Additions in red.
talking about the American word zit, meaning pimple or skin blemish (in Scots: pluke), the English comedian Jasper Carrot continued, “I’ve got this mole.” He then paused, “it’s playing havoc with my lawn”. This is an example of elision or the confusion between two meanings that share one term. Elision, or the act of eliding, is permissible in comedy, but not in philosophy or in logical argument and it is logic systems I want to discuss in this post.
[For those of you whose first language is not British English or who are not European mole here means a skin blemish and also a small mammal that burrows. That’s the problem with language; it’s not just used for communication but manages to set up barriers between people. It is not my intention to exclude anyone from the discussion.]
There are three main systems of logic in basic use: inductive, deductive and abductive. Inductive logic is the most commonly used one, basically as a phenomenon has occurred tat least twice it may be assumed this phenomenon will always occur: for example, that swan is white, the next swan is white; therefore all swans are white. Clearly, this method is very fragile as even if there is only one instance that does not fit the perceived pattern, that is, a counter-example, then the theory is wrong, that is, it is refuted. Turning back to the example of the swans, in Australia, there are black swans; in New Zealand, there are black-necked swans. With just one counter-example, the theory proposed that all swans are white is refuted.
The inductive logic system is also known as the Aristotelian. It is also the one most used every day as we use it to confirm patterns, for example, the Sun will rise tomorrow morning as it has always done before.
You will have noticed that I have introduced the words theory and refutation. Both these words have been very much misused at times. But a theory can be just your conjecture that a phenomenon exists, and if you have a theory, then a refutation of that theory is the piece of evidence that proves that theory to be false. Note that a theory can be confirmed countless times, but one valid counter-example invalidates it. The theory may continue to be useful, for example, Newton’s theory of gravity has been refuted but is still used as a useful approximation to reality. Note however that is it is not a wild conjecture but an honest attempt to explain facts (amongst other things) and has only been superseded by the more accurate Einsteinian theory.
Turning now to Deductive logic and we have a logic system that iff used correctly, that is if its rules are followed, will always give true results. Please note that iff is correct and not a misprint for if. Iff stands for if and only if. This is an important term in logic as-is or and note that or can mean either one thing or another but not both those things or can mean one thing or another or both those things, so or is ambiguous and must be used with care. The first meaning is exclusive or (which can be called xor) and the second is inclusive or (which can be called ior).
A deductive argument, or syllogism, at its most basic consists of two premises, that is two statements that when put together lead to a conclusion. (Arguments can have several premises and several sub-conclusions and these can then become further premises.)
A deductive is judged in two equally important ways. Firstly, it is sound iff, when specific rules are followed, the premises lead to a correct conclusion, that is, given the premises, the conclusion follows from them. Secondly, the premises themselves must be true and the conclusion must follow from those premises for the argument to be valid.
To complicate things, you can have an argument that seems to have only one premise leading to a conclusion. The missing second premise is a hidden premise; it does exist, but the arguer will assume it is well known and not needing to be stated.
A valid argument has at least two factually true premises leading to a conclusion.
A sound argument is one where the premises lead to the conclusion regardless of whether they are true.
This is a sound and valid argument.
Deductive argument is powerful and so can be misused, for example, a premise can be false, the rules misapplied or when the conclusion sought is already one of the premises. There will now follow some really bad arguments.
“Cases are going up in the U.S. because we are testing far more than any other country, and ever expanding,” Trump declared in an early morning June 23 tweet. “With smaller testing we would show fewer cases!” [From https://www.factcheck.org/2020/06/trump-falsely-says-covid-19-surge-only-due-to-testing-misleads-on-deaths/]
Trump’s argument is you can’t find CoVid-19 without testing, CoVid-19 is found by a test for CoVid-19, therefore testing causes CoVid-19.
I am sure many people were going to reject the argument as it comes from US President Donald Trump as they would suppose any argument from him would be bound to be wrong. This is known as ad hominem or judging an argument not on any extrinsic worth but on who argued it. It is best to look at an argument without seeing who made it, so it can be judged fairly.
In the above argument, it would just plain wrong whoever made it. CoVid-19 exists whether it is tested for or not.
The second example of a bad argument is actually laid out as if its protagonist knew what he was doing. I have not named him as I thought it would be kinder not to. It is as follows.
“Premise 1: According to third law of Logic, (Law of excluded middle
.) Everything which exist are created or un-created
Premise 2: Everything which had a beginning (created) has to be created by either un created things or by self creation
Self creation is a logical fallacy, called Circular reasoning
, so the only way of created things to exist logically is created by the un-created things
These un-created things we call as gods/GOD, which are eternal by definition”.
Premise one is confused. The law of excluded middle is misapplied. Either a proposition is true or its negation is true, but there is no proposition here, merely a claim things have either been created or un-created. However, a thing could be self-created or partially created and partially not. The law has been used illegitimately.
Premise two brings in the definition of created, which should have been a separate premise, so let’s set out the argument more clearly.
Premise 1: everything which has a beginning is created
Premise 2; everything which exists is created or un-created or self-created
Premise 3: everything which is created has to be created by either un-created things or by self-creation
Premise 4: nothing can be self-created (seemingly because “Self-creation is a logical fallacy, called Circular reasoning”)
Conclusion 1: there is something (or somethings) which is uncreated that is responsible for creating other things
Conclusion 2: the only way of creating things to exist (logically) is created by the un-created things
Conclusion 3: un-created things we call as gods/GOD, which are eternal by definition.
Having sorted this out we can see that no premises are known to be true (they may be, but are not known); 3 sounds the most possible as it seems to cover all possible states (except and we have dropped the misunderstood use of Excluded Middle. Premise 4 asserts that self-creation is impossible but it is claimed that is because it a logical fallacy and that logical fallacy is called circular reasoning, except that self-creation is not a case of circular reasoning and there is no issue about circular reasoning, unless it is viscous, that is there is no way to break out of the circle. As none of the premises is true then conclusion 1 fails. Even if the premises were true, then conclusion 1 is as far as we could go. Conclusion 2 makes a leap from creation to sustained existence and Conclusion 3 just makes no sense being just a definition added on at the end for no other reason than the originator wanted to have this argument ‘prove’ that ‘God’ existed.
Conclusion 1 is claimed by its originator to have only one thing ’which is uncreated that is responsible for creating other things’, but gives no reason for this.
Conclusion 3 has the claim that ‘gods/GOD’ are eternal by definition. This again is a contentious claim. There are belief systems where supernatural beings of this sort are not eternal, but immortal or even mortal.
With the premises not being true, this brings us to discussing facts, that is, things which are true and facts are tricky things. According to the poet Robert Burns, “facts are chiels that winna ding” (facts don’t change), and from his eighteenth-century perspective this looked certain. The problem is that many facts do change and very few seem to be eternal. Part of the problem is that we cannot prove a fact as true, although we can feel certain of it. The best we can seem to hope for (and it is good enough to establish knowledge) is a web of facts that support one another (an example of useful circular reasoning). Of course if one fact changes, this may affect other facts.
We can now turn to the third system to examine. Abductive logic is the one that Sherlock Holmes (that is, the character created by Arthur Conan Doyle) claims is deductive logic, but as we have discussed that in some length, we can see that is it not. Abduction is the one where the conclusion reached is one that fits the facts, but is not impossible. The abductive argument can be laid out much like a deductive argument with premises and conclusions, but of course, the conclusion is provisional as it necessarily admits that there may be a better explanation to be found. Using this logic also admits that the conclusion reached may be proven wrong as the premises may change. It does not have the certainty of a valid and sound deductive argument.
There is quite clearly a great difficulty in actually proving things, so instead should we just consider if there are good grounds to hold that something is true? I would say so. Are there good grounds for the above Conclusion 1 and Conclusion 3. Conclusion 1 may become more plausible, but I doubt it. Conclusion 3 remains just as implausible.