On Logical Fallacies

Do you not recognize that you’re using a logical fallacy, or do you not care?

It’s a question I’ve asked many people lately, typically those who are anti-vaccine, anti-GMO, or pro pseudoscience in general. This is not to imply that sceptics are immune to logical fallacies; many use them just as often as the overly credulous do. I even catch myself using them from time to time.

This article will detail what a logical fallacy is and why they are bad arguments.

What is a logical fallacy?

A Logical Fallacy is an error in logic. It occurs either when the logical structure of the argument is invalid, or when the structure is sound but one or more premises are false. The first type of fallacy is called Formal, the second is called Informal.

Before going further it is important to define some terms. The first is Formal. A formal argument is one that is deductive, meaning that one can deduce the conclusion of the argument from the premise(s). In other words the conclusion necessarily follows from the premise(s). An example of this would be:

Premise 1: All men are mortal
Premise 2: Socrates is a man
Conclusion: Socrates is mortal

This is contrasted with informal or inductive argument which the conclusion likely, but not necessarily, follows from the premise. A third type of reasoning is abductive reasoning in which the premises do not guarantee the conclusion, but rather help form a working theory or “best guess”.

A formal argument can either be valid or invalid. Likewise a valid argument can either be sound or unsound.

A valid argument is one that has the correct structure, typically in the form of one or more premises and a conclusion. The conclusion must necessarily follow from the premises.

A sound argument is one that contains both the correct structure and true premise(s).

We should strive for arguments that are both valid (correct form) and sound (correct premise(s)) because if this is the case, the argument must by definition lead to a true conclusion.

Logical Fallacies take many forms. There are formal fallacies, which are always wrong because the argument is invalid. An informal fallacy has the correct form (i.e. is valid) but either the premise or arguments are unsound. Lastly, there are conditional fallacies, which are only fallacies on the condition that one or more of the premises are wrong and is accepted to be true.

Formal Fallacies

Formal fallacies are always wrong. This is because, as described above, the form of the argument is invalid. An example would be:

P1: Some men are named Socrates
P2: Socrates has a beard
C: Therefore all men have beards

As you can see, both P1 and P2 are true, but they do not necessarily lead you to the conclusion that all men have beards. A more concrete example is the Base Rate Fallacy:

P1: African Americans are more likely to commit murder
P2: That man is African American
C: That man is likely to commit murder

In this instance both P1 and P2 are true, but the conclusion doesn’t follow because the individual ignored the base rate of African American Criminality. Although African Americans do have higher rates of criminality than other ethnic groups, that rate is less than 0.01% higher.¹⁾Based off of the FBI’s Unified Crime Report for 2011: out of 42 Million African Americans, 4149 committed murders, with a rate of 0.0099% Because the base rate is so low, he cannot conclude that any single African American is likely to commit a crime.

Informal Fallacies

Unlike Formal Fallacies, Informal Fallacies do not contain errors in logic per se (in other words their form is valid) but rather one or more of the premises are false. For example:

P1: All cats are mammals
P2: All mammals are plants
C: All cats are plants

In this instance, P1 is correct, and the conclusion may have been correct if P2 were correct. Changing “plants” to “animals” would correct the argument and it would no longer be a fallacy.

Informal fallacies tend to be more common than formal fallacies, mainly because individuals may not be aware that one or more of their premises are false. One common example is the Shill Gambit:

P1: Kevin Folta claims that GMOs are safe
P2: Kevin Folta is a paid shill of Monsanto
C: GMOs are not safe

In this instance, Kevin Folta is not a paid shill of Monsanto. In fact, the Shill Gambit borders on being a Formal fallacy because even if an individual is a paid employee of an industry does not necessarily mean that he or she is lying about an industry’s product.

Another informal fallacy is the Appeal to Nature:

P1: This substance is natural
P2: Natural substances are beneficial
C: This substance is healthy

or alternately:

P1: This substance is not natural
P2: Unnatural substances are not healthy
C: This substance is not healthy

An easy refutation to the Appeal to Nature is this: arsenic is natural. Antibiotics are not natural. In both of these instances P2 is incorrect as not all natural substances are healthy, with the inverse being true about unnatural substances.

Another common Informal Fallacy is the Correlation Fallacy, also known as the False Cause fallacy or Post Hoc, Ergo, Propter Hoc (after this, therefore, because of this):

P1: This child was vaccinated shortly before he was diagnosed with Autism
P2 (usually unstated): Something that happens shortly before something else must necessarily have caused it
C: Vaccines cause Autism

In this instance we see that P2 is typically unstated for a reason: it is obviously false that a prior event necessarily causes a following event. Changing the terms of the argument renders this:

P1: This rooster crowed shortly before the sun rose
P2 (usually unstated): Something that happens shortly before something else must necessarily have caused it
C: The rooster crowing cause the sun to rise

obviously fallacious argument. There is no evidence (based on this argument) that the rooster crowing actually causes the sun to rise. Likewise, there is no evidence (based on this argument) that vaccines cause autism. In order to infer causation, one must design a rigorous, controlled scientific study.

Another popular Informal Fallacy is an Appeal to Emotion. This takes many forms, usually something like this:

P1: X is scary.
P2: (unstated) Scary things are bad.
C: X is bad.

Once again, P2 is where the error lies, as not all scary things are necessarily bad.

Conditional Fallacies

A Conditional Fallacy is related to the Informal Fallacy in that the logic is (usually) valid, and the fallacy lies in the premises. In this instance, the fallacy depends on the condition where one or more of the premises are accepted.

Not all instances of conditional logic is necessarily fallacious. For example, the Appeal to Authority (and Argument from Popularity):

P1: 97% of climate scientists agree that Climate Change is man-made.
P2: Something that is agreed to exist by over 97% of climatologists is probably true.
C: Climate Change is probably man-made

Although it is true that something is not necessarily true just because an authority states it to be so, the likelihood of it being true increases with the legitimacy of the authority. An example of when this is a fallacy is:

P1: This blogger states that GMOs are harmful
P2: This blogger is an authority on GMOs
C: GMOs are harmful

In this instance it would be false to accept P2 because someone who is a blogger is not necessarily an authority on GMOs. This does not mean that someone who is a crop scientist and a blogger would not be an authority.

Another version of this fallacy is:

P1: These 300 mothers state that vaccines cause SIDS
P2: Mothers authorities in their children
C: Vaccines cause SIDS

In this instance P2 is wrong because although mothers do have the most amount of knowledge about their individual child (all things being equal) they are not medical nor scientific authorities. In addition, the number of mothers has no bearing on how true the mothers’ opinions are.

Fallacious Rhetoric

Lastly, we come to situations where individuals use fallacious rhetoric, in addition to one or more actual fallacies, to distort or discredit their opponent. This comes in several forms. Although the logic in these instances may, or may not, be sound, they are still fallacious for one or more reasons.

One such example is the Straw Man, which follows this format:

P1: X (their argument) is Y (the strawmanned argument).
P2: Y (the strawmanned argument) is false.
C: X (their argument) is false.

Although re-stating someone’s opinion in order to make it easier to understand is a valid and acceptable form of rhetoric, when an individual mis-states what their opponent said (either intentionally or unintentionally) this is a fallacious Argument. In this instance P2 is correct, yet P1 is incorrect because of the misrepresentation of the argument, therefore the conclusion is false.

Another example of this is the Galileo Gambit:

P1: Galileo was ridiculed
P2: Galileo was correct
P3: I am being ridiculed
C: I am correct

In this instance, Galileo was not correct because he was ridiculed, and nothing about being ridiculed indicates the fact that you are correct. Another version of this argument can be summed up as:

When you get close to the truth is when they start to attack you

Which may or may not be true, depending on who “they” are. However, Galileo was correct because he had the evidence to back up his claims. In this instance the conclusion does not follow from P1, P2, and P3 and is therefore a formal fallacy, although some versions of the Galileo Gambit are Informal Fallacies.

Lastly, we come to Non-Sequiturs and Red Herrings. Non-Sequiturs are Formal Fallacies and are often blatantly ridiculous. These are typically used by trolls or individuals wishing to shape the discussion away from a certain topic. An example would be:

P1: You are a woman
C: Therefore you are wrong

Here the non-sequitur (in the form of an Ad Hominem) is obvious (and blatantly sexist). A more subtle example would be this:

Topic 1: Vaccines Cause Autism
Topic 2: Vaccines are manufactured by Big Pharma
Topic 2a: Big pharma is evil

In this instance the conversation has been switched from the Vaccine/Autism link to the evils of Big Pharma. Although possibly related, if one can find evidence that both Big Pharma is evil and that their evilness has something to do with the Vaccine/Autism link, it does not add anything to the discussion. If vaccines cause autism (they don’t) it could easily be a mistake perpetrated by a benevolent, yet incompetent, pharmaceutical manufacturer.

Conclusion

These examples provide a brief description of some poor arguments and the reasons why these are poor. These are not poor arguments just because someone states so, but rather because of the errors in logic which I hope have been described appropriately here. Hopefully, individuals will strive to form better, more logically valid (and sound) arguments on both sides of the debate.

Media Credit

The featured image for this article is Socrates BM by Marie-Lan Nguyen. It is licensed under the Creative Commons Attribution 2.5 Generic license.