Basics of logic part 2

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In the first post, I dealt with deductive arguments, which is the “classical” form of arguments. They are such that if their premises are true the conclusions are true. Deductive reasoning forms the core of the scientific method, is what most people regard as being logic. Deduction is most famously cited by Sherlock Holmes as his method of inquiry, the process of deduction is reasoning from one or more premises to reach a logically certain conclusion. In the application of the scientific method, the premises are often data regarding observations.

Inductive arguments on the other hand, are such that the truth of their premises, makes the conclusion more or less probable. Inductive arguments are either strong or weak. The premises within an inductive argument are viewed as supplying strong evidence for the truth of a conclusion, unlike the deductive where the premises are viewed as being true. In colloquial use, inductive reasoning is often defined as progression from particular/individual instances to broader generalization. While the philosophical definition is more nuanced, it is sufficive for this article to outline that an inductive argument indicates some degree of support for the conclusion, but does not entail it.

Abductive reasoning, is a form of inference which goes from observation to a theory that accounts for the observation. As with inductive reasoning, the premises do not guarantee the conclusion, and a colloquial way of understanding it would be “inference to the best explanation“.

Deductive, Inductive and Abductive Arguments

The three forms of reasoning all serve different purposes within the field of logic. Deductive arguments allows deriving b from a only when b is a formal logical consequence of a. Inductive reasoning allows inferring b from a where b does not follow necessarily from a. Abductive reasoning allows inferring a as an explanation of b, thus it permits the precondition a to be abduced from the consequence b. Abduction therefore is formally equivalent to the logical fallacy of affirming the consequent, because there could be multiple other explanations for b.

Examples of deductive, inductive and abductive arguments:

Deductive argument: 

Major premise: All cars have tires. 

Minor premise: A Volvo is a car. 

Conclusion: Therefore a Volvo has tires. 

Inductive argument: 

Major premise: All snakes we know of are carnivorous 

Minor premise: An anaconda is a snake. 

Conclusion: it is probable that an anaconda is a carnivore. 

Abductive argument:

Major premise: The lawn is wet

Minor premise: if it rained last night, the law would be wet.

Conclusion: It rained last night.

One of the key things about deductive arguments is that the form decides validity, rather than the content of the argument. This was famously spoofed by Ludvig Holberg in the play “Erasmus Montanus” published in 1723.

Major premise: A rock cannot fly

Minor premise:  Nille (a character) cannot fly. 

Therefore:  Nille is a rock. 

From a logical perspective, the argument above contains the informal fallacy argument from ignorance, which is a type of false dichotomy. Inductive and abuductive arguments are often seen as less credible than deductive arguments with good reason, as deductive arguments will be valid and sound if the premises are valid and sound. In this sense, a deductive argument is a case of binaries, while abduction and induction are probabilistic. This however means that the latter two forms of argument are more applicable to day to day life, than the former.

Basic forms of formal arguments

The forms here are all in the form of a deductive argument, for simplicity and comparability.

Modens ponens: If P, then Q, P, therefore Q.

Major premise: The butler’s shoes are dry.  

Minor premise: It rained last night. 

Conclusion: Therefore the butler was not outside.

Modens tollens: If P then Q, not Q, therefore not P

Major premise: If dad got laid, he would be whistling when he came home.  

Minor premise: dad did not whistle. 

Conclusion: Therefore dad did not get laid. 

Disjunctive syllogism: P or Q, Not P, therefore Q

Major premise: The Patriots or the Packers are going to win the superbowl. 

Minor premise: The Packers did not win the superbowl.

Conclusion: Therefore the Patriots won the superbowl. 

Leibniz’s Law: A is F, A=B, therefore B is F

Major premise: Jane is the bank manager. 

Minor premise: Jane is a bitch

Conclusion: Therefore, the bank manager is a bitch. 

Syllogism: All Fs are Gs , a is an F, therefore a is a G. 

Major premise: All men are bastards

Minor premise: Alan is a man

Conclusion: Therefore Alan is a bastard. 

Forms of Reasoning and Rhetoric

The three forms of reasoning are all present in rhetoric. Interestingly enough, the most persuasive approach is to fake the appearance that deductive reasoning is the form being used, to create false dichotomies. This is very similar to how phenomenology, grounded theory and positivism are all research paradigms, and thus have high credibility. However, out of the three only positivism tends to have the highest level of rigor and wide applicability.  When speaking, nuance is less persuasive than presenting highly limited options, furthermore, it is easier to question a speaker utilizing induction or abduction out in the open.

The effect of setting up inductive or abductive reasoning as deduction is in fact to create a false dichotomy of sorts, wherein a conclusion is presented as certain despite being only one among many options or interpretations of premises or facts. The reason why this approach is effective in rhetoric is that in a debate, there is rarely time to sit down and evaluate arguments and premises in detail, and thus a series of fallacies often slip under the radar.

This is very similar to how studies are often cited without reference to their sample sizes or sample population. When evaluating an argument, it is important to first determine if the form of the argument is valid. Is it phrased correctly, what are the axioms required, is it a deductive, inductive or abductive argument? Secondly, it is important to evaluate the premises for soundness, there are countless examples of arguments that are valid, yet are unsound. For instance, the Kalam Cosmological argument is a cause of an abductive argument that is often presented as a deductive argument, this argument has been formulated in many ways but here is how William Lane-Craig formulates it:

Major Premise: Whatever begins to exist has a cause

Minor Premise: The Universe began to exist

Conclusion: Therefore, the Universe has a cause.

In this case, the argument takes a valid form, and thus it is a valid argument. However, both the major and minor premise are questionable from the perspective of soundness. In the case of the minor premise, scientist do think that the universe came to exist, however, this is not a certainty. In the case of the major premise, we have observed that everything we know to exist has a cause, yet we cannot know if this is the case of the Universe. The form that would be the most sensible for this argument, is the inductive form:

Major premise: What we know to exist has a cause

Minor premise: The universe began to exist

Conclusion: Therefore the Universe probably has a cause.

However, in terms of rhetoric, if facing a speaker who is nuanced, balanced and reasonable, this speaker will appear uncertain next to one who project certainty. To quote William E. Gladstone, “Men are apt to mistake the strength of their feeling for the strength of their argument. The heated mind resents the chill touch and relentless scrutiny of logic“.

 Summary and Conclusions

The three forms of logic all have their respective spaces where they excel, deductive logic is the most suited for most of the scientific research being conducted. However, many a positivist research project started from a theory formed after an observation, using inductive or abductive logic. Much like the research paradigms, the choice of logical weapon must be adapted to the situation at hand. If you are aiming to persuade, limiting options and increasing certain through use of deductive logic is advisable, if you are seeking truth, then choosing the most effective form for your purse is recommended. Many times just as research often progresses from qualitative or grounded theory research on small sample sizes to positivism and large sample sizes, logical arguments may transition from inductive, to deductive or deductive to abductive, depending on the situation.

A familiarity with the forms, allows permits one to pinpoint which form a speaker presents an argument in, and which form it should be in, given the data provided.

More reading

How to win every argument: The Use and Abuse of Logic

A Rulebook for Arguments

 

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2 comments on “Basics of logic part 2

  1. […] I’m going to start by breaking down rhetoric in the same way I did logic in “The basics of logic 1” and “The basics of logic 2” […]

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