# Are "if smoke then fire" arguments deductive or inductive?

I'm new to philosophy and have a question regarding deductive vs. inductive reasoning:

I'm told that "John ate a strange plant in the forest and got sick. Clearly, the plant made John sick."

I believe that the usage of "clearly" makes this deductive, but I also see it as possible within normal language use for the word "clearly" to leave some wiggle room for the possibility of being wrong. If it is deductive, I am certain that it is invalid, as there's a very real possibility John was made sick from something else.

Any thoughts? Deductive and invalid, or inductive and strong? Apologies for the novice-level question as I am just beginning to piece together the basics of critical thinking.

• It is 'abductive' reasoning, which by modern standards is a form of inductive reasoning. (I dislike this use of 'inductive' to mean 'absolutely everything other than deductive', rather than in the Humean sense, but that is a historically lost argument, It is now the usage. Conifold agrees with me, but as NB points out, we are officially wrong.) The argument does not give a previously agreed upon reason for the inference, and deductive logic is tied together entirely by stating reasons.
– user9166
Sep 26, 2017 at 17:26

Such inferences are neither deductive (which assumes application of a valid inference rule) nor inductive (which assumes a generalization from a pattern of cases). This type of inference is called abductive, or "inference to the best explanation", see abductive reasoning. "Clearly" indicates that the explanation inferred is the best available. According to Harman, who coined the term "The inference to the best explanation" corresponds approximately to what others have called "abduction," the method of hypothesis," "hypothetic inference," "the method of elimination," "eliminative induction," and theoretical inference". Some authors still call any non-deductive reasoning "inductive", but such use is a bit archaic.

The form of reasoning in the OP example is this: A explains B; B, therefore A. If we try to translate this into classical logic by reducing "explains" to "implies" this amounts to concluding A from A → B and B. This form is the fallacy of affirming the consequent, which is of course deductively invalid, "where there is smoke there is fire" is the proverbial example. Nonetheless, in everyday reasoning, and even in science, we often rely on such inferences and consider them plausible, indeed we would not be able to figure out anything of substance without them. While deductively invalid, in proper contexts they produce hypotheses which have a good chance of being true, and are therefore relied on in planning behavior and in scientific methodology. Of course, as any hypotheses they may be refuted by subsequent evidence. The notion of abduction was introduced by Peirce, he credits Aristotle as inspiration:

"It is necessary to recognize three radically different kinds of arguments which I signalized in 1867... I suppose that the three were given by Aristotle in the Prior Analytics... Aristotle, in that chapter on Abduction, was even in that case evidently groping for that mode of inference which I call by the otherwise quite useless name of Abduction -- a word which is only employed in logic to translate the "apagoge" of that chapter." [second Prior Analytics, chapter 25].

The three modes of inference, and abduction in particular, featured in Peirce's attempt to codify the "logic of science", see SEP's Deduction, Induction, and Abduction in Peirce:

"Prior to about 1865, thinkers on logic commonly had divided arguments into two subclasses: the class of deductive arguments (a.k.a. necessary inferences) and the class of inductive arguments (a.k.a. probable inferences)... The most important extension Peirce made of his earliest views on what deduction, induction, and abduction involved was to integrate the three argument forms into his view of the systematic procedure for seeking truth that he called the “scientific method.”

Scientific method begins with abduction or hypothesis: because of some perhaps surprising or puzzling phenomenon, a conjecture or hypothesis is made about what actually is going on. This hypothesis should be such as to explain the surprising phenomenon, such as to render the phenomenon more or less a matter of course if the hypothesis should be true. Scientific method then proceeds to the stage of deduction: by means of necessary inferences, conclusions are drawn from the provisionally-adopted hypothesis about the obtaining of phenomena other than the surprising one that originally gave rise to the hypothesis. Conclusions are reached, that is to say, about other phenomena that must obtain if the hypothesis should actually be true. These other phenomena must be such that experimental tests can be performed whose results tell us whether the further phenomena do obtain or do not obtain. Finally, scientific method proceeds to the stage of induction: experiments are actually carried out in order to test the provisionally-adopted hypothesis by ascertaining whether the deduced results do or do not obtain."

It should be clear now that reading "A explains B" as merely "A implies B" is insufficient, the relation of implication is too weak, and may be accidental. It turned out surprisingly difficult to state precisely what "explains" amounts to beyond that, usually it is expected that it fall under some unifying account of phenomena, see Theories of Explanation. Even so, more than one explanation may be possible and abduction must select among them based on additional criteria, hence inference to the "best" explanation.

• cf. the Commens Peirce Dictionary on "abduction" for quotes where C.S. Peirce uses the term abduction. See also "hypothetic inference." Sep 19, 2017 at 0:29
• "abduction |əbˈdʌkʃn| noun [ mass noun ] 1 the action of forcibly taking someone away against their will: they organized the abduction of Mr Cordes on his way to the airport | [ count noun ] : abductions by armed men in plain clothes. • (in legal use) the illegal removal of a child from its parents or guardians. the man is also accused of the attempted abduction of another youngster. 2 Physiology the movement of a limb or other part away from the midline of the body, or from another part. The opposite of adduction (see adduct1)." (Apple Inc. Oxford Dictionary of English, 2.2.1 (156)) Sep 19, 2017 at 8:28
• @MarquardDirkPienaar - this is not the correct def: "the term abduction was coined by Charles Sanders Peirce in his work on the logic of science." Sep 19, 2017 at 11:51
• @MauroALLEGRANZA, do you mean the full definition in the Oxford Dictionary of English, which I gave above, exists because Peirce's definition was excluded and changed. I doubt you mean that. The etymology of "abduction" does not support that. It is interesting though because it seems cosmological views and ontological views are relevant at "abduction". etymonline.com/… Sep 19, 2017 at 12:09
• @MarquardDirkPienaar - Peirce gave a new meaning (in the philosophical context) to the old term "abduction". Now it is quite commonly used in the philosophy of science discussions. Sep 19, 2017 at 13:43

If the question is raised in an intro to philosophy course (like critical thinking or scientific reasoning), the answer should be that the above inference is an example of inductive logic. There are two kinds of inductive reasoning. One is generalization, as Conifold suggests. But there is also an inductive inference of John Stuart Mill whose purpose is to find the most plausible cause of an event or phenomenon. In his System of Logic: Ratiocinative and Inductive (1848), Mill offered five inductive inference rules: the method of agreement, the method of difference, the joint method of agreement and difference, the method of residues, and the method of concomitant variations.

So which method of induction is used in the above example: "John ate a strange plant in the forest and got sick. Clearly, the plant made John sick."? While the example needs some detail to be conclusive, I think the best candidate is the method of difference. We want to know the cause of John's illness. John was fine when he ate all the familiar plants (needed detail). This time however he ate a strange plant. Afterwards, John got sick. The only difference for him to be fine and to get sick is eating the strange plant. Therefore, the plant is the cause of his illness.

• Why do you suggest that in an intro class it should be classified as inductive? I think it's quite common to distinguish inductive from abductive inference, especially in intro classes. There is admittedly debate over whether abduction is a form of induction (or vice versa), I'm just curious why you think that an intro course calls for the Millian terminology and deciding in favor of counting abduction as a form of induction? Sep 19, 2017 at 16:07
• It's simply because I taught Mill's inductive logic in a scientific inference course, where most students majored in psychology or some sort of 'soft' science. At UCSD the course name is PHIL12. Sep 19, 2017 at 16:25
• fair enough. I had (mistakenly) thought you had reason to believe it was a pedagogically superior approach. Sep 19, 2017 at 16:29
• Whether abduction is a form of induction is a good question for phil graduate students, but for undergraduates with non-phil background, a lecturer has to be a little bit dogmatic, since otherwise, students get confused. Sep 19, 2017 at 16:32
• Agreed. I wasn't suggesting that be discussed. Just asking whether there was a pedagogical reason to present abduction as a form of induction rather than to present abduction as a distinct, third type of inference along the lines of "inference to the best explanation" (staying silent on whether that was a form of induction or vice versa). I agree that a bit of dogmatism is needed. Sep 19, 2017 at 20:10

Deductive thinking can exist when thinkers know, with a high probability, causal relationships within something, and use that knowledge, for example, when mechanics fix an engine or general practitioners diagnose illness. By investigating causality they can pinpoint the cause of a problem. If an engine is not firing, i.e., mechanics will, investigate parts, which usually cause firing, and identify working parts. If a part is found to be working the part is eliminated as not a cause of the problem. The procedure continues until a broken part is found. The investigation only takes place in the line of causes, which cause firing. The benefit in the case of machines is, due to knowledge of engines, all parts of engines do not have to be tested, when looking for the cause of engines, not firing.

Induction according to my comprehension is usually creative thinking, i.e. originating an idea for a new engine, which works differently than existing engines. It usually deals with the future. It would be interesting to see how others explain, especially, induction.

Deductive reasoning, when it is done right, is more certain than inductive reasoning.

• I'm afraid that all of your terminology here is rather uncommon. Deductive inference is essentially non-probabilistic and requires that the premises (if true) necessitate the truth of the conclusion. What is known and to what probability is irrelevant -- it's all about truth preservation. Inductive inference is the probabilistic one of the pair you discuss. It renders the conclusion likely to the degree that the sample size is representative of the whole class of entities under discussion. Nothing to do with creativity, except insofar as the conclusion isn't "contained" within the premises Sep 19, 2017 at 2:05
• @Dennis, as far as I remember the explanation and example for deduction was given in "Zen and the art of motorcycle maintenance". It was published in 1974 and initially 5 million copies were sold. "Nothing .. except", means creative doesn't it? Your explanation makes sense to me. How about putting your explanation in an answer, I will up vote it. Sep 19, 2017 at 5:55
• Creative conclusions are usually "contained" in premises, acknowledged by people reaching creative conclusions. Others who did not reach creative conclusions did not see all the premises. Deduction and induction are thus relative because it depends on who the thinkers are. Sep 19, 2017 at 6:13
• I should have qualified that the terminology is uncommon within academic philosophy and the study of logic. Much of philosophy's terminology has other, non-technical uses in everyday speech ("valid" being a chief example). I would add an answer but I think Conifold has already given a good answer, there's not much to add imho. Sep 19, 2017 at 7:12
• @Conifold used "abduction" in a way, which does not appear in the Oxford Dictionary of English. Is his use cosmological or ontological? Comparing it to the current Oxford definition, it looks ontological, because the current Oxford definition looks rather cosmological. Sep 19, 2017 at 8:43