Let’s start with two of the basic premises you stated that they belong to homeopathy, namely the law of infinitesimals and the law of chronic diseases. First, you wrote, "The second law, the law of infinitesimals, says that as you dilute the substance it becomes more potent—in direct violation of the very real laws of physics and chemistry,"(2) as well as, "I want the public to be aware of the fact that most homeopathic solutions are diluted far past the point where there is likely to be a single molecule of active ingredient left—and therefore claims for the homeopathic ‘law of infinitesimals’ violates the law of mass action and the laws of thermodynamics."(3)

Now let’s turn to the official definition of genuine homeopathy and its fundamental principles. Forgive me for this very long definition that Hahnemann wrote in the preface of the last edition of his Organon but it is the most complete and most unequivocal one: "Hence homeopathy avoids everything in the slightest degree enfeebling,* and as much as possible every excitation of pain, for pain also diminishes the strength, and hence it employs for the cure ONLY those medicines whose power for altering and deranging (dynamically) the health it knows accurately, and from these it selects one whose pathogenetic power (its medicinal disease) is capable of removing the natural disease in question by similarity (similia similibus), and this it administers to the patient in simple form, but in rare and minute doses so small that, without occasioning pain or weakening, they just suffice to remove the natural malady whence this result: that without weakening, injuring or torturing him in the very least, the natural disease is extinguished, and the patient, even whilst he is getting better, gains in strength and thus is cured—an apparently easy but actually troublesome and difficult business, and one requiring much thought, but which restores the patient without suffering in a short time to perfect health,—and thus it is a salutary and blessed business.

"Thus homeopathy is a perfectly simple system of medicine, remaining always fixed in its principles as in its practice, which, like the doctrine whereon it is based, if rightly apprehended will be found to be complete (and therefore serviceable). What is clearly pure in doctrine and practice should be self-evident, and all backward sliding to the pernicious routinism of the old school that is as much its antithesis as night is to day, should cease to vaunt itself with the honorable name of homeopathy."(4)

You will notice that in this detailed definition, Hahnemann answers the question that you asked me during the debate regarding the use of compounded(5) versus "accurately" known, simple medicines, and that such a practice, as well any other form of practice that don’t abide to the just-cited fundamental principles "should cease to vaunt itself with the honorable name of homeopathy." However, you will not find in this definition of homeopathy and its fundamental principles, or in any other of Hahnemann’s works or writings, any reference to a law of infinitesimals or a law of chronic diseases that you mentioned during the debate.

Returning to what you have written, "in order for an argument to be sound all of its premises be true," and given that these two basic premises you claimed for homeopathy unequivocally don’t exist or apply to genuine homeopathy, and are therefore false, aren’t all their subsequent arguments unsound or completely false, such as " ‘the law of infinitesimals’ violates the law of mass action and the laws of thermodynamics" and "the very real laws of physics and chemistry"?

As a responsible man of science, what steps are you going to take to correct these gross and completely unscientific misrepresentations of the fundamental aspects of homeopathy and any of their subsequent logical fallacies, which you have repeated for many years in numerous articles and presentations, and that can currently be found on numerous websites(6)? Also can you precisely describe what laws of chemistry or physics, homeopathy violates, if any at all, once these two completely fabricated laws of homeopathy are eliminated from the equation?

(1) Steven Novella. How to argue. Neurologicablog. March 19, 2009
(2) Steven Novella. Homeopathy at the Huffpo. Skepticblog. Oct. 19, 2009.
(3) Steven Novella. Quietus and homeopathy awareness week. Neurologicablog. April 13, 2010.
* Homeopathy sheds not a drop of blood, administers no emetics, purgatives, laxatives or diaphoretics, drives off no external affection by external means, prescribes no hot or unknown mineral baths or medicated clysters, applies no Spanish flies or mustard plasters, no setons, no issues, excites no ptyalism, burns not with moxa or red-hot iron to the very bone, and so forth, but gives with its own hand its own preparations of simple uncompounded medicines, which it is accurately acquainted with, never subdues pain by opium, etc. (4) Samuel Hahnemann. Organon of Medicine. Sixth edition. Translated by William Boericke. Philadelphia: Boericke and Tafel, 1922: 18-19.
(5) Unproved compounded medicines or combination remedies sold under the name of homeopathy are clearly not part of homeopathy. However, they could be sold under the name of homeotherapeutics.
(6) Such as theness.com/neurologicablog, skeptico.blogs.com, sciencebasedmedicine.org, skepticblog.org, randi.org, csicop.org, friendofreason.wordpress.com, illuminutti.com, lippard.blogspot.ca, trusted.md, lizditz.typepad.com, startleddisbelief.com, skepdic.com, skepticalteacher.wordpress.com, etc.

Dr. Novella’s Response: 
I find the claim that Samuel Hahnemann did not endorse a "law of infinitesimals" to be misleading in many respects.

First, it is a "No True Scotsman" logical fallacy – arguing that examples of infinitesimals within homeopathy do not demonstrate that homeopathy follows such rules, because such examples are a-priori "not true homeopathy."

The undeniable fact is, that homeopathy, as it is widely practiced today, including the many homeopathic products sold on the market, do follow the basic concept that ingredients are diluted to extreme degree. While the exact extent of dilution varies considerably, very common dilutions include those that exceed the point at which any original ingredient is likely to remain.

I further find it either an example of intellectual dishonesty or extremely poor and selective scholarship to claim that Hahnemann did not endorse extreme dilutions. He may not have written the words "law of infinitesimals" himself, but he certainly endorsed the principles that are captured in that phrase.

A review of his writings (http://www.homeoint.org/books4/bradford/chapter83.htm) documents quite thoroughly that Hahnemann began with a belief in using the smallest dose possible in order to treat a patient, but that this belief evolved over his career until he was recommending extreme dilutions (what would now be called 30C, or 1/100 dilutions repeated 30 times).

From the Organon fifth edition he writes:

That sounds pretty clear to me – you can dilute something without limit, and the more you dilute it the greater the effect. Is that not the law of infinitesimals as it is understood today?

Here he specifically endorses 30C as a common dilution (again from Organon fifth edition).

Further, Hahnemann clearly supported the notion that homeopathic remedies worked through their "spiritual" power.

In the "Spirit of the Homoeopathic Doctrine," published in 1813, he says :

This next section is from a letter in which Hahnemann was defending himself from critics, published in Samuel Hahnemann, His Life and Work, page 116.

That seems pretty clear too. The "infinitesimal size of the dose" contain "nothing" and cannot be detected by "chemical analysis," and yet has its effect because of his new art of healing – the peculiar choice of remedy.

Regarding Hahnemann’s theory of disease, his own quotes again clearly make the case that he was using his own peculiar theory of illness. From The Life and Letters of Dr Samuel Hahnemann Chapter 13:

I maintain that the historical record, and well as modern implementation, support the following premises:

• Homeopathy is based upon the notion that solutions can be diluted beyond the point that any active ingredient remains, while retaining (and even enhancing) its potency.
• Effectiveness of remedies is not based upon any scientific notion (chemical or biological) but rather on the notion of the spiritual action of preparations which contain the essence of what was diluted in them.
• Shaking preparations transfers essence and adds potency
• Effectiveness of homeopathic remedies are based upon the peculiar and completely unscientific notions of similar
• Hahnemann based much of his thinking on peculiar notions of chronic illness (psora) that are completely unscientific.

There are many more examples in the references I gave, and in many more. The samples I provide, however, clearly establish the points I outline above.

In short – Hahnemann absolutely endorsed the principles captured in the phrase "law of infinitesimals" and these principles remain the core of modern homeopathy. All further criticism that derives from this premise is both valid and sound.