Thinking about thinking straight
[ disappearing up your own backside ]
Key points in this article:
1. Rational is not logical
2. Valid arguments
3. Logical thinking
4. Guilty until proven innocent
5. Worked examples
Some physical exercise
I'VE BEEN THINKING. I physically have, looking for things to think about where I come up against the buffers, really physically, inside my head. You are trying to work something out and it feels physically impossible to get any further. I have read that the process of thinking is actually physical and not just electrical impulses or whatever. The idea is that pushing yourself walking fast up a steep hill to improve fitness is only half the story. The other half is in your head, so push and keep pushing and hit the buffers to improve physical brain fitness. This seems good. Read more »
I like to think I think rationally and logically rather than believe in stories, so why not think about thinking.
Rational vs logical
Being rational and being logical are not the same thing. Rationality is about making decisions that give the best results in particular circumstances. Is robbing a bank rational? It may be if you're broke and you won't get caught.
Logic, on the other hand, ignores the circumstances and the desirablity of the results. It means conclusions based on sound premises and irrefutable facts. Robbing a bank isn't logical because if everyone did it, banks wouldn't exist and that doesn't make sense, but it could still be rational to rob one yourself.
My rational behaviour in a particular situation may not be the same as yours because of our different circumstances and natural tendencies, but if we both act logically, we both do the same whatever our circumstances. So I think rational thinking is particular to the individual whereas logical thinking is the same for everybody.
Whenever I have read about logic it hasn't made much sense. I read about logic, for example, in 'Rationality', a 2021 book by Steven Pinker in which he says that "to be fully rational you should study logic, game theory, probability, and statistics." Logic deals with arguments that can be correct or incorrect depending on their premises but oddly, it doesn't always seem intuitive.
Start with a proposition then use 'building blocks' of logic to see if it's true.
- The proposition » the sky is blue.
- The premises » the sky exists, visible colours exist, blue exists, the sky has a visible colour.
- The argument » the sky looks blue, therefore the sky is blue.
- The conclusion » the argument is correct based on the premises so the proposition must be true and the sky is blue.
Much of it hangs on the premises. If the sky has no visible colour then the sky is not blue. The confusion arises when each side of an argument is based on different premises – or none at all. There are different kinds of argument as well, and the discussion soon gets complicated with inferences, assumptions, fallacies, best explanations etc.
Truth table for P AND Q
P
True
True
False
False
Q
True
False
True
False
P AND Q
True
False
False
False
P and Q are propositions and P AND Q (together) is a proposition being examined. The truth table represents all the possible truth combinations. If either of P or Q is false, "and" is false so P AND Q is false.
Truth table for P OR Q
P
True
True
False
False
Q
True
False
True
False
P OR Q
True
True
True
False
In the truth table above, P "or" Q is true as long as at least one of them is true and false only when both are false. OR in this table is 'inclusive', which means P "or" Q is true when either or both propositions is true. In other words, OR means AND / OR. Alternatively – and the table would be different – OR can be 'exclusive' to mean P "or" Q is true when one (not both) propositions is true.
Truth table for valid arguments
A
True
True
False
False
B
True
False
True
False
If A then B
True
False
True
True
A
True
True
False
False
Conclusion (B)
True
False
True
False
The table above evaluates the truth of the premises "If A then B" and "A", and the conclusion "B" for all combinations of truth for propositions A and B. Whenever "If A then B" is true and "A" is true, the conclusion "B" is also true.
Note also that when "If A then B" is true, "B" is true even if A is false. That's why I suggested above that formal logic is not particularly simple, intuitively.
What use is all this? Well, I haven't tried it myself but truth tables can be far more complex than these and used to evaluate complex logical arguments – not so much in a court of law perhaps but in disciplines where truth actually matters. Systematically examining all possible combinations of truth can determine the validity of an argument, the point being: "nobody can deny it" so everyone involved has to sign up to it, no argument.
Most people lucky enough to live in a civilised country would probably agree that life is generally better than it was a thousand years ago, say, even when now, it may be difficult for them personally. Things could be a lot worse, in other words (and were, once). Less people starve, less people get murdered, public services exist and laws protect individuals from others. It seems to show rational thinking rather than logical thinking (all helped along by natural selection). Probably though, a lot of the discourse is logical nonsense, factual error, wishful thinking, fallacy and lies. Sometimes it matters, other times it doesn't and might even be helpful for building a cathedral or a multi-billion £ aircraft carrier that serves little purpose and doesn't work properly anyway.
It's partly because of words like "if", "or", "so", "and", "could" and "might" which can infer different things in different circumstances. If you are trying to work out what to do about a certain problem you have, you think differently than when you want to persuade someone of something.
Logical fallacies
An aim of 'thinking straight' is not making mistakes and logical thinking is probably helpful. "Always be doing the right thing" is a good mantra but has a subjective element in "right", which means "right in your opinion." Even so, when you have decided what's right, logical thinking should help, and that means avoiding logical fallacies.
It goes without saying that another aim of thinking straight is to not let yourself be easily fooled by 'external factors' such as another person using logical fallacies to persuade you to do things their way. If you are frightened of something, say, you might more easily be fooled by a 'conspiracy theory' (say) because you would rather believe it than the truth. History is full of this or there wouldn't be pyramids and Gothic cathedrals (just a couple of harmless examples – a cathedral is perhaps rational, a religious war isn't, and neither seems logical).
Incidentally (and being pedantic) I could have said "pyramids and Gothic cathedrals" to literally mean both and not one or the other, or I could have said "pyramids or Gothic cathedrals" to mean one or the other but not both, or actually both. Either way, in plain English the meaning is clear but, to be exact and eliminate the risk of a logical fallacy, it would need a truth table with logical "ands" and "ifs" (what I mean by disappearing up your own backside).
All forms of human communication can contain fallacies. There is a great long list on Wikipedia so there is no point going into it all here even if I knew, which I don't. The main thing is thinking straight and being able to recognise things for what they are and not (i) fooling yourself or (ii) being fooled by others – because if you believe what a politician says, you probably are. If you believe what your friend says, you probably aren't.
Topical
At present in the UK, a criminal conviction is receiving attention after the guilty person received fifteen life sentences and, as things stand, will never be free. It's receiving attention partly because of the testimony of a witness for the prosecution. The following passage is interesting, put by someone on a website discussing the matter and who understands logical reasoning:
The reasoning [by the witness] seems abductive. That is to say, infers one thing (A) as the most likely explanation of something else (B and C). This stands in contrast to deductive reasoning, where we say that having assumed A and B, we can conclude C; and it is also different to inductive reasoning, in which we say that having observed that A and B is the case, we can conclude C. Deductive reasoning forms particular conclusions from general things, A + B = C; inductive reasoning forms general conclusions from particular things – also A + B = C but rooted in probability due to uncertainty. Abductive reasoning is a form of inductive reasoning in which the reasoner takes whatever facts are to hand and draws the best available conclusion, A = B + C. [the witness] reasons abductively as follows:
A. There is no evidence of a natural cause.
B. Therefore a natural cause can be excluded as a possibility.
C. Therefore the harm inflicted must have been intentional.
... this approaches an informal fallacy. In its starkest form, it takes on the pseudo-deductive and fallacious quality of something like: "We haven't found any exculpatory evidence, therefore the accused must be guilty."
So guilty until proven innocent (reversing the legal standard). Any belief can be maintained by putting the burden of proof on anyone who disagrees.
Deductive reasoning ensures a conclusion which can't be false if all the premises are true and with 'correct arguments' that any rational person (eg: on a jury) would find convincing 'beyond reasonable doubt'. Abductive reasoning, based on "the best explanation", starts from an observation and looks for reasons to explain it. Inductive reasoning leads to conclusions based on a pattern of individual observations like "all cats have fur." Abductive reasoning seems particularly dangerous in a court of law because we are all human and it's natural to be uncomfortable with uncertainly and grasp an explanation when one is offered.
[ this seems far from over ]
Worked examples
Deductive reasoning A + B = C starts with A, then B, then deducing C.
- A: The post mortem states that the victim was poisoned.
- B: The accused was seen administering the poison to the victim.
- C: This proves the victim was poisoned by the accused.
Abductive reasoning infers A as an explanation of B + C but doesn't exclude other explanations, so A remains a hypothesis and is not proven.
- A: The accused probably poisoned the victim because
- B: the accused has access to poison, and
- C: was often seen with the victim and with poison.
Inductive reasoning infers a principle A from a body of knowledge B and C which experience suggests is probably true.
- A: The accused might have poisoned the victim because
- B: the accused is a type of person likely to poison someone and
- C: victims like this are vulnerable to people like the accused.
Deductive reasoning proves guilt, abductive reasoning suggests guilt and inductive reasoning suggests the potential for guilt but not much more (all depending on the particulars of the case).
Each type of reasoning obviously has its place. Everything in the world is held to be only a probability. Much of it must be assumed to be true for humans to move forward – with the one exception of something proved to be true; not just a probability but an irrefutable fact. That's the theory. It happens to be the same theory as mine, which proves it!
The process of thinking
Thinking is considered to be a process involving a series of consecutive physical states. Arguably, everything is physical in nature (it isn't me who argues it but experts). The release of neurochemicals occurs and thoughts are transmitted via neurotransmitters such as dopamine and oxytocin. All this is physical.
Brain research is always ongoing. Some studies, for example, indicate that playing video games not only changes how brains perform but also their physical structure. A question is whether thinking about one thing transfers benefits to thinking about something else. I have not seen a conclusion about this. It seems reasonable to suppose that if video games can be 'cognitive training' for video games, then problem-solving exercises can do the same for problem-solving, and so on.
I have read that juggling and playing a musical instrument can both help to restore brain size (a juggling experiment by the University of Oxford). There is enough research evidence to suggest that thinking hard about things is good for being able to think even harder.
Related: If this, then that | Explaining Bayes Theorem
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