Formal vs Informal Fallacy and Their Abuse
One can only truly understand how a formal fallacy is qualified, by understanding the relationship between first order logic and formal theory construction. This allows the philosopher to examine flaws which might serve to negate propositions because of a failure of formal theory. These are called formal fallacies. Informal ‘fallacy’ on the other hand – is an ignominious title ascribed to every bit of circumstantial critique which falls outside of this class of fatal proposition error – or might be boasted as inappropriate basis for an attempt at refutation.
Formal fallacies are fatal to their associated proposition, but in no way serve to prove nor disprove any purported truth. Informal ‘fallacies’ most of the time are abused by those pretending to cite something fatal to the argument at hand. Such is rarely the case; ironically demonstrating a formal fallacy of its own in the offing.
First Order Logic – Predicate Calculus
In First Order Logic, one entity possesses an effect resulting in another entity or entity state via a principle or a mechanism; or simply by means of an observed relationship if the principle or mechanism is not clearly defined or understood. This relationship between one individual entity and another is called a condition of Predicate Calculus. An apple, released from its tree branch, will fall to the earth. I do not have to identify nor understand the M-theory mechanism(s) which cause this, rather just simply observe it to be (consistent) true. This order of reason is known commonly in philosophical prior art as the modus ponens or ‘If P then Q’ proposition. (1 Rosen)
/philosophy : argument : formal structure/ : the necessity that an argument follow a form of claim such that its soundness and formal structure can be followed by others. A discipline featuring the formal structure ‘If P then Q‘ premise in its expression such that claims may not be slipped by surreptitiously inside a condition of poor scientific method, fallacy or little or no actual study or supporting fact whatsoever.
I have made an effort to demonstrate the simple and elegant nature of Predicate Calculus below, in term of cracker crumbs (Q) and cracker eating (P). Please note that in the context of Predicate Calculus, for the sake of parsimony and reduction clarity and/or value, ‘crumbs’ is excluded necessarily – as it is an entity class – and entity classes serve to violate the singular nature of a Predicate Calculus. Whereas ‘cracker crumbs’ and cracker eating are individual entities. Always bear in mind that we, in order to avoid the ambiguity or organic untruth practiced inside social skepticism, are restricted to an individual entity in First Order Logic and typically want to avoid propositions involving unqualified entity classes (see Discerning Sound from Questionable Science Publication). (1 Rosen)
Eating Crackers Seems to Always Produce Cracker Crumbs (modus ponens)
Example of modus ponens discipline usefulness in detecting deception ambiguity or organic untruth:
Ambiguous Statement “There is no evidence for this claim”
Proposition form Q
modus ponens version “[specific studies completed showed] there is no evidence for this claim”
Proposition form [If P then] Q
Claim validity Not Sound – premises are assumed or are incorrect
Formal Theory = Predicate Calculus + Logical Calculus
Predicate Calculus as we have seen, establishes the relationship between two individual entities. This type of parsimonious proposition usually stems from an empirical observation set. Newton is credited with formulation of the theory of gravity, through his observing of an apple falling from an apple tree. Hence definition of the “If two massive bodies, then attractive acceleration by formula of characteristic mass and distance” (If P then Q) proposition by observation. (2 Newton) Note that the principle or mechanism which creates the relationship, or even the characteristic mathematics of such a relationship, if either or both are known, is called the Logical Calculus. (1 Rosen) Below we have depicted both a Predicate Calculus and a Logical Calculus packaged into what is commonly known as The Formal Theory of Gravity:
Apples and gravity are salient to arguments about force and acceleration (salience)
An apple, released from its tree branch, will fall (accelerate) to the earth. (modus ponens)
Objects accelerating are consistent in context and mathematical mechanism to physical action of gravity (sequitur)
If two massive bodies, then attractive acceleration by formula of characteristic mass and distance, given by the following (3 Wikipedia):
note: the above represents an observation proof through straightforward replication and mathematical confirmation. Most arguments are not so easily resolved. Other types of logical calculus might involve mathematical derivation, or assembly of arrival distributions, premises, constraints, logical relationships and mechanisms which justify a proposed conclusion.
So when we as professors of philosophy have stepped beyond a condition of Predicate Calculus and developed a proposition which explains such Predicate Calculus, ie. the Logical Calculus, we have the basis of what is called Formal Theory. When we screw up the calculus, salience or sequitur which is crafted to make such a proposition, this is called a Formal Fallacy.
Formal and Informal Fallacy
Skepticism therefore, is not a process by which one decides consensus or falsification outcomes (science), rather it is a process of identifying when the predicate calculus or logical calculus has been abrogated inside a claim to truth (proposition). For instance, were Newton to cite that
- Object A and B attract each other.
- Men and women are objects.
- Therefore men and women are attracted to each other.
This proposition would feature three formal fallacies: 1) affirming the consequent, 2) entity class characterization by single entity and 3) two equivocal substitutions of logical entities (Masked Man fallacy. Please note that employment of equivocation in order to accomplish a substitution of equivalents, is a formal fallacy, despite the fact that equivocation itself is an informal fallacy of ambiguity. In this context, equivocation is not employed inside a context of solely ambiguity). The distinguishing formal factor here is that each flaw is FATAL to the critical path logical calculus of the argument itself. The conclusion just happens to accidentally also be true, but its logical critical path is invalid. Accordingly, the answer or ‘truth’ versus ‘untruth’ entailed as the conclusion of a formal fallacy, still may or may not be correct, regardless of the status of the proposition under examination. This serves to elucidate what should be going on in the mind of the ethical skeptic:
Our job as skeptics therefore is not to probe truth itself, nor to pretend to step in and act in lieu of science; rather, our job is to bear vigilance inside the processes by which we arrive at scientifically derived truths. A skeptic who enforces uncertain truth at face value, or by appeal to fallacy (fallacy fallacy), or does so by means of surreptitious advocacy (rhetoric), or by means an inverse negation (informal fallacy), is not a skeptic at all – rather an agenda bearer. This is best discerned in how the supposed ‘skeptic’ deals with an ability to suspend judgement as to what is held as truth – regardless of a particular proposition’s state – or what is called epoché.
A formal fallacy therefore is the singular state wherein, a skeptic can indeed declare a proposition to be in error by means of its predicate (modus ponens), sequitur or logical construction. This does not mean that the truth attempting to be sought is wrong – simply that the means employed to getting there is fatally flawed inside its own structure (the orange box in the graphic above). An argument from fallacy, or fallacy fallacy, would be an instance wherein a faking skeptic employs either a formal, or even more a general critique or informal fallacy, to declare a subject or truth to be therefore, false. Also know as an ‘appeal to fallacy’, such an error in predicate calculus is also itself, a formal fallacy.
Appeal to Fallacy (Fallacy Fallacy)
/philosophy : argument : formal fallacy : pseudo-invalidation/ : when an arguer employs either a formal, or even more an informal fallacy, to stand as the basis to declare a subject or claimed truth to be therefore, false. A formal fallacy or redress on the basis of soundness or induction inference, only serves to invalidate an opponent’s argument structure. All three flaws serve to tender nothing about the verity of the argument’s conclusion, which may or may not be independently also true. As well, any instance wherein a circumstantial, expression, personal or informal critique or other informal fallacy is inappropriately cited as a mechanism to invalidate an opponent’s argument or stand as basis for dismissal of a subject.
An unsophisticated arguer’s flawed attempts for instance, to justify the nearby-Earth existence of aliens, does not serve to justify a position therefore that aliens do not exist nearby Earth. Only science can validate/invalidate such an argument – and not an armchair philosopher. That is why I do not delve into the subject of nearby-Earth aliens often. As an ethical skeptic I possess scant information on nearby aliens with which to work. I cannot make any comment on the matter – save to observe the chicanery of the religious certainty on both sides of the construct (belief on the part of UFO fanatics and null hypothesis abuse on the part of those seeking UFO denial). I have been in every single continent on this Earth except for Antarctica, and almost every one of its deserts and jungles, save for a few I still have on my bucket list. There are rather astounding mysteries to be found. Why people have such an emotional investment on such an issue, with scant investment in their own research, is beyond me. But I digress…
“A fallacy is, very generally, an error in reasoning. This differs from a factual error, which is simply being wrong about the facts. To be more specific, a fallacy is an “argument” in which the premises given for the conclusion do not provide the needed degree of support.” (Michael Labossiere, philosophy professor, Florida A&M)
“However, not just any type of mistake in reasoning counts as a logical fallacy. To be a fallacy, a type of reasoning must be potentially deceptive, it must be likely to fool at least some of the people some of the time. Moreover, in order for a fallacy to be worth identifying and naming, it must be a common type of logical error.” (Gary Curtis, author, The Fallacy Files)
/philosophy : predicate or logical calculus : paralogism/ : a violation of any rule of formal inference —called also paralogism. Any common flaw in the sequitur nature of premise to conclusion, logical or predicate structure which could be cited as the fatal basis of a refutation regarding a given proposition or argument.
The proposition that is formally fallacious is always considered wrong. However, the question in view is not whether its conclusion is true or false, but whether the form of the proposition supporting its conclusion is valid or invalid, and if its premises provide for logical connection into the argument (i.e. sequitur context, and not the validity per se of the premises themselves, which pertains to salience and soundness). The argument may agree in its conclusion with an eventual truth only by accident. What gives unity to different fallacies inside this view is not their characteristic dialogue structure, rather the nature of integrity inside the concepts of deduction and (non-inductive) proof upon which the proposition is critically founded. (4 Hansen, SEOP) (5 Wikipedia)
One thing to be made clear here is the issue of soundness and premises. The soundness of an argument relates to the validity of its premises. However, the linkages in sequitur logic which make the premises salient to the argument, do pertain to formal fallacy. Many fallacy definitions miss this distinction – that the salience or sequitur nature of a premise does not solely relate to the issue of soundness. It is part of the Predicate Calculus as well. The graphic above helps me differentiate between informal fallacy soundness (yellow box) and formal logic (orange box) and circumstantial informal critique (grey box).
This circumstantial informal critique category in the graphic above, introduces an even weaker from of counter argument, perhaps even more appropriately cited as a ‘criticism’ or ‘disputation’ involving a focus on informal ‘fallacies’. An informal fallacy does not serve to fatally invalidate an argument, rather only cast suspicion onto the nature of its expression.
/philosophy : proposition expression : flaws/ : flaws in the expression, features, intent or dialogue structure of a proposition or series of propositions. Any criticism of an argument by means of other than structure (formal) flaws; most often when the contents of an argument’s stated premises fail to adequately support its proposed conclusion (soundness), or serious errors in foundational facts are presented.
An informal fallacy is really anything else which is circumstantially wrong with an argument, which does not relate to its predicate, salient, sequitur or logical construction. For instance, relevance is an informal fallacy (ad hominem or an appeal to skepticism as examples of irrelevant informal ‘fallacies’). When the contents of an argument’s stated premises fail to adequately support its proposed conclusion – this relates to the soundness of the argument. It has nothing to do with the logical calculus or predicate modus ponens (the yellow box in the graphic above). Nor in reality, is citing a lack of soundness a form of informal critique. It rises to a position of equal significance with both factual error and error in structure. This certainly a much more important feature set than say, an ad hominem ‘fallacy’.
The Ethical Skepticism Alternative
However, in philosophical circles, this raises the question as to whether or not ‘informal fallacies’, aside from issues of argument soundness, are even fallacies at all – or simply an attempt to promote the perception of technicalities into the appearance of invalidating an argument (by conflating anything and everything to involve the soundness or logic of the argument), which they do not indeed invalidate. This is a common magician’s trick of social skepticism.
One exception exists however in the form of the informal fallacy of ‘lacking soundness’. Soundness is the condition wherein supporting assumptions solidly underpin the validity of an argument’s logical calculus, and not the strength of the logical calculus itself. Therefore, a lack of soundness, despite not being regarded a formal fallacy of logic, is fatal to an argument just as is a formal fallacy (not fatal however to its conclusion necessarily). So soundness is an all important first step in the evaluation of an argument’s strength, despite its existence as an informal fallacy.
Moreover, if we hold this as one bookend of deception, the false employment of formal and informal fallacy, on the other end of deception is the use of purported ‘facts’ inside a science which is unsound, logically a failure, and provides no inductive strength. Facts in this situation are useless. They are mere tidbits of propaganda which happen to be correct, but their domain of induction extends very little. The fact spinner will never relate this weakness and imply the contention that fact ≡ science. This is nowhere near the case. Most of science revolves around a principal called plenary condition.
/philosophy : scientific method : inductive and deductive strength : completeness/ : a conclusion of science or a method of science which is fully researched, complete in alternative address, entire in its domain of necessity-based research, absolute in its determinations and unqualified by agenda, special pleading or conditions. A conclusion which is complete in every reasonable avenue of examination; fully vetted or constituted by all entitled to conduct such review/research. This plenary entitled group to include the sponsors who raised Ockham’s Razor necessity in the first place, as well as those stakeholders who will be directly placed at risk by such a conclusion or research avenue’s ramifications.
Therefore, we see that the simply playground of ‘fallacy and fact’ is not sufficient basis from which to determine sound scientific conclusion. Instead, I carry in mind a framework of argument theory, involving a hierarchy of the five primary argument issues in descending order of importance, which is prioritized like this
/philosophy : argument strength : evaluation heirarchy/ : the formal and informal methods of evaluating the robust, weak or fatal nature of argument validity.
1. Coherency – argument is expressed with elements, relationships, context, syntax and language which conveys actual probative information
2. Soundness – premises support or fail to adequately support its proposed conclusion
3. Formal Theory – strength and continuity of predicate and logical calculus (basis of formal fallacy)
4. Inductive Strength – sufficiency of completeness and exacting inference which can be drawn
5. Factualness – validity of information elements comprised by the argument or premises
6. Informal Strength – informal critique of expression, intent or circumstantial features
Articles 1 through 3 above are often potentially fatal to an argument, while article 2 is the only Formal Fallacy concerned item. Articles 4 and 5 may only serve to weaken an argument or its propositions. However, articles 4 and 5 may also be used as pretense and distraction.
This is why fake skeptics scream so often about ‘facts’, ‘evidence’ and (informal) ‘fallacies’, because
- Facts constitute a relatively weak form inference as compared to soundness, predicate and logical deduction; offering a playground of slack and deception/diversion in the process of boasting about argument strength or lack thereof, and
- Most faking skeptics do not grasp principles of soundness, predicate and logical calculus, nor the role of induction inference in the first place. ‘Facts’ are the first rung on the hierarchy which they possess the mental bandwidth to understand and debate.
- A deductive falsification finishes its argument at the Soundness and Formal Theory levels of strength assessment. It is conclusive regardless of circumstantial informal issues. These are rendered moot precisely because falsification has been attained. Faking skeptics seek to distract from the core modus ponens of a falsification argument by pulling it down into the mud of circumstantial ‘facts’ instead; relying upon the reality that most people cannot discern falsification from inference.
- Informal ‘fallacies’ sound like crushing intellectual blows in an argument, when in fact most of the time they are not. These are tool of those who seek to win at all costs, even if upon an apparent technicality. An arguer who possesses genuine concern about the subject, is not distracted by irrelevant or partially salient technicality.
- Provided that articles 1 through 4 are sound, observation is always stronger than philosophy. This includes instances of accusation of anecdote, once an Ockham’s Razor necessity is established. Fake skeptics hold this relationship in reverse, and in the resulting promotion of article 5 above its normal importance, conduct pseudoscience.
It is not that facts and evidence are not important, rather it is the critical modus ponens in how they are employed, which is salient (see The Tower of Wrong). So the philosopher must be careful about how such mechanisms as informal critique and facts are employed. It is usually ethical to maintain discipline around your formal and informal critiques of an opponent’s argument. Point out fatal flaws – but only ask questions concerning informal fallacies and facts, because they may be immaterial to the issue at hand. In the end, either technique is employed so as to help the opponent become more clear (and hopefully valuable) in their argument, and not as a means of destroying and bashing a person, nor an attempt to make one’s self appear to be ‘smart’.
Such motives are not indicative of a concern over the subject at all, rather simply an ego which is out of control (an informal ‘fallacy’).
1. Rosen, Stanley; The Philosopher’s Handbook: Essential Readings from Plato to Kant, Random House Reference, New York, April 2003; pp. 581 – 589.
2. Newton, Sir Isaac; Mathematic Principles of Natural Philosophy (The Principia); Propositions: Proposition 6, Theorem 6; London, 12 Jan 1725.
3. Wikipedia: Newton’s law of universal gravitation; https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation.
4. Hansen, Hans, “Fallacies”, The Stanford Encyclopedia of Philosophy (Summer 2015 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/sum2015/entries/fallacies/>.
5. Wikipedia: Formal Fallacy; https://en.wikipedia.org/wiki/Formal_fallacy.
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