Week 2 - Induction vs Deduction

This week we are studying deductive and inductive reasoning and the role they play in Scientific research. I pasted the lecture notes below. This is going to be the only reading for this week. It is a very short reading so please do it. A PDF version is uploaded to filepost and the link to the file is:

Week2: Deduction_vs_Induction.pdf

They are the same, except for two graphs I put on the PDF version. You can use either version. That is, if you prefer to read the blog you do not have to download and print. However, it is a good idea to download the pdf file and archive it so that you can easily access it when you are working for the assignments later in the semester.

I will see you all next week.

IREU 150 Essential Academic Skills for International Relations

Fall 2012

Week 2 – Induction & Deduction

Notes prepared by Eser Sekercioğlu

In scicentific research, as in logic, we often refer to the two broad methods of reasoning as the deductive and inductive approaches. We will start with the way deduction and induction are defined in logic, then we will discuss how the scientific method relates to both reasoning methods.

Inductive reasoning

Common example:

Observation: All left-handed people I know are creative

Murtaza is left-handed

Generalization: Murtaza is creative.

This is the common structure of inductive reasoning about . If all left-handed people I have seen are creative then the next left-handed person I meet must be creative too. But, this conclusion about Murtaza can be applied to all left handed people that I have not met yet. So, the general form of the inductive reasoning becomes:

Observation: All left-handed people we have tested were found to be creative

Generalization: All-left handed people are creative.

Induction is based on regularities in experience and observation. If we observe and/or experience something with increasing regularity our brain tells us (even without our conscious mind noticing it) that this observation is likely to repeat itself. And when the observation is about a relationship between two concepts or events then whenever we observe one of the connected parts (a left handed person) we expect to observe the other connected part (being creative).

Inductive reasoning can be extended to include probabilistic statements as well.

Probabilistic statements might be about generalizations to a whole class/population, for example

                Observation: 85 % of people we interviewed were right-handed

                Generalization: 85 % of the population is right-handed

Or, observations can be used to make generalizations about a single case. (this is called statistical syllogism)

                Observation:  95 % of left-footed football players are also left-handed

                Murtaza is a left-footed football player.

Generalization: There is a 95% chance that

               

Induction is a bottom-up process. We start with gathering observations and when the regularity in our observations reach a certain level we generalize to the population/or class of things we are investigating. For a long time (and some philosophers still insist to believe in this) science was thought to be inductive. Because scientist collected data, analyzed data, made generalizations, classifications etc. many philosopher of science pictured the scientific research process as an inductive practice.

And because of this scientific method in general was criticized. We will discuss this a little later but we must first turn our attention to deduction.

Deduction

Deduction uses the reverse process as induction.  In the process of induction, you begin with some data, and then determine what general conclusion(s) can logically be derived from those data. Whereas  In the process of deduction, you begin with some statements, called 'premises', that are assumed to be true, you then determine what else would have to be true if the premises are true. In logic the most often given example to deductive reasoning is:

Premise: All men are mortal

Observation: Socrates is a man

Conclusion: Socrates is mortal

In the perfect world of logic premises are always true or they are unquestioned. Therefore conclusions based on deductive reasoning are also always true. Similarly in mathematics many theorems are derived from axioms which are accepted to be true. For example all of planar geometry (all geometry topics you studied in high school) are derived from Euclid’s five axioms. Deduction offers absolute proof. But everything depends on the truth of the promises. If, for example, Euclid’s axioms were wrong all geometry would collapse. If we were to find an immortal man, then we can no longer conclude that Socrates is mortal.

We can symbolize deduction in logic very simply as follows:

 P à Q (this reads: If P then Q)

P (P is observed)

àQ (reads: then Q. This means that Q must be observed as well)

In normal grammar: If a condition P is satisfied then the result Q must be observed. We observe that condition P is observed, then we must also observe Q.

Deductive arguments are evaluated for their validity and soundness. A deductive argument can be logically valid but not sound.

Every left-handed person is a genius.                                                                                    

                Murtaza is left-handed

                Murtaza is a genius.

This argument is valid. If the premise that all left-handed persons are geniuses is true than Murtaza must really be a genius. However, we know that the premise is not true. Therefore the conclusion may or may not be true. Therefore the argument above is not sound.

Applied to scientific inquiry, deduction is a top-down approach.  We might begin with thinking up a theory about our topic of interest. We then narrow that down into more specific hypotheses that we can test. We narrow down even further when we collect observations to address the hypotheses. This ultimately leads us to be able to test the hypotheses with specific data -- a confirmation (or not) of our original theories. In other words, deductive reasoning works from the more general to the more specific.

These two methods of reasoning have a very different "feel" to them when you're conducting research. Inductive reasoning, by its very nature, is more open-ended and exploratory, especially at the beginning. Deductive reasoning is more narrow in nature and is concerned with testing or confirming hypotheses. Even though a particular study may look like it's purely deductive (e.g., an experiment designed to test the hypothesized effects of some treatment on some outcome), most social research involves both inductive and deductive reasoning processes at some time in the project. In fact, it doesn't take a rocket scientist to see that we could assemble the two graphs above into a single circular one that continually cycles from theories down to observations and back up again to theories. Even in the most constrained experiment, the researchers may observe patterns in the data that lead them to develop new theories.