wonder born of your ignornace of how axioms are actually formed.... there's nothing miraculous about a priori reasoning... I'd simply say that all reasoning of any type requires the axioms of existence and identity, seeing as in order for anything to exist, these axioms must be part of its nature by definition!

Actually, it's impossible to build a basis for logic by appealing to the supernatural, and attempts to make logic 'transcendent' are incoherent. I'd call those 'problems.'

The reality is that all you do is assert "god did it" without exploring why this cannot work. You merely beg the question.

You've failed to respond to anything I've said. In fact, at times, you seem to simply ignore the refutations.

Again, I am also speaking prior to deductive logic, - I am speaking about the axioms that classical deductive logic rests upon.

Again I ask: how can something exist without existing? How can there be a thing without it having identity?

I can only ask: are you talking about cosmology? About physics? About why there is a universe? Because otherwise your complaints are very odd. Because once we have a brain that can reason, these axioms are necessary. So I can only assume you are asking why there are sentient brains in the first place.

Again, how can we reason without them? How can you reason without existing?

Answer that, and you'll see why these axioms are unshakeable!

The very nature of reason includes the fact that reason exists and that it exists as something. Ergo these axioms are part of the foundation of reason itself.

I will again ask you to explain how a sentient, reasoning brain can exist without existing, without the axioms of existence and identity being necessary true.

And I can tell you that any attempt to invoke a supposed higher power leads to incoherence. This is the discovery of negative theologians.

1) I already point out the problems in assuming a Uniformity of "God". I will repeat them for you below.

2) To exist is to exist, and to exist as something... hence the axioms of existence and identity are necessary whether an existent was created is entirely moot.

Appealing to a "Uniformity of God" - if this is what you are doing, is a non solution, as is any appeal to uniformity*

Let me show you why:

The Christian "solution" to the supposed problem of logic or induction (usually this argument is used contra Induction, Presupp) usually is an appeal to revelation: "God told me (via the biblical revelation) that he promises to uphold the general uniformity and intelligibility of nature"

But, even accepting this as true for the sake of argument, this assertion does not solve the 'problem' The problem has just been pushed under the rug. Simply predicating a uniformity of nature on a Uniformity of "god" (who will purportedly uphold the uniformity of nature) does not change the problem. We can ask the same question of the presuppositonalist about the foundation for their belief in the uniformity of God as they ask about the assumption of a uniformity of nature: Leaving aside, for a moment, the insurmountable ontological problems with the 'god' term, on what non-question-begging grounds can you justify your expectation that God will keep his promise, or that God will be as he is tomorrow as he was yesterday?" You run into the same meta-problems that follow from using the uniformity of nature argument.

In addition, simply appealing to "revelation" as some form of knowledge distinct from empirical, sense-based inference doesn't work, because the "problem of induction or deduction" is one of logic and reason - not one restricted to inferences based upon materialistic sense-input. And revelation is just one more form of experience. Whether the Christian encountered God's "revealed" claims in an old book, or whether he even wishes to claim God beamed an experience of revelation right into his mind...the same question is begged: "On what grounds do you have the expectation of uniformity, that your experience of God means that God will be the same tomorrow as it was today?"

If one simply retreats to "Well, part of my presupposition is that God is immutable", then one has still failed to justify or solve the problem - one has just "presupposed" it away. You have offered no more rational justification than anyone else who holds the mere expectation that nature will remain uniform - the very expectation he says secularism supposedly fails to justify! And since the Christian's God claim does absolutely no more epistemological duty than the mere presupposition that nature is uniform, one can hardly claim it's necessity. And we all tend to (as a matter of habit) presume nature will remain uniform anyway.

1) You don't explain 'how' - does 'god' just 'do it'?

2) The strength of the 'conviction' would merely be an emotional factor! It would have no bearing on the matter as emotions are moot here. What matters is that axioms such as the axiom of existence are necessary truths, that they are unavoidable, that they are part of reason and part of every statement we make, and that they are defended through retortion.

Again, until you explain how something can exist without existing, your 'dilemma' has been solved.

No, it does not.

The explanation for why axioms 'work' is given above. Emotional convictions are immaterial, and references to the supernatural are incoherent.

You've not actually given me an explanation as to how your appeal to the supernatural 'works', you've merely asserted that 'god' 'somehow' gives you a feeling of conviction. But I've demonstrated that feelings are moot, and that existence is unavoidable - given that you exist! In addition, your reference to 'god' is not only unnecessary, it's incoherent.

Precisely. 

1) I've never studied logic

2) Therefore, god did it. 

It works for anything you are ignorant of.... 

  I've never met a presuppositionalist who's actually interested in learning what logic is, or how it works.  Knowing about logic would just get in the way of being a presupper... 

And whenever you try to get a presupper to show how their appeal to supernaturalism 'justifies' logic, they simply can't answer... they merely assert that this god somehow provides a 'feeling'.

You could also ask how they know its a god providing this feeling, and again, they'd just have to assert and beg the question, because their 'argument' is entirely negative - they can't defend their position, they merely assume its true by default - it's based on their ignorance of what logic is....