Inference- Deduction (deductive)

This post is about deduction (deductive inference). If you have taken an introduction to logic class then you are familiar with deduction. Research methods tends to be where we teach induction these days, and logic is where we tend to teach deduction (at least explicitly).

Deduction: The process of moving from (possibly provisional) acceptance of some general and some specific propositions, to acceptance of specific propositions

With causation considered:

Deduction: The process of moving from causal relations and some specific cause, to acceptance (or expectation) of a specific effect. (This is what we do when we are deciding on a treatment; strength training (ST) makes muscles stronger (MS);  ST, therefore I expect MS)

The primary distinction between induction and deduction is that when deduction is done correctly (that is has a proper form; does not have a fallacy), if the premises are true, then the conclusion follows necessarily, the conclusion is true. This is where we get the language, “it follows that…..”

With deduction there are ”valid forms.” With a valid form the truth of the conclusion follows from the truth of the premises. This is not the case with induction. With induction we have what is called the induction problem, highlighted by Hume, but a more popular treatment can be found in Nasim Taleb’s “Black Swan Theory.” Taleb puts more emphasis on randomness than on an epistemological problem of induction, but essentially it means the same thing. With induction our conclusions tend to be a summary of observations and one observation to the contrary makes it incorrect.

For example (induction):

A study samples 1000 swans from a population of swans in North America.

All the swans were white.

Therefore, all swans are white.

Note - the presence of a single black swan refutes the conclusion; while the premise of the induction, the observations, were not refuted. This is the problem of induction. It may happen because of randomness, that is one category of error leading to inductive problems. Essentially, the methods of observation, and analysis should be attempts to minimize the inductive problem. Whenever reading a paper we can considering it’s “external validity” (also called generalizability) by considering the likelihood that the study has an induction problem (will be refuted in some case).

Back to deduction:

With valid forms of deduction, the only way for a conclusion to be false (un true) is for one of the premises to be found untrue.

For example:

All swans are white (premise)

There is a swan in the other room.(premise)

Therefore that swan must be white. (conclusion)

Note that here we have a conclusion that might be true or false. It could be a black swan. But, if it is false it is only false because a premise is false.

The other way for a deductive conclusion to be false is to be a logical fallacy, for some of them you can see this page (see the “Formal Syllogistic Fallacies” for fallacies of deductive form).

Deduction is what we do in clinical practice to decide our next action. Using our set of general premises of how things are (which may include conclusions of prior inductive inference), we apply these premises along in an iterative sequence of information gathering and decision making.

Respiratory muscle training strengthens respiratory muscles.

Patient does respiratory muscle training.

Patient will have stronger respiratory muscles.

This is a VAST simplification of the thought process going on at the time. But it allows us to notice that with deduction in practice we are usually thinking of the conclusion we want and manipulating one premise. Here we accept the first premise, we want the conclusion to be true, so we intervene with the second premise. That is how most interventions are determined - some premises are accepted, a conclusion is desired, the premises that are needed to get from the existing premises to the desired conclusion are acted on (intervention).

We can expand the example:

Premises:

Respiratory muscle training strengthens respiratory muscles.

Weak respiratory muscles cause dyspnea on exertion.

This patient has weak respiratory muscles.

This patient has dyspnea on exertion.

Patient does respiratory muscle training. (Intervention)

Desired conclusions:

This patient no longer has weak respiratory muscles.

This patient no longer has dyspnea on exertion.

But we also know this is not always the case. Not every patient with weak respiratory muscles and DOE that participates in respiratory muscle training has a complete amelioration of DOE. So there are issues.  While weak respiratory muscles can cause dyspnea on exertion; there are other causes of dyspnea on exertion. So it is possible for conclusion 1 to be true, but conclusion 2 to be false. It turns out we have snuck in an informal fallacy.  We have attempted to go from:

Weakness -> DOE (We have observations about this - we can conclude this is true)

to

No Weakness -> No DOE

But this premise IS NOT equivalent to Weakness -> DOE; so we have actually changed the premise when we made our conclusion. We switched from Weakness implies DOE to No Weakness implies no DOE and that is an error. This is called the “inverse” and the inverse of an implication is not equivalent to the implication; whereas the contrapositive is equivalent to its implication. Now we need to be careful. By not being equivalent I do not mean it is automatically untrue. Just that the truth of an inverse is not determined (assured) by the truth of the original implication.

The conclusion we have drawn is based on the premise we did not use explicitly. We snuck this premise in implicitly and used it on the assumption that it was equivalent when it was not equivalent. We then need to ask - is the premise we actually used true?

No weakness implies no DOE

The answer is no, we do not believe this statement is true we have too many contraries to believe this statement is true. We understand that there are more causes of DOE than respiratory muscle weakness.

Thanks for bearing with this discussion. It was helpful to me. I continue to believe that trying to break down the reasoning that is being done in practice, systematically, to identify the forms will improve practice and improve research by highlighting what we know and what need to know. I believe thinking systematically helps us recognize the flaws (formal or informal) in our reasoning. And I believe that inductive, deductive (and you will see abductive) inference are done so dynamically so that to proceed with an evaluation and hierarchy of evidence in an EBP manner without recognizing how the empirical observations are used in a rationale process to generate knowledge and then how that knowledge is used in practice creates a gap. I believe we are witnessing that gap with the proliferation of articles on the lack of adoption of “evidence based practice” by clinicians, and the lack of incorporation of clinical practice guidelines. A knowledge based practice might be a solution, but it is not being developed as a solution. It is being developed because I believe it is a better system of thought, by better I mean I believe it has a stronger foundation (critical realism over empiricism), and I believe it is more encompassing of the full spectrum of thought in practice (by including cause, models and inference as critical components).

 

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