If one is truly Catholic, there is only one way to present the truths of faith; one way to discuss and dispute points of doctrine with others and to prove the truths of faith. That way was laid out long ago by St. Thomas Aquinas. Pope Leo XIII champions it here as the only method of demonstration to be used in defending Catholic truth.

" The knowledge and exercise of this science of salvation have certainly always brought the very greatest help to the Church; whether it be for the right understanding and interpretation of Scripture, or for reading and expounding the Fathers with greater safety and profit, or for laying bare and answering different errors and heresies. This doctrine flows from the brimming fountain of the Sacred Scriptures, of the Supreme Pontiffs, and of Holy Fathers and Councils. Now indeed, in these last days, it is in the highest degree necessary to refute heresies and confirm the dogmas of the Catholic Faith. For now have come those dangerous times of which the Apostle speaks. Now men, blasphemous, proud, deceivers, go from bad to worse, wandering from the truth themselves and leading others into error…Scholastic Theology, [Pope Sixtus V] tells us, 'has an apt coherence of facts and causes, connected with one another; an order and arrangement, like soldiers, drawn up in battle array; definitions and distinctions very lucid; unaswerableness of argument and acute disputations. By these the light is divided from the darkness, and truth from falsehood. The wiles of heretics, wrapped up in many wiles and fallacies, being stripped of their coverings, are bared and laid open.' But these great and wondrous gifts can only be found in a right use of that philosophy which the masters of Scholasticism, of set purpose and with wise counsel, were everywhere accustomed to use even in their theological disputations…

" There are many, who with minds alienated from the Faith, hate all Catholic teaching, and say that reason alone is their teacher and guide. To heal these men of their unbelief, and to bring them to grace and the Catholic Faith, We think that nothing, after the supernatural help of God, can be more useful in these days than the solid doctrine of the fathers and the Scholastics. They teach firm foundations of Faith, its Divine origin, its certain truth, the arguments by which it is commended to men, the benefits that it has conferred on the human race, and its perfect harmony with reason. They teach all such truths with a weight of evidence and a force that may well persuade even minds unwilling and hostile in the highest degree." PRAY GOD IT IS SO!

Below please find fallacies of argument taken from Logic, by Rev. Joseph Walsh, S.J., 1940. Logic is a science that supplies us with the rules that govern scholastic philosophy. We have done our very best here to follow these rules. For no science or art can be said to be true if its rules are disobeyed. Unfortunately others do not seem to hold these rules in high esteem. Below we will demonstrate how these rules have been violated.

I. Fallacies in diction
A. Equivocation: Using the same word(s) in different senses within the same argument.
B. Amphiboly: A sentence or phrase whose structure makes its meaning ambiguous.
Example: See Pre-election Heresy
C. Composition: Taking collectively what should be taken separately.
D. Division: taking separately what should be taken collectively.
E. Accent: When two similar words are confused by wrong accentuation, or when a wrong meaning is given to a sentence by stressing the wrong words, (in verbal argument only — Walsh).

II. Fallacies extra dictionem
A. Accident or A Dicto Simpliciter ad Dictum Secundem: Assuming that what is true generally is true in every circumstance, when circumstances alter the case.
Example: Circumstances do alter the case. We're talking here of a layman elected Pope by lay people with no hierarchy present to ordain and consecrate the one elected. We are also talking about an unprecedented crisis in the Church on an unimaginable scale, with obstacles never or rarely anticipated by those of the past.
B. A Dicto Seundum quid ad dictum simpliciter or Special case: Concluding what is true in a certain restricted case or cases is true generally.
C. Ignoratio Elenchi: Missing the point, arguing beside the point, evading the issue, proving the wrong conclusion.
Example: Bawden has employed all these methods, arguing every point but the one in question. He simply denies that he has promoted the heresy of lay investiture and refuses to discuss it.
1. Appeal to the populace by arousing passions and prejudices.
Example: This is what Bawden has done or attempted in this case by approaching this author's family members and followers who are long time acquaintances.
2. Appeal to the venerated positions of those holding the same opinions.
Example: Bawden's remaining followers keep appealing to him as a valid authority.
3. An appeal to the ignorance of the hearers, tricking them by statements they are unable to test.
Example: Scarcely less than the Traditionalists, Bawden's remaining lay followers suffer from ignorance in doctrinal matters and must rely on his interpretation in matters of faith. Pray God that in most cases their ignorance is invincible and not culpable, yet affected ignorance (wishing to remain uninformed because of the trouble it would entail to inform oneself) cannot be confused with truly invincible ignorance. No right-minded Catholic would fail to investigate the entirety of those truths of faith necessary to salvation — especially where heresy is concerned — on the off chance he could plead invincible ignorance at his private judgment. Thus Pope St. Pius X, and Pope Benedict XIV before him rightly taught: "We declare that the greater part of those who are damned have brought the calamity on themselves by ignorance of the mysteries of the faith, which they should have known and believed, in order to be united with the elect."
4. Argumentation ad miseracordium, or an appeal for sympathy.
Example: From all appearances, this argument also has been used.
5. Argumentation ad hominem, including personal attack, abusive language, ridicule of an adversary, charges of inconsistency.
Example: Despite the almost continual pleas over the years for charity to neighbor issued by Bawden, this is the approach of choice, practically to the exclusion of all else. Most of these written communications have been in way of personal correspondence and correspondence to followers, some who have now departed. All the elements above can be found in these attacks.
6. Argumentation ad balculum: appeal to physical force by threats…
Example: Veiled threats by others and promises of "formal excommunication" by Bawden himself have been employed, but no physical violence has been implied.
7. Petitio principii or begging the question: Assuming as true that which has yet to be proved, (that he is truly pope).
Example: Bawden completely ignores the fact that he has advanced absolutely no reasonable arguments or believable proofs that he is innocent of heresy, and hence is a true Pope. He reverts instead to insistence on obedience and submission to the "Roman Pontiff" in this matter when questioned, completing the vicious circle.
8. Consequent: An ill-constructed syllogistic demonstration resulting in a false conclusion.
9. False cause: reducing a proposition to an absurd consequence.
Example: Bawden claims that any baptized male without exception can be elected Pope by the laity, in the protracted absence of the hierarchy. He insists that such men could be ordained and consecrated without receiving the Minor Orders, which involve extensive investigation and examination. Without this examination the following consequences or any combination of these consequences could result:
a) A teenager could be elected Pope;
b) a practicing homosexual or child molester could be elected Pope;
c) a lapsed Catholic could be elected Pope;
d) a drug addict could be elected Pope;
e) any convicted (Catholic) felon on parole could be elected Pope;
f) one of borderline intelligence could be elected Pope;
g) one with debilitating medical problems could be elected Pope.
Four of the above could not exercise the office properly or at all, given the absence of hierarchy, effectively leaving the Church as She was — without a functioning head. The other four would likely bring disrepute or scandal to the papacy and the Church.
10.Post hoc, ergo propter hoc: Attributing an effect not to its true cause, but to something antecedent in time.
11. Many questions: So phrasing a question that to answer either way will affirm or deny something the one asking doesn't wish to confirm or deny.
12. False analogy: When an argument is drawn from another subject which only in appearance resembles the subject in question.
Example: Bawden's two cases of Bishops elected while still catechumens. Under St. Ambrose, the Catholic Encyclopedia explains that it was a custom in the early ages of the Church to delay baptism indefinitely, long after the catechumen was well versed in the faith and ready to be baptized. The inference here is that neither of these bishops was especially distinguished in any way, when already Ambrose was esteemed for his great holiness and learning. Also, neither of these cases refer specifically to one elected Pope.

If one can demonstrate that at least an attempt has been made to follow the rules of Scholastic philosophy, then certain conclusions can be drawn from this. For an opponent who cannot follow the rules of scholastic philosophy most likely does not possess the proofs necessary to establish a defense. As the rule of law goes, facts are not presumed; they must be demonstrated. Here we have readily demonstrated the facts not from merely probable sources, but from unimpeachable sources. These infallible sources themselves cannot be questioned, as Rev. J. C. Fenton explained in his work Sacred Theology. "Since the certitude of theology is from divine knowledge, it cannot be explained merely in function of the syllogistic process by which its conclusions are derived…Theological demonstration is a complex process, and the theological conclusion is not extrinsic to the body of actually revealed doctrine…The meaning of divine revelation, as it is proposed in the infallible magisterium of the Church, is so clear that demonstrations directed toward bringing out that meaning can possess a superior certitude…It was precisely the certitude of sacred theology that led to the unmasking of the various heresies which have appeared during the course of Christian history." This is why, as Can. 1827, tells us, "He who has a presumption of law in his favor is freed from the burden of proof which is then shifted to his opponent. If the latter cannot prove that the presumption failed,…the judge must render sentence in favor of the one on whose side the presumption stands."