Post No.: 0066
All dogs have butts,
I am a dog,
Therefore I have a butt.
The above syllogism is sound. A sound argument is one with true premises and valid logic. An argument is valid if and only if it’s impossible for all its premises to be true and its conclusion false.
But not all valid arguments are sound, and not all invalid arguments present an incorrect conclusion. A sound argument must be valid as before, plus have all its premises be true.
An informal fallacy is fallacious because of its content. A formal fallacy is fallacious because of its logical form or structure. It sometimes helps to think in terms of mathematical logic and to draw or visualise Venn diagrams to work out an argument’s logical validity.
So to counter an argument – show that the premise(s) are false, the conclusion does not follow from the premise(s), or show that some other fallacy has been committed. We must hold beliefs that are sensitive to the truth i.e. if a premise hadn’t been true, you wouldn’t have believed it to be true, as much as if a premise had been true, you would believe it to be true. It’s also wrong to infer ‘truths’ from false beliefs.
Deductive arguments are based on logical reasoning – they’re about deducing a guaranteed specific conclusion from a general rule. They are either ‘valid’ or ‘invalid’. For example, ‘all animals that have no backbones are invertebrates, this animal has no backbone, therefore this animal is an invertebrate’ is a deductive argument because it is by definition that an animal without a backbone will be categorised as an invertebrate.
Inductive arguments are based on probabilities rather than guarantees – they’re about trying to infer a general rule from specific examples. They can only be either ‘strong’ or ‘weak’. For example, ‘these are zebras, they have black and white stripes, therefore all zebras have black and white stripes’ is an inductive argument because it might not be the case that all zebras can be generalised to have black and white stripes. To counter a generalisation – you only need one valid counterexample i.e. finding one zebra without black and white stripes in this example. When inductive arguments are made, ask – are the premises of the generalisations true or justified (query the quality of research and how that information was attained)? Was the sample size large enough (e.g. did they look at lots of zebras)? Was the sample group biased (e.g. did they look at zebras from every country possible and across all of history too)?
Abductive arguments are based on intuition, heuristics and creative thinking – they’re about inferring one’s best guess or explanation from the incomplete information observed, ideally to find the simplest and most plausible explanation (an inference to the most plausible explanation). This is like how we intuitively reason answers in a lot of situations in life. For example, ‘this dog looks guilty, guilty-looking dogs have done something wrong, therefore this dog has done something wrong’. But like with all intuitions and heuristics they can be fallible i.e. plausibility is not the same thing as probability. (Dogs most likely only look guilty because they’re reacting in fear to their owner’s tone of voice and body language towards them, and possibly even their smell.) Woof.
Whilst an inductionist would say, “I’ve driven in this car with no problems so far, so I’ll have no problems with this car in the future either”, a counter-inductionist would say, “I’ve driven in this car with no problems so far, so I’m due for a problem soon”. Another example is an inductionist who’s had several successes in a row may not see failure come easily to mind thus making him/her overconfident, whereas a counter-inductionist who’s had several failures in a row may also feel overconfident because he/she will believe that ‘after all these failures, surely the next one’s going to be a win’. Yet another example is that an inductionist would say, “No one wears shoes here, so there’s no market for shoes here”, whilst a counter-inductionist would say, “No one wears shoes here, so there’s a massive market for shoes here”!
Neither inductionist nor counter-inductionist logic in isolation is reliable for coming to a conclusion. Neither type of reasoning is more correct than the other, hence a stalemate. Without further information, they’re both just as logical as each other yet they come to directly opposite conclusions. This is how it can sometimes be extremely subjective how we personally interpret conclusions even with agreed and undisputed objective data (e.g. without taking any other logic or data into account – whether ordinary citizens should have vastly fewer guns or even more guns to defeat gun crime in a state that already has lots of guns). If more data is known though, such as the long-term mean or average of a set of results, then logic should point to results soon regressing back towards the mean (e.g. regarding attaining several successes or failures in a row, if a run of results have been lower than average for a while then there’s a high probability that the next result will be higher, and vice-versa).
Someone might believe ‘I’ve been wrong all along so this time I’ll be correct’, or think ‘this lottery number hasn’t come up for a long time so this time it’ll come up’ (and the longer it continues to not come up, the more strongly they’ll feel it’ll come up the next time) – but these examples involve independent trials, where past outcomes have no bearing on future outcomes (e.g. the past frequency for the number ‘8’ appearing does not affect the present or future probability of the number ‘8’ appearing if the draw is fair i.e. that number will still have at the start of each draw a 6/59 chance of appearing in any individual draw if 6 balls are drawn out of 59 each time). But human intuitions tend to illogically or superstitiously read into patterns where any perceived patterns are only illusory (well, unless you suspect the lottery machines and balls are somehow rigged by the organisers?)
This is just a very brief introduction to logic that has hopefully whetted your furry appetite for exploring the world of syllogisms, logic and argumentation. Understanding logic can help you better analyse the arguments made by e.g. politicians, lawyers, salespeople or anybody else who is trying to convince you to believe in something, and can help you make fewer logical mistakes yourself. It is best worked out using ‘system two’ critical thinking than ‘system one’ intuition.
Woof. And I can confirm that I have a butt – not that it therefore means that all things with butts are necessarily dogs!