How People Think Their False Ideas Are True

How People Think Their False Ideas Are True

This is the complete Appendix from Everything You Believe Is Wrong.

Brace Yourself

The Two Ways Arguments Go Wrong

At this point, I am hoping the reader does a little work. It is not strictly necessary, but to be complete we should investigate the nature of arguments, what they’re like in essence, before we can say why one is good and another is bad. The mental labor required is not much, but it is not nothing, either. It looks much more complicated than it is, especially on a first reading. You can leave this section now and come back to it when needed. But if you plow through it first, your rewards will be greater.

Two broad forms of error in arguments can be identified. They are these: (1) the argument itself is flawed, or (2) a reason why a flaw might but does not exist in a sound argument is itself taken for a flaw in the argument. The second form sounds confusing, but in its class are perfectly valid arguments that are dismissed because they are not grasped, they are distasteful, they are offered by the unliked, or for other similar reasons. You’ve heard versions of this mistake hundreds of times. One example: “Don’t listen to him, he’s an bigot”, where our man being bigot is irrelevant to the soundness of his argument.

Bad Genes

This mistake is formally called the Genetic Fallacy—but I like the tag Suspicion Fallacy better. This has its own Chapter. You might hear it used by critics of this book who assert that the arguments in this book do not have to be addressed because its author is a bad person. It is comforting to know that anybody who uses the Suspicion Fallacy has admitted logical defeat—though they may well win the political battle.

Given that an argument is flawed, and thus a fallacy, the origin of its fallacy can arise in only one of two ways. Let’s look at them.

Here is a simple argument: “There are fewer than four apples here; therefore there are fewer than five apples here.” All arguments fit the framework, or schema, “P therefore C”, where P are the list of premises assumed or implied, meaning they are there but not necessarily stated or even actively thought of, and C is the conclusion, or proposition of interest. The conclusion is said to flow or be deducible or to be derived from the premises P. Here, P = “There are fewer than four apples here”, and C = “There are fewer than five apples here.”

Given this P, or assuming P is true, then it is necessarily true that the conclusion C is true. C is deduced from P. There are several unstated premises here, too; they are tacit and understood by all. One is that 4<5; another, which is always—as in always—present, is the grammar and definition of the words used. These implied premises, though tacit, are never trivial: many fallacies are committed by misunderstanding or misapplying grammar and word definitions. We’ll meet several examples.

I apologize, but I can’t let this go so easily. I want to say one more time that the words and grammar are tacit premises of each and every and all arguments, from now to eternity. Forgetting this leads to tears, recriminations, and the gnashing of teeth.

Logical Links

In fallacies, the premises themselves may be flawed in some way or are not appropriate. The connection between the premises and conclusion can also be corrupted. Conclusions themselves are propositions which contain the main items of interest. We almost always start with conclusions (the propositions of interest), because we desire or suspect them to be true, and then work backward toward the premises which we believe prove the conclusion.

This is an acceptable strategy, but there are pitfalls. If the desired conclusion cannot be proved true by the premises we offer, it must be that the premises are in error or that connections between premises P and conclusion C are at fault. The connections are the sinew, the logical cords which tie the Ps to the Cs; the map from P to C, if you will. This sinew might have snapped or was never connected, and the map starting from P may lead into a dark forest and not to C.

The connection in our simple apple example was the reason that because some number was less than 4, that same number must also be less than 5. We write symbols for the P and C, and of course for numbers, but we don’t do this for our ordinary reasoning process. There are no symbols to show how we mentally grasp connections, though we can draw symbols for the connections. The connection we make between P and C is every time a real mental leap; it lets us “see” in this case that if x<4 then necessarily x<5. See is used in an analogical sense. The work takes place in our intellects.


Why speak of these complexities? Because if somebody cannot see the progression of P to C, there is nothing we can do about it to make him see. The mental leap is never a small thing; without it, no argument works. Not one. Not ever. Logicians and philosophers invent symbols for these leaps, as I said. But they are only that: symbols for mental processes we may not fully understand.

All symbols are only shorthand for deeper thought, a fact that can be forgotten when, through constant use of symbols, the symbols seem to come alive. When this happens, the Deadly Sin of Reification (a fallacy) is committed. We will meet this sin later in the book.

Syllogisms are excellent teaching tools, though not all arguments are syllogisms. Take the old standby, (written in shorthand) P = “All men are mortal and Socrates is a man” and the C = “Socrates is mortal.” We have to move intellectually from P to C. This step, this leap, is not explicit. It has to be undertaken inside the mind.

How does it work? We first understand there are many unstated but implied premises inside P and C. Knowledge of the definition of the (here, English) words and grammar, as above, count for most of these tacit premises. We then see—or don’t see—how to get from here to there. Logical blindness is not uncommon. Is it really obvious that everything that is “in” P implies C? Or can it be taught systematically to unthinking machines?

Toughen Up

Let’s make this harder. Keep the same P (“All men…”) but adopt a new C: “Socrates like red cloaks”. Now it might be true that Socrates likes, or liked, red cloaks, but we can’t get from our “All men are mortal…” to this conclusion. The tissue doesn’t connect, even though P is itself true. There is, to repeat, nothing wrong with the premises, which are true. It is the connection that is broken here—which is something else that has to be seen (that broken link). The seeing process cannot be proved: it is implicit. Because P is true, however, it follows that true premises do not guarantee true conclusions (derived from P). Keep this in mind when arguing with an opponent.

Even better advice is to keep the following in mind: any conclusion or proposition by itself has no need of any argument to be true. Any conclusion is true or false on its own.

This point is of the utmost importance. We do not create the truth or falsity of any conclusion or premise because of our arguments. A conclusion (which is always a proposition) is true or is false because that is The Way Things Are. The world is built that way. Our knowledge of whether a conclusion is true or false is an entirely different affair from whether the conclusion is true or false. Our thoughts do not make Truth. Arguments, therefore, are purely epistemological, matters only of our judgment, and do not have existence. Arguments have no causal power. (This is why they are rarely convincing.)

Local Versus Universal Truths

In The Neighborhood

We have to also guard against arguments that prove conclusions to be only “locally” true. If there is any subtle point that will be missed in this book, it will be here. By a local truth, I mean one that follows from the accepted premises, but where the premises are themselves limited or flawed. The sometime goal of a local-truth argument is to fake what is false as true.

Local truths are different from universal or necessary truths. A universal or necessary truth is one which is true no matter what, true regardless of what anybody believes, true with complete indifference to anybody’s feelings or desires or party membership. The proposition “4<5” is a necessary truth (accepting as tacit premises about the meaning of the symbols). Given the essence of nature of man, so is the proposition “All men are mortal.”

We always aim for universal or necessary truths, but we all too often miss. Often when we argue over complex propositions, it is often one side has in mind a local truth and the other a necessary truth. The battle is not wrong versus right, per se, but right versus right. The problem is that most local truths are fallacies, considered against universal or necessary truths. But because they are truths of a sort they are appealing and even mesmerizing.

Based Frogs

Example: If we accept or believe that P = “On Tuesdays, frogs can sing in French, and today is Tuesday”, then it is locally true that C = “Frogs can sing in French.” But the premises are absurd, so it is not universally true Frogs can sing in French. Even if, as the Brits say, the French are Frogs, thanks to equivocation.

Here’s the reason for pestering you with this distinction. It is always possible to discover, or to create, an argument which proves any conclusion to be locally true. That brutal truth, coupled with our boundless desire to be right, is why so many people believe false things.

Another example. I want to believe C = “My enemy George should get it in the neck”, which is my proposition of interest. I next conjure some evidence, such as P = “All bad persons should get it in the neck and George is a bad person”. My conclusion is then locally true given or assuming these premises. But the conclusion is not universally, necessarily true. There is nothing in the universe which necessitates that my enemy George must get it in the neck. Here the premises are obviously universally false. So there is no way for the conclusion to be universally true.

Going In Circles

A permanent standby for generating local truths is this: P = “C”. In other words, the conclusion is just a restatement or rewording of the premises, and where the rewording is taken as justified. Given this P, for any C we like, C is always locally true! This is the so-called circular argument.

How do we know C is true? Because C is true! You might enjoy thinking this sort of mistake is too crass to be made by our betters. Alas, it is all too frequent. We’ll meet one version of this later, which takes P = “The poor have less money than the rich” to C = “The poor will pay proportionately more for this service or good.” This fallacy is a variant of the infamous headline “World Ends: Politically Favored Victim Group Hardest Hit.”

Humble Contingency

Let’s return to C = “George should get it in the neck”. This kind of conclusion, like most of our common judgments of everyday affairs, is of the sort that cannot be necessarily true or false, and must always depend on shifting premises. This kind of conclusion is therefore called contingent, indicating its impermanence.

Mistakes in contingency are caused by bad reporting, misstated data, lack of education, and so forth. Somebody might rely in some argument on a premise about the murder rate for white perpetrators in a certain year, and be mistaken. Or somebody might claim, as some people do claim, that the man Jesus, around whom a well known religion formed, never existed. Simple errors in fact are contingent errors. These are low errors, yet brutally frequent, but they will not interest us much here. Any argument found to contain such errors should be easy to discredit, and usually is, except when the Meta Fallacy strikes. If somebody is relying on the premise “It rained last Tuesday”, which is false in fact, it suffices to show it is was dry. There is no point for us to dwell on factual errors on these kinds. We’re going after more glorious glitches in thought.

Likewise, we will not tackle political or aesthetic arguments per se. Thus C = “Ty Cobb was the greatest baseball player”, which, while it is surely true, is not capable of absolute proof, nor is it a question of any great fascination. The same holds for propositions like C = “We should decrease the tax rate by x%”. Good arguments exist on either side, but the uncertainty in which premises to accept is far too great to arrive at a definitive answer. These arguments often mix up whether or not a argument is good or bad and what will happen were a certain course to be taken, as in the Harm Fallacy. Decisions are not arguments, so they will not detain us.

Seeking Necessary Truths

The type of arguments, and conclusions, of interest to us are not (for the most part) contingent. Instead we shall speak about conclusions that can in principle be shown to be necessarily true or false. Examples of such conclusions are C = “To murder is always wrong”, C = “God exists”, C = “Women have a right to do what they like with their bodies”, C = “He is on the wrong side of history”, and so on.

Some of these might have contingent premises that qualify the conclusions—a woman surely has the right to peel potatoes in the manner she prefers, but she does not have the right to kill for the sake of convenience—but in general it is possible, at least in principle, to find strictly true premises from which we can prove these kinds of conclusions necessarily true or false.

This is why the distinction above between local and universal or necessary truths was made. Again, there is always a set of premises P that makes any conclusion C locally true. Take C = “Global cooling will kill us all by 2004. No: 2010. No: 2014. No: 2025”. This is a contingent matter because there is nothing in the universe which makes this conclusion necessarily true or false. We can find a P to make it locally true, such as P = “This is 2021, man is a cancer on planet earth, and man causes deadly global-cooling-of-doom that will kill us all within four years”. Given this P, C is locally true. But, despite claims you may have heard, nobody knows a P which makes C necessarily true.

None can exist, either, because C is contingent. Besides, we can find other P that make C locally false, such as P = “Predictions of man-caused environmental apocalypse have always been wrong” (P is thus far observationally true, but is itself not necessarily true).

Universal Necessity

There certainly are universal or necessary truths. Example: C = “The length of the long side is 5”, assuming P = “Here is a right triangle with two short sides having lengths 3 and 4.” Given this P, this C is necessarily true, meaning it is true no matter what, meaning it is true even if you don’t want it to be. Many necessary truths are in our age undesirable.

As above, there are a welter of tacit premises inside thus Pythagorean P, a miles-long string of prior deductions, that come along for the ride. Mathematicians are keenly aware of these hidden premises in statements like this. In other areas, like morality, even the best of us make mistakes.

A frequent one is equivocation, where a word or term, in the tacit or even the active premises, has double (or more) meanings, with its meaning unanchored because of a missing premise which says this and not that meaning. My all-time favorite joke relies on an equivocation of this type. Two cannibals are eating a clown, and one says to the other, “Does this taste funny to you?”

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  1. “The mental leap is never a small thing; without it, no argument works.”

    I love this one:
    “There are two types of people in the world. Those who can extrapolate from incomplete data.”

    I have it on the wall outside my classroom. No student has ever asked me about it. 🙂

  2. brad tittle

    THis may be off topic, but I think it is at least adjacent. I am listening to “The Real Anthony Fauci”. Suddenly they hit MMR vaccines and the toxicity of the mercury. They had me fully onboard, but then I got triggered.

    Jenny McCarthy Body Count wants to be scientific about how anti-vaxxers are killing people. But the CDC isn’t nice enough to provide the vaccination status of people when they get things. Before we go accusing anti-vaxxers of being anti-science, I prefer to keep my feet solidly in the science. That forces me to ask… “how many of those people who got sick with pertussis, were vaccinated against pertussis?” If I don’t see that answer in the science, I start questioning the science. I admit that I might be wrong. But not having that simple little data point seems to be contrary to the goals of those who seek to do things “Scientifically”.

    Kirsch is correct to point at the great increase in numbers in VAERS with regards to Bruce Willis getting aphasia. But I sort of want to see the gross numbers on Aphasia outside of VAERS in the same breath.

    I knew people who had strokes. My grandmother had 2. I know strokes have happened to lots of people. Except I haven’t run into them until now suddenly 2 people in 2 weeks 1 degree away from me have had strokes. Is this just age? The people in question are at the age where strokes happen. But that little jab is still there yapping at me.

    Brignell (of and “Sorry, Wrong Number!”) pointed out that smoking may not cause lung cancer but rather be the fertilizer. The jab may not cause the problems, it is just fertilizing them into prominence.

    And the arguments start tap dancing in circles.

  3. The True Nolan

    That logical leap from propositions to conclusion is, as you say, a mental leap and not one that can be simply mechanized. When one attempts to do so an infinite series of statements results. Lewis Carroll wrote a nice bit about it back in 1895.

    @brad tittle: “But not having that simple little data point seems to be contrary to the goals of those who seek to do things “Scientifically”.”

    Yes, exactly. Those missing data points happen so often and in such a single direction (ie in the “there’s not enough data to disprove what we want you peons to believe” direction) that I do not think it possible to blame simple human error. All those heavily funded regulatory bureaucracies and healthcare corporations seem congenitally unable to collect basic information! What on earth could be the cause of that?

    Of course one gives up the old fashioned idea that the agencies and companies have our best interest at heart, there will many causes that become obvious. Sadly all those causes point to the existence of a great evil.

  4. Back when I took a debate class, it was made obvious to us that semantics (language grammar and symbol definition) mattered. You must have agreement on that, first, before you can get anywhere in trying to support or dismantle arguments (logically). No agreement there entails rejection of one, or more, premises being used by the participants.

  5. There is a bit of misplaced HTML, causing most of the article to be in italics:

    which is <em>always</em>—as in <em>always—present,

    The &8212; probably ought to be </em>.

    Delete this comment as you see fit, and thanks!

  6. Briggs

    Thanks, Paul.

  7. 1 – A very interesting lecture.

    The business is of “seeing” is thought provoking (going back to your ideas on IQ some time ago). My son, who’s very bright and will soon earn his 1st degree in math and computer science, is zipping through his calculus courses like it’s trivial, but cannot “see” the solution to a wire puzzle called the Cowboy’s hobble. (Took me some time too) but the point is that there appear to be bounds on “seeing” that vary with the person.

    Secondly, you skipped inductive logic (I see why, but still..) and seem to imply that there is ultimately only one functioning Logic. I don’t think so, there’s only one of the form prolog tries to implement (and you discuss) but there are other forms. For example, a 1920s IBM tabulator performs mechanical logic (if pattern A is found, and then Pattern B, do action C). That mimics human logic, but in cell action braiding a molecule onto the end of dna strand does not seem to follow human logic, but either works or fails according to a very large set of rules that I certainly don’t understand (and doubt anyone else does either) – except that it appears to place A+B –>C into a parallel system like A,B + C,D –>E where the A.B connection is not serial and seemingly not dictated by general or prior conditions a’b’ etc. It must (?) be generated by local conditions – but that’s beside the point – which is that the logic of this does not appear to be programmable in either prolog or stutter (aka lisp) and so does not fit your model.

  8. “That logical leap from propositions to conclusion is, as you say, a mental leap and not one that can be simply mechanized.”

    Great point. It’s an example of the immaterial operations of the intellect that cannot even in principle reduce to objective matter.

    But I would emphasize that there’s nothing weird going on in my extrapolating C from A and B (if all are true and properly connected), it’s simply that C is inherent in the meaning of the other two.

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