How does thinking work? And where does it go wrong?

How does thinking work? And where does it go wrong?

A philosophical account of thinking does not need to give a biological account of it. At the same time it should not contradict a compelling version of such an account either. One aspect of the biological account I want to take along, is that neurons form neural networks and a thought is an activation of many neurons forming a uniquely patterned network of such activated neurons.

Without pretending to know what those neurological of activated patterns do, beyond ‘firing’ and passing on a chemical message through synapses, it is worth reminding ourselves that, to do its work, thought requires a conceptual network, a frame of reference, structuring those concepts that can vary in number and conceptual richness.

A concept is an entity made through our differentiating and mereological activity whereby we divide the behaviour of the universe into entities on the basis of properties we can differentiate and conceptually make into wholes. Concepts are made up of networks of other concepts.

As such, a concept is a thing made up, or rather that draws from, many concepts. These in turn are shared as properties by yet other concepts. Think of the properties of redness, table-ness, mine-ness, all three form different but overlapping sets and thus form different networks of associated connections to make a coherent thought.

Conceptual richness refers to the number of conceptual properties a concept is dressed in and how well it is dressed in those properties.

This conceptual structure creates a space of implications when two or more concepts are made to engage with each other on the basis of the properties they are attributed or dressed in, regarding some intention or intentional proposition, (that is a proposition that is about something) such that inferences form of the sort P → Q (if P then Q)

Rules of inference

What I am going to do here is to give you a breakdown of the most important patterns of inference whereby legitimate conclusions follow from the premises offered. I have included their official names simply because it is useful for a thing to have a name. I have provided each with commentary in order to lead the discussion to when things go wrong and why things go wrong. So after this section we shall deal with so-called fallacies. So here goes.

First of all we need to be able to say something and then say something about it. “This is a chair and you can use it to sit on.”

Formation Rules: These define which combinations of symbols constitute valid formulas. For example, if

P is a predicate symbol and t1,…,tn are terms, then P(t1,…,tn)c is a valid formula. So we can say that Socrates is Mortal where P stands for is mortal and Socrates is a term to which the predicate applies.

In this way we form concepts. In everyday life is might go something like this: “See that?” “Yeah…” “Do you know what that is?” ‘Eh… no.” “It’s a Brobdingnag” “a what?” “A Brobdingnag” “What’s that?” “A human being eleven times larger than you” “what…. that?” “Yeah, that..” “Doesn’t look eleven times larger..” “Yeah well that’s because she’s very far away”.

The person being introduced to a Brobdingnag now has a concept forming a network of a number of properties. a. Human b. 11 times larger than me. c. standing very far away. And usefully this typifying set of properties has a name: a Brobdingnag.

With these we can then start reasoning.

First we look at Predicate Logic rules of inference. These handle quantifiers (like “for all” and “there exists”). Here’s a structured breakdown:

1. Universal Instantiation (UI) If something is true for all objects, then it’s true for any particular object.

  • Example:
    • All humans are mortal.
    • Socrates is a human.
    • Therefore, Socrates is mortal.

Here we start forming patterns by looking at relationships between universal ideas (Humans) and particular instances of those ideas (Socrates) through properties (mortality)

2. Universal Generalization (UG) If something is true for an arbitrary object, then it’s true for all objects.

  • Example:
    • Suppose we prove that any arbitrary triangle has 180° angles.
    • Therefore, all triangles have 180° angles.

Here we start universalizing particular things. I have two legs. Do all humans have to legs? Well, it turns out, after extensive experience with these things, that that is true for the majority of people I have come across, and for the minority that it is not true for, I have discovered that they have lost one or both of them or that something else has happened. You can see how we form norms.

3. Existential Instantiation (EI) If something exists with a property, we can name it with a constant.

  • Example:
    • There exists something that studies.
    • Let’s call that something a student.
    • Therefore, students study.

Here we start with the property and name the thing that has this property with a constant.

4. Existential Generalization (EG) If a property holds for a specific object, then there exists something with that property.

  • Example:
    • Alex studies hard.
    • Therefore, there exists a student who studies hard.

So here we try to generalize the particular by admitting at least one instance of it. This can then serve as a marker for what to look for in others. Do other things share that property?

5. Combining Quantifiers with Propositional Rules Predicate logic rules often combine with propositional ones (like Modus Ponens).

  • Example:
    • All dogs bark.
    • Max is a dog.
    • Therefore, Max barks.

Well, this is a nice bridge to the propositional rules for inference. Now what we have concepts divided into universals and particulars holding properties we can start playing with them inferentially.

1. Modus Ponens (Law of Detachment) which says that if a conditional statement and its antecedent are true, then the consequent is true.

  • Description: If p → q and p are true, then q must be true.
  • Example:
    • If it rains, the ground gets wet.
    • It is raining.
    • Therefore, the ground is wet.

Notice that the statement is very simple. The wetness of rain engages with the potential of the ground to get wet when rain falls on it, so that only one simple conclusion can follow. This is the restrictive nature of the patterns of reasoning which in everyday life can get very complex very quickly as many modes of inference are mixed so that legitimacy is extremely hard to ensure in a normal conversation.

2. Modus Tollens (Law of the contrapositive) which says that if a conditional statement is true and its consequent is false, then its antecedent is false.

  • Description: If p → q and ¬q are true, then ¬p must be true.
  • Example:
    • If the alarm is set, it will ring.
    • The alarm did not ring.
    • Therefore, the alarm was not set.

Essentially this is not so different from the Modus Ponens except that it turns it round and looks at things from the point of view of negation.

3. Hypothetical Syllogism (Chain deduction) which… well chains two conditional statements together.

  • Description: If p → q and q → r, then p → r.
  • Example:
    • If I study, I’ll pass the exam.
    • If I pass the exam, I’ll graduate.
    • Therefore, if I study, I’ll graduate.

Certainly in daily life this is an extremely useful one as it allows to engage with any number of concepts as long as you keep your conceptual administration in order.

4. Disjunctive Syllogism, which says that if a disjunction is true and one disjunct is false, the other is true.

  • Description: If p ∨ q and ¬p, then q.
  • Example:
    • Either I’ll eat pizza or pasta.
    • I won’t eat pizza.
    • Therefore, I’ll eat pasta.

The delight of having choices made for you. The pizza place was closed.

5. Conjunction, Conjunction Introduction (or ∧-introduction)which says that if two statements are true, their conjunction is true.

  • Description: If p and q are true, then p ∧ q.
  • Example:
    • I am hungry.
    • I am tired.
    • Therefore, I am hungry and tired.

This one is more subtle than you might think. It allows two things to co-exist without contradiction. I can be a bachelor and hungry, but I cannot be a bachelor and married, unless of course bachelor refers to a bachelor student who can be married at the same time as doing their bachelor.

6. Simplification, Conjunction Elimination (or ∧-elimination) which says that if a conjunction is true, then each of its conjuncts is true.

  • Description: From p ∧ q, infer p (or q).
  • Example:
    • I am hungry and tired.
    • Therefore, I am hungry.

This is kind of like an aha erlebnis, discovering what is already implicit in something I might not have known about.

7. Addition Disjunction Introduction (or ∨-introduction)

  • Description: From p, infer p ∨ q.
  • Example:
    • The sky is blue.
    • The sky is blue or I’ll eat my hat!

This one looks a little weird at first sight but it is a useful one. It is a truth-preserving move because for an “or” statement to be true, only one of its components needs to be true. It is often used to make q sound so ridiculous that you are beguiled into accepting p. There lies its danger.

8. Constructive Dilemma

  • Description: If p → q and r → s, and p ∨ r, then q ∨ s.
  • Example:
    • If it’s sunny, we’ll go to the beach.
    • And if it’s raining, we’ll go to the museum.
    • It’s either sunny or raining.
    • Therefore, we will either go to the beach or to the museum.

The problem with the constructive dilemma is that it can quickly get you into black and white mode. There are quite a few other possibilities between it being sunny and it raining. So here we have to be careful for the False dilemma (see below under the list of fallacies)

These rules form the backbone of logical reasoning. They ensure that conclusions follow validly from premises, both in mathematics and everyday life. At the same time they hold many dangers that are discussed below in the section on fallacies. That is where thinking goes wrong. But not always in ways that can be easily prevented. But before we get to the fallacies we need to ad one more rule of inference:

9. The Syllogism in grass (thanks to Gregory Bateson)1

Some propositions are meant to be metaphorical or show up some analogy.

  • Grass dies;
  • Men die;
  • Men are grass.

Of course, strictly speaking this is an invalid conclusion as it affirms the consequent: 1. If P, then Q.   2. Q.   3. Therefore, P. This is certainly not allowed in normal rules of inference. However, if we do not allow this syllogism, we do not allow poetry, we do not allow metaphor, simile and analogy, all of which would want to make use of this possibility and all of which are in fact crucial for the creative exploration of the possible within logical space. It is crucial, because without it none of the arts (i.e. no intentional behaviour) including that of science, would be possible. So it is imperative that we include it in the rules for thinking.

In order to make sure that we do not abuse this syllogism, because it can get you into real trouble, ordinary language has found a way out by introducing the prepositions ‘like’ or ‘as’, whereby two different things sharing a property become like each other through that property.

Knowing this the original syllogism sounds more acceptable: Grass dies, men die, men are [like] grass. Compare Isaiah 40:6-7:

“The voice said, Cry. And he said, What shall I cry? All flesh is grass, and all the goodliness thereof is as the flower of the field: The grass withereth, the flower fadeth: because the spirit of the LORD bloweth upon it: surely the people is grass.“

Perhaps one might say that this is the thin end of the wedge, if we allow reasoners to affirm the consequent then where will it end? In pure madness? Well, it would not be a bad thing if we had a formal language for all possible uses and abuses of language. It would make the discipline of logic a much more accurate reflection of what being a thinking human is. But there is as yet no formal language for analogies and metaphors, despite quite a few attempts to develop one.

Fallacies show up constantly in everyday thinking, conversation, advertising, and even news commentary. I will not be the person to investigate this, but I would lay a wager that most of us are often swayed by fallacious reasoning. I often am, even conscious of the step I am taking. The reason for this is that much of our decision making is normative, that is based on norms and values that often have no greater authority than that they are norms and values. But as they have proved their worth in the past, I am happy to invest in their authority over me. Below is a simple guide with everyday examples for each major type of logical fallacy — grouped by category. And what surprises is how persuasive many of them are…

1. Fallacies of Relevance

These happen when the reasoning distracts from the real issue.

1. Ad Hominem (Personal Attack)

“Don’t listen to Jamie’s argument about climate change — she’s not even a scientist.” (Attacking the person instead of the argument.)

Notice that science is used by many not as a reference to a certain protocol of activities for doing things to guarantee a certain outcome but as a value. Scientists are admired and indeed their value is hard earned through the rigorous dedication to that protocol. No doubt because of that science has become an extrinsic motivation because of its value. It has set scientists up as authorities.

2. Tu Quoque (You Too / Appeal to Hypocrisy)

“You say smoking is bad, but you used to smoke!” (Rejecting someone’s argument because they don’t or haven’t in the past lived by it.)

We learn from our mistakes: don’t do as I do, or have done, but do as I say because I have seen the error of my ways. And yet the adagio to teach by example is very powerful.

3. Appeal to Authority

“This shampoo must be good — my favorite actor uses it!” (Using a famous or irrelevant person as proof.)

But we do this all the time! If someone we admire says something, we take note. They have authority on the basis of our admiration for them, which in turn begs the question (see below)

4. Appeal to Popularity (Ad Populum)

“Everyone I know is investing in crypto — it must be a smart move!” (Assuming something is true because it’s popular.)

Leonardo da Vinci even suggested that popular appeal should be taken on as a serious criterion for quality. I am guilty of the opposite. If things are popular I have to overcome a deep-seated revulsion before being amenable to considering the popular thing on its own merits.

5. Appeal to Emotion

“You have to adopt this puppy — look at its sad eyes!” (Using emotion instead of logic as proof.)

Well, this is one of the most popular fallacies, and it is not a strange thing as our emotions and feelings play an important and seminal part in reasoning and thought. All reasoning is started and cut off by a feeling: one of curiosity or dissatisfaction to begin a process of reasoning, and one of satisfaction and perhaps even joy when it all comes together.

6. Appeal to Fear

“If you don’t vote for this candidate, the country will collapse!” (Trying to scare people into agreement.)

I don’t think I need to explain the compelling nature of fear as a reason to do things. And when there is not just a threat of cataclysm or apocalypse but of violence to yourself or your loved ones, such reasoning becomes understandably persuasive. Indeed I can put it in something that resembles the Modus Ponens form:

  • If I don’t do as he says he will kill my child
  • He is threatening to kill my child
  • I will do what he says

Now the conclusion is not necessary so what has gone wrong here? Well, he is only saying that he will do it. Is he bluffing? Moreover, I have other options: threatening with counterviolence, offering my child up to the greater cause. (Think of Agamemnon’s offer of his daughter Iphigenia to Artemis to ensure a safe journey to Troy. As such many statements look like valid arguments but in fact are not because they are not stripped down to their simplest form so that the premises that would allow just one conclusion.

7. Appeal to Tradition

“We’ve always done it this way, so it must be the best way.” (Assuming something is right because it’s old or traditional.)

Traditions are habits formed over time. Often for good reasons. At some point those reasons are lost and just the habit remains, or the original reason (a practical one or a hygienic one) is replaced by another reason (a religious reason). If the habit remains and the reason is lost, but the consequence of acting according to tradition is still of benefit, then the reasoning might be fallacious but the outcome is still good. Similarly if the habit has exchanged reason, but you subscribe to the religion that has adopted the practice as ritual, then what is the problem?

8. Genetic Fallacy

“That idea came from the internet, so it’s probably false.” or “The idea was published in an ISI journal, so it must be true” (Judging an idea by where it came from, not what it says.)

This type of fallacy is as common as the appeal to authority. Our academic system is deeply engaged with this fallacy and with the appeal to authority. We try to set up journals that achieve authority for the paper published in it, rather than considering the findings and arguments of the paper on its own merits. This is deeply troubling.

2. Fallacies of Ambiguity

These rely on unclear language or shifting meanings.

9. Equivocation

“The sign says ‘fine for parking here,’ so I thought it was fine to park!” (Using one word with two meanings.)

I love ambiguities. And of course they rule comedy.

10. Straw Man

“You think we should have stricter gun laws? So you want to ban all guns?”(Misrepresenting someone’s position to make it easier to attack.)

This is a dangerous one, that creeps up on those who enjoy nuanced thought. Before you know it your interlocutor removes the nuance and makes you the object of ridicule or guilty of a social faux pas. WHich is not so easy to extract yourself from.

11. Amphiboly

“I saw the man with the telescope.” “Eh…who had the telescope — you or the man?” (Ambiguous grammar causes confusion.)

I love ambiguities. They often get us into awkward situations.

12. Accent / Emphasis

“I didn’t say she stole the money.” Each word emphasized changes the meaning. (Changing meaning by stressing different words.)

Try it, its fun. And literally every word in this sentence when carrying the emphasis changes the meaning of the whole. It shows how important the music of our spoken language is and explains why our written words often confuse us and anger us. The invention of the emoji was, in this sense a great moment in the history of writing.

3. Fallacies of Presumption

These assume too much or start from false premises.

13. Begging the Question (Circular Reasoning)

“I’m trustworthy because I always tell the truth.” (The conclusion repeats the premise.)

It is surprising how often we beg the question in our thinking and reasoning. The circularity can sometimes disguise itself well in the complexity of the conversation we are having.  Take the following example: “The court’s decision must be fair because it was made by an unbiased judge and jury”. This is a fallacy because the premise—that the judge and jury are unbiased—assumes the conclusion that the decision is fair without providing independent evidence. 

Why it’s a fallacy: The argument assumes the judge and jury are unbiased, which is the very point that needs to be proven to show the decision is fair. The premise of the argument is the same as the conclusion it is trying to support. 

The claim: The decision is fair.

The reason given: The judge and jury were unbiased.

14. False Dilemma (Either/Or)

“You’re either with us or against us.”

(Ignoring other possible options.)

Well, I am not sure I need to go further into depth here. The example probably speaks for itself. But it is quite frightening how often it is made use of: people assuming there are only two options. Why it is so tempting is that it is true in simple binaries: Either Pierre is there or he isn’t. Indeed in this example there are no further options with regard to the question formulated. But if we then ask where might Pierre be if he isn’t there? He might be just around the corner, or doing something very important, both of which would change the implications of his not being there.

15. False Cause (Post Hoc)

“I wore my lucky socks and we won the game — they must be magic!”

(Assuming one thing caused another just because it came before.)

16. Slippery Slope

“If we let students redo one test, soon they’ll expect to redo every assignment!”

(Assuming one step will lead to a dramatic chain reaction.)

Not completely sure this is a fallacy. Precedent is an important aspect of much of what we do. A sheep jumps from a cliff because other sheep have gone ahead….

17. Hasty Generalization

“My neighbor is rude — people from that city must be awful.”

(Drawing a broad conclusion from too little evidence.)

Yeah well, Do we need to comment on this one. Of course that is a bad thing. And yet. HAsty generalization haunts us in all fields.

18. Composition

“Each player on the team is great, so the team must be unbeatable.”

(Assuming what’s true of parts is true of the whole.)

Again, all I can say is please do not do this!

19. Division

“The team is great, so every player must be amazing.”

(Assuming what’s true of the whole is true of each part.)

And this!

20. Loaded Question

“Have you stopped being lazy yet?”

(Question assumes something unproven — any answer traps you.)

It’s the way that the answer you give traps you. The best response is: “have you?”

4. Fallacies of Weak Induction

These use weak or irrelevant evidence.

21. False Analogy

“Employees are like nails — you have to hit them to make them work.”

(Comparing things that aren’t truly similar.)

22. Appeal to Ignorance

“No one has proved aliens don’t exist, so they must be real!”

(Using lack of evidence as proof.)

23. Gambler’s Fallacy

“I’ve lost five times — I’m due for a win next!”

(Thinking past random events affect future ones.)

24. Anecdotal Fallacy

“My uncle smoked his whole life and lived to 90, so smoking can’t be that bad.”

(Using a single personal example instead of data.)

25. Middle Ground Fallacy

“Some say the earth is flat, others say it’s round — maybe it’s kind of both.”

(Assuming the truth lies halfway between two extremes.)

5. Fallacies of Irrelevance in Everyday Reasoning

26. Red Herring

“Why worry about pollution when we still have poverty?”

(Changing the subject to distract from the main issue.)

27. Moralistic Fallacy

“That can’t be true, because it would be terrible if it were!”

(Rejecting a fact because it feels unpleasant.)

28. Naturalistic Fallacy

“It’s natural to eat meat, so it’s morally right.”

(Assuming ‘natural’ means ‘good’.)

We know of this falacy quite some time and yet it must still be the single most popular reason people give. And what they see as “natural” defies belief. I believe it is the result of a faulty understanding of how evolution works. People cannot get their head around the idea that human beings are products of nature and wht human beings do is perfectly natural. But that much of this naturalness is far from attractive or beneficial to all sorts of stakeholders.

29. Fallacy of the Single Cause

“Teen violence is caused by video games.”

(Ignoring other contributing factors.)

Yeah well.

30. Nirvana Fallacy

“Electric cars aren’t perfect, so we shouldn’t use them.”

(Rejecting a solution because it isn’t flawless.)

© jacob voorthuis, 2025. Please cite Jacob Voorthuis as the author, The Theoria Project as the title and the page address as the location. This work is licensed under a Creative Commons Attribution 4.0 International License. You are free to: Share — copy and redistribute the material in any medium or format Adapt — remix, transform, and build upon the material for any purpose, even commercially under the following terms: No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits. Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made.

  1. Gregory Bateson & Mary Catherine Bateson, Angels Fear, Towards an Epistemology of the sacred, (1988) ↩︎