Formal and Informal Logical Fallacies

Logical fallacies are important to be aware of when engaging in persuasive speaking or debate, either in listening or delivering. I think the main reason to be aware of them is to better understand rationality itself, to understand which points follow and fail to follow from others, or to become more clear about which points being contested actually need to be contested, or else revised, in order to have a desired conclusion, or to know which positions are in dire need of supporting reasons or justification, without which they should be rejected, since no one should believe anything without justification or reasons to do so.

Logical fallacies are of two types: formal and informal. A formal fallacy is really a mistake about deduction, or of supposing that a conclusion follows from some premises, when it does not. A conclusion follows from a set of premises if and only if the conclusion cannot be false if the premises are true. So a formal fallacy is one that involves supposing that the conclusion is true because a set of premises are true, when the conclusion does not have to be true, even if the premises are true. Put briefly, a formal fallacy involves selling an argument as deductive when it is in fact not. Making sure an argument is deductive is a way, among other things, of getting clear about which premises are really at stake or that should be debated or supported, in order to have the desired conclusion. This is why if an argument is really committing a formal fallacy, then there can be an issue about which statements should even be debated. I will give two examples of formal fallacies after covering an informal ones, since it will provide an example of a deductive argument.

An informal fallacy, on the other hand, has nothing to do with whether or not the argument is deductive. Rather, it has to do with a lack of reasons or justification. Take, for example, an appeal to authority. Suppose an inquiring mind wants to know why it’s not always safe to fly a kite with a metal key at the end of it in a thunderstorm. Suppose I answer, “because Benjamin Franklin said so”, and leave it at that. Now, translating ‘because’ logically is perhaps not always straightforward, but here, it would seem to imply the truth conditions of the if-then statement: If Benjamin Franklin says “it’s not always safe to fly a kite with a metal key at the end of it in a thunderstorm” then it’s not always safe to fly a kite with a metal key at the end of it in a thunderstorm. And he said so, so we get the conclusion that it is so. Translated thus, it is clearly a deductive argument (viz. modus ponens), but it is a fallacy in an explanatory or justificatory sense, since it is not explained how Benjamin Franklin’s saying this is so makes it so, and the claim appears to completely lack justification.

Now, if I explained that Benjamin Franklin had all sorts of experience with electricity, and found out much about it that was not safe regarding flying kites in thunderstorms, this would be a different story, one that may have not just a bit of justification, but a whole lot. More straightforwardly, I would likely best give a reason for not flying said kite in said storm not by bringing up anything that anybody said, but by explaining how a lot of electricity going through one’s body makes one prone to death or ill health, and that holding said kite in said storm is prone to give one a lot of electricity. Informal fallacies often involve giving false explanations, for containing reasons that are unjustified. Additionally, such reasons are easily subject to either counterexamples (e.g. coming up with one thing the person appealed to said that is not true), or to counter reasons that are obviously true (e.g. that talk is cheap: saying something does not make it so).

One formal fallacy that I think is common amongst fallacies of everyday life is called affirming the consequent. This occurs when we say that one fact follows from another, and we claim that other fact is true, so we conclude that the one fact must be true. For example, suppose that if I drop an apple, it falls on the ground. Someone knows this, finds an apple on the ground, and then claims to know that I dropped it. Yet clearly I didn’t have to be the one to cause its dropping to the ground. My dropping apples on the ground, no matter how frequently I do so, would say nothing about all the other ways that are sufficient for apples to fall to the ground that do not include me at all. Such a fallacy is a formal one, having to do with making a deduction that is not permitted, since the premises can be true while the conclusion false. If capital letters denote a statement (an utterance or sentence that is either true or false, and not both), then the form of affirming the consequent is: suppose that If A, then B; B; therefore, A. Yet this is simply not how the truth value of the statement “If A, then B and B” works. The statement can be true (i.e all of its components can be true) and yet A be false. To explain in other terms, take ‘If A, then B’ to mean that A is enough or is sufficient for B. It is saying what follows from the presence of A. Yet it says nothing at all about what follows from the presence of B. So on adding B to the mix, we cannot say that A follows. Something else undiscussed may have granted B without A. thus, affirming the consequent is always invalid. However, this does not mean that the conclusion is false. I may have dropped that apple after all. It’s rather that the argument made to support this fact is invalid, and so on its own is no reason to grant the conclusion.

Now, I want to caution: some who love to write about logical fallacies are sometimes prone to spot one behind every utterance resembling a consideration that proceeds from some thought or other. This is not always charitable to the thinker. For a clear example, suppose that the streets are wet. A great conclusion to draw is that it has rained, and this is despite the fact that its raining does not deductively follow from the streets being wet (I suppose that it’s raining does not entail that the streets are wet either; perhaps they are covered up–yet we could amend it to refer to uncovered streets, and include that these streets are indeed uncovered. As a further aside, if you enjoy thinking about whether or not causal relations have a sort of necessary connection akin to deduction, I made a post on this here). We can draw this conclusion because we often consider happenings in terms of probabilities. If you’ve never experienced the streets as being this wet by anything other than rain, and have frequently experienced such an occurrence, and it is that wet now, then there is just no reason to suppose that it is so other than because it has rained. This is perfectly logical thinking. Alternatively, the conclusion could be reached logically in a way that does not have to involve probabilities at all. This point is pertinent to the philosophy of cognition. It could rather be thought that the wet streets that are experienced just preclude its being wet by any other means. That is, it is considered that these streets, so situated and in this vicinity, would not be the wet streets they are now without its having rained. If this accurately reflects the thought, then this is indeed a sort of deduction on our part, for if we are mistaken about rain being the cause here, then we were mistaken about which sort of street this was, or in how it was situated. That we do seem to be mistaken about this as well would indicate that we indeed think deductively about such matters. However, this is not to reject that we nonetheless also think probabilistically. For example, perhaps I see the possibility that a fire plane dumped a bunch of water on my street by mistake, and that nonetheless this has a low probability of occurring, with rain having the highest probability.

This surprisingly leads me to the final fallacy I will cover, one that can occur often enough amongst academics. In the above, I argued that we think about events deductively as well as probabilistically. A few sincerely bright individuals would have an issue with this proposition along the following invalid lines. They would say something like: we either think deductively about a given topic, or we think probabilistically about it. We think probabilistically (or deductively as the case may be). Therefore, we do not think deductively (or probabilistically as the case may be). This is a formal fallacy called affirming the disjunct. In logical notation, it says A or B; A (or B); therefore, not B (or not A). Yet, logically, A or B, if meant as a binary logical connective, is so in the inclusive sense (see my post on the exclusive OR for some issues related to making it a binary connective, here). If it is meant in the exclusive sense, however, then we could simply add the implicit premise of not A or not B (again, this ‘or’ is meant inclusively, but an interpretation where both disjuncts are true would be inconsistent with the premise A or B). This would patch it up into a valid argument as far as a logical translation goes, yet the speaker may not have brought up such a proposition at all as not A or not B.

If not A or not B is supposed to just be obviously true, then we arrive at an interesting feature of this fallacy. If it is a fallacy, it is now an informal rather than formal one. To illustrate, we now understand that the point of contention will be centered around debating the merits of our new premise not A or not B. Going on the above example, we would focus on the proposition that our thinking about a topic is either not probabilistic or it is not deductive. Yet it is clear, for all that has been said by our sincerely bright individual, that nothing has been brought up for thinking why it is either not one or not the other. Indeed, I just gave a pretty good line of reasoning for supposing that the proposition is false! Thus, if we were to have a reasoned debate on this, and my opponent just leaves his words at the above argument, then s/he has made the informal fallacy of providing no reason or justification for the required premise in question, and, furthermore, for providing no rebuttal to my reasons against it. This would indeed be an informal logical fallacy. The informal version of affirming the disjunct is called giving a false dichotomy. This is when someone presents two statements as being mutually exclusive when there is no reasons provided for why they are mutually exclusive, or when there are apparent or explicit lines of reasoning that indicate they are not mutually exclusive.

Unfortunately, I think examples of false dichotomies in philosophy are never too difficult to find. Some examples I feel like I must have read somewhere include, but are not limited to:

*Everything is possible; therefore, nothing is necessary.

*Space is relative; therefore, space is not absolute.

*Truth is relative (e.g. to a statement, attitude); therefore, truth is not absolute.

*Money is money because of our attitudes or beliefs; therefore, money is not made up of attitude-less or belief-less matter.

*Perception of external objects involves external objects; therefore, perception of external objects does not involve anything that’s in the head.

*Account A accounts for fact B; therefore account C does not account for B.

Note: In these, I have left the “or statement” implicit, since it usually is not explicitly stated. So, that everything is either necessary or possible would be an implicit premise of the first example, and similarly for the rest.

Some of these conclusions might be true, but showing that they are would need to involve more than presenting an affirmation of one disjunct. As it stands, the disjuncts do not have to be viewed as being in complete opposition to each other, and so the conclusion amounts to no more than a mere assertion without reason or justification. On the other hand, if it meant to be deductive, it is not so at all, and anyone should reject the conclusion on the grounds of being invalid from the premise.


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