Philosophical Naturalism is logically self-refuting

Definition: 

Determinism, a theory or doctrine that acts of the will, occurrences in nature, or social or psychological phenomena are causally determined by preceding events or natural laws

A self-refuting idea or self-defeating idea is an idea or statement whose falsehood is a logical consequence of the act or situation of holding them to be true.

Examples: 

1) Truth cannot be known (If so, then how does one know this truth claim?)

2) Language cannot carry meaning  (If language cannot carry meaning, then what about this claim? Is it meaningful?)

3) Science is the only way to determine truth, or I only trust things I can determine through a scientific process  (Can science determine if that statement [about science] is true or what scientific experiment provided that conclusion for you?)

The problem:

Justification [the action of showing something to be right or reasonable] requires some kind of "cognitive freedom" - you need to have control over your deliberations, over what you do [or don't accept] on the basis of evidence, reason, However, determinism [the belief that all actions and events result from other actions [i.e not you - so people cannot in fact choose what to do] makes this freedom impossible. 

Therefore, the person who argues for determinism, or is tempted to accept it, is in a weird position: their conclusion apparently undermines the very reasoning process they're using to justify it.

The Argument:

Philosophical Naturalism is the belief that nature is all that exists, and that all things supernatural (including gods, spirits, souls and non-natural values) therefore do not exist. It is sometimes called Metaphysical Naturalism or Ontological Naturalism to distinguish it from Methodological Naturalism. Philosophical Naturalism entails physical determinism

Methodological Naturalism is the assumption of philosophical naturalism when working with the scientific method. Methodological naturalists limit their scientific research to the study of natural/physical causes for all events and phenomenon. From Rationalwiki - An online rationalist skeptical resource with is decidedly anti-religious, anti-theistic bent.

Michael Ruse an atheist and Philosopher of science in The Oxford Handbook of Atheism writes "It is usual to distinguish between "methodological naturalism" and "metaphysical naturalism" whereby the latter we need a complex denial of the supernatural - including atheism as understood in the context of this publication - and by the former a conscious decision to act in inquiry and understanding, especially scientific inquiry and understanding as if metaphysical naturalism were true. The intention is not to assume that metaphysical naturalism is true, but to act as if it were.  [p383]

That's methodological naturalism - assuming naturalism is true, or acting as if it were, in one's methodology.

Philosophical Naturalism holds that any mental properties that exist are causally derived from, and ontologically dependent on, systems of non-mental properties, powers or things (i.e. all minds, and all the contents and powers and effects of minds, are entirely constructed from or caused by natural phenomena). 

Philosophical Naturalism entails physical determinism - all events are physically determined, including human thoughts. 

To do science one must only presume that the universe is orderly, i.e. disposed in some order or pattern, or governed by law.

1) Reason is the basis for all knowledge, since all epistemological theories or methods must employ it.

2) Every truth claim requires the laws of logic. It is impossible to deny the laws of logic without using them. Thus, logic reason, and critical thinking are an aspect of reality. In fact, everyone is using logic in this discussion, so it seems evident that all believe that logic is an aspect of reality.

3) All debates presuppose a reality that exists. Each debater is trying to show that their claims are closer to that reality or are best explained by that reality.

4) Critical thinking's definition is contested, but the competing definitions can be understood as differing conceptions of the same basic concept: careful thinking directed to a goal. [source] Critical thinking is purposeful, reasoned, and goal-directed; an intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action.

5) Under Philosophical Naturalism all actions, including human thoughts, words and deeds, are the result of matter which must act in accordance with antecedent physical conditions and the physical laws without exceptions.

6) 4 above is incoherent under Philosophical Naturalism; logic, reason, and critical thinking are an aspect of reality that cannot be explained via Philosophical Naturalism, since no one has dominion over their thoughts - i.e. no one makes any molecule act in a manner inconsistent with the physical laws, as they must act only in accordance to the physical laws Note: Just saw this vid where William Lane Craig agrees with this point

7) The best explanation for the existence of logic is that there is an aspect of reality that is free from the constraints of the physical; i.e. not being caused to do something by causes other than oneself. It is up to me how I choose, and nothing determines my choice. One's decisions are differentiated from natural events by being done by the agent himself for reasons the agent has in mind.

J. P. Moreland in his book, “Scaling the Secular City: A Defense of Christianity" offers a perfect summary: “Physicalism cannot be offered as a rational theory because physicalism does away with the necessary preconditions for there to be such a thing as rationality.” If a naturalist wants to argue that rationality does not exist, they will be making two grave errors: 1- They would be claiming to be non-rational, and 2- they would be making a rational argument that rationality does not exist. It seems the rational decision one ought to come to is that naturalism is irrational, and therefore, false.

In Daniel O. Dhalstrom's Heidegger's concept of truth the author writes: There is, for example, a metaphysical sense of naturalism that Husserl deems self-refuting: the theoretical pretense that everything - including, preeminently, ideas and consciousness - is part of "nature", conceived as the ensemble of empirical facts governed by laws uncovered by natural science....The claim is self-refuting and a pretense because it cannot justify itself; 

Conclusion: Philosophical Naturalism is not simply less likely to be correct, it is logically self-refuting and is necessarily false since it cannot account for reason - careful, purposeful, intellectually disciplined, goal directed thinking as a guide to belief and action. Under PN every thought action is physically determined. Thus, the existence of logic is best explained in a reality where more than the physical exists - something that is not bound by physical restraints - which allows one the freedom of not being caused to do something by causes other than oneself.

As Haldane once said, “It seems to me immensely unlikely that mind is a mere by-product of matter. For if my mental processes are determined wholly by the motions of atoms in my brain I have no reason to suppose that my beliefs are true. They may be sound chemically, but that does not make them sound logically. And hence I have no reason for supposing my brain to be composed of atoms.”

Either “reason” is merely an illusion of physics—in which case there is no justification for relying on it to produce truthful beliefs—or “reason” is something more than physical—in which case naturalism is false. If human reason is driven by mindless particle interactions, it does not necessarily correspond to truth. If we believe reason corresponds to truth, we cannot also believe reason is determined purely by physical means.

No belief is rationally inferred if it can be fully explained in terms of non-rational causes.

Objection A: We live in a natural world. There is no supernatural. Deal with it

Reply: Yes, we live in a natural world, that's not the question. Which is, is reality encompassed by just the natural world?  Given the above argument, that's not likely. 

Objection B: Naturalism is not a presumption. Its induction. If you have only ever seen white swans, and you have to guess what color the next swan you see will be, the best guess is white.

Reply: How does this show that only the physical exists? 

Objection C: this argument does not sufficiently demonstrate that philosophical naturalism is self refuting. So it still stands.

Reply: This is an assertion. It can be, and should be, lopped off with Hitchens's razor: what can be asserted without evidence can also be dismissed without evidence. If you have an argument, please provide it. 

Objection D: Quantum Mechanics shows that the world/universe that is just physical isn't necessarily deterministic

Reply: While that is true, it hardly solves the problem of grounding rational, logical, goal-oriented thoughts in a physical world where there are only determined thoughts or random thoughts.