If you have read any of my posts, you will recognize my sign off, “question everything.” This post is meant as both a caveat and an attempt to run that sign off through a line of inquiry.
What do I mean by question everything? Basically, I mean to have an inquisitive mind and method of doubt prior to acceptance. The main inspiration for this method is the concept that humans are fallible – we can be wrong. More than that, we can be wrong and believe ourselves to be right. We can go out with beliefs that are in fact false and propagate them, all the while thinking that we are spreading the truth. Without a method of doubt we might believe anything we hear- including concepts that are incompatible/contradictory.
For an example of contradictory beliefs, consider a racist. I do not believe it beyond doubt that a racist could believe the claims that i) all Atlanteans look alike, and ii) some Atlanteans are distinguishable visually (or that there is some exception to the rule). These claims are contradictory because one (i) is a universal affirmative, while the other, (ii) is a particular negation. Essentially, the truth of one implies the falsehood of another. If one single Atlantean is visually distinguishable, then it cannot be the case that all Atlanteans are visually indistinguishable.
The way that these two statements interact, the relationship between the universal affirmative and the particular negation, is part of a field I understand as quantificational logic. This field of study is concerned with the relationship between: existence, properties, and classification; truth about claims of either in relationship to the other; and the implications of those claims.
I digress. It has been some time since I have discussed logic and I find the subject interesting. Not in the least because there is something happening here that appeals to my inquisitive nature – some security.
How so? The universal affirmative always implies the falsehood of the particular negation. While the truth of the claims themselves must be established, once that truth is held we can move on to other truths via assumption. The logic is so tight that if we had two apparent truths on a universal affirmative and a particular negation, it is not the relationship between the claims that would be called into question, but rather the held truths. It is not possible for all x to be n and for one x not to be n. We arrive at this by virtue of the system of logic.
I spoke of semantic truths in my last post, and I believe that the universal affirmative plays a large role in these truths. For you see, when we use language to label something we often also are classifying alongside that label. Of course all triangles have three sides. The name triangle is a product of the form of the polygon – there are three angles. Logically it follows that each angle is a connection of one of the sides, therefore triangles have three sides. It is not possible to conceive of a triangle with more or less than three sides because you have already assigned yourself that quality when you limited yourself to triangle.
Logical relationships and connectives are the building blocks of understanding how things are, in large part because of the stability of the system. It is that stability, however, that may lead to a false sense of security. While the inferences that logic justify us to make are powerful methods of establishing truth, argument, and persuasion (after all, logic is a warrant that holds across understandings), the number of form of inference is finite; there are only so many ways logic works justifiably. There are, however, conceivably infinite possibilities for how to maneuver logic to justify claims.
Logical fallacies involve making inferences that are not dictated by logical implications yet present themselves in very much the same way that logic does. Consider the following two syllogisms: (a) If it is raining, then the ground will be wet. It is raining. Therefore, the ground is wet. (b) If it is raining, then the ground will be wet. It is not raining. Therefore, the ground is not wet. (a) is referred to as Modus Ponens, a logical implication of the function of a conditional statement. (b) is a logical fallacy known as negating the antecedent, and it is dubious. While the conditional claim “if it is raining, the ground will be wet” always guarantees that should the antecedent (if it is raining) hold true, then the consequent (the ground will be wet) will also be true, the negation of that antecedent (it is not raining) does not have any implication on the consequent.
The thing is, though, we may observe an instance where the ground is not wet and it is not raining. As a matter of fact, the logical implication Modus Tollens guarantees us that if the ground is not wet, then it is not raining (assuming the conditional is true). What is not guaranteed, however, is the negation of the antecedent negating the consequent. The absence of rain has no effect on the wetness of the ground, as there are other factors that can impact that.
Negating the antecedent is just an example of an appealing logical fallacy. Any logician could identify this fallacy and several others because of the finite number of valid inferences. Someone less steeped in the language of logic, however, might be easily confused by the nuances the field has. This post alone might confuse people and have them looking for negative antecedents in hopes of spotting fallacies, but antecedents themselves can be negatives, so a negation results in a positive.
I realize now (and actually a couple of paragraphs ago) that I’m likely talking either above or below the head in hopes of giving examples. This is a difficult subject to present to an audience who may not have any formal study in the area. Unfortunately, that difficulty is a positive for those that would abuse logic and level logical fallacies.
Logic offers a way to justify propositions in relation to each other and to make inferences that are guaranteed pending the truth of the components. It helps us understand relationships in the external world, helps us categorize and distinguish, but it is not without reasons for concern.
While we might be able to get away with relying on logic it is imperative that we understand the logic upon which we rely. No, there will never be a triangle with less than or more than three sides. Questioning the matter will not change that possibility. What will arise out of that question, however, is why you can never have a triangle with more than or less than three sides. Likewise, questioning the viability of an inference will not change the viability of that inference. It may, however, help us understand the viability of that inference, how it functions (and does not), and what other implications those relationships might have.
In other words, while we might not get what we usually do out of questions, namely answers, when we question logic, we can arrive at an understanding and appreciation. That understanding will help us identify instances where the system is being abused or not upheld. Those questions have outcomes, even if the topic itself is beyond question.
So, as always,
question everything.
-SS
Post-Publication Addition:
Thanks for reading through this. Discussing such heavy matters is difficult, especially without determined organization. I hope you came away with a healthy amount of inquiry about logical systems and fallacies.
What are some logical fallacies you typically encounter?
How do you go about engaging someone who is attempting to use a fallacy to appeal to you?
Which fallacy do you find yourself drawn to in discourse? (mine, in all honesty, is slippery slope)
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