Chapter 3, Tutorial 2
Argument Structures for Ampliative Reasoning

Informal, inductive argument is meant to cogently amplify the evidence we have. So, unlike a deduction that performs something of a calculation on premises. Informal thinking makes a best guess about what the evidence means. Let's reiterate and add a bit to the types of inductive, ampliative reasoning we say in tutorial one.

Inductive Argument Types

There are various sorts of informal, inductive arguments. Here are eight kinds. Exercise 3.2a asks you to do some "field work" and uncover some inductive argumentation. You will typically find that a number of these types of reasoning are used in interesting, real life reasoning.

  1. Causal Reasoning: The example of Chris-in-love is inference to a cause. The best -- but not the only -- interpretation of the data about Chris is that he is in love. Still, attributing causation can be very difficult. Here we make a guess about an emotional state given behavior.
         Often times there are correlations between types of events but no causal link. I'm told that there is a positive "correlation" between increased salaries for religious workers and increased consumption of alcohol. But this doesn't mean there's a causal relation. This does not mean priests of various sorts are responsible for the increase in drinking! Instead, both increases are the result of a common cause: increase in overall wealth in the economy.
         In any case, causal reasoning can move from premises about correlation to conclusions about causation, or a premise about a cause to a conclusion about an effect (I see a flash and conclude that a boom is about to occur) or from an effect to a cause (you hear the scratching noise and conclude that the cat is at the door).

  2. Argument from Authority: Very often are best reasons for believing something is expert testimony. Smoking causes cancer. I believe this but have never done the study. The experts tell us this is so. But once was the time when the tobacco industry paid "experts" to testify that there was no causal link but just a correlation. One needs to be careful to make sure that
    • spokespersons cited as authorities truly do know the field of knowledge in question, and
    • there are not other equally good authorities taking an opposed position.
    Like all inductive arguments, those from authority offer no guarantee that their conclusion is true. But, if the authority cited is a good one, and there is no other evidence to the contrary, then the conclusion is likely true.

  3. Generalization: One of the most common sorts of inductive argument is from particular cases to a more universal statement about all members of a group. For example, one may notice that each and everyone you've contacted in PHL 102 thinks that symbolization of 4.5 is difficult. Then one might want to conclude that 4.5 is difficult for everyone.
          But be careful. It may be that your contacts only come from the postings. It could be that there are people finding 4.5 easy and not bothering to post. When one generalizes from a "sample", one needs to be careful that the sample is a good representation of the whole group. (So, we ask for a "representative sample" when generalizing.)

  4. Statistical Generalization: Sometimes the generalization is not universal. Instead of saying "everyone finds 4.5 difficult", one might conclude that most people do. A more sophisticated sampling, e.g., in election polling, will sample from a big group and conclude that x% of voters will vote for y. Again, one needs to be very careful that that the generalization be based on a sample that is representative of the whole group being portrayed!

  5. Statistical Inference: This sort of reasoning moves from evidence about a group, often a very large group, to a conclusion about an individual or another group. Often the groups are explicitly described in statistical terms: "90% of my group got an A" or "most US citizens distrust tyranny". Two important types of statistical inference are treated separately below: Arguments from Analogy and Predictions. In all cases of statistical inference, generalizations about groups are applied to make conclusions about particular individuals or particular groups of individuals. Such reasoning is the reverse of generalization.
         Often, we start have statistical information about a group and make an inference about particular members or subclasses. Perhaps it's a given that 37% of students at O.U. are transfer students from other universities. Then, I can expect that some of my students will be transfer students. But because my class is small and may not be an average grouping I would not jump to the conclusion that 37% of the class are transfers. In any case, the study of statistical inference of this sort -- from percentages in a whole to particular sample class -- is as tricky as statistical generalization.

  6. Argument by Analogy: Attempts to show a conclusion that some thing X has a quality q given that similar things Y, Z, etc. all have quality q. (Perhaps I notice that you don't really like doing truth tables, "boring" you call them, so, I conclude that like other people who have had that reaction, you will prefer doing formal derivations because they present a little strategic challenge.) So, an argument from analogy is be a special case of a statistical inference to a particular. For an argument from analogy to be a good one, certain considerations must hold.
    1. Number of instances. (How many analogues X, Y are there? The more the better for the quality of the inference.)
    2. Instance variety. (If we are to generalize from a number of analogues, the better reasoning includes variety of instances supporting the conclusion. The variety indicates that our individual X is less likely to be completely different from Y, Z, etc.)
    3. Number of similarities. (The more the better.)
    4. Relevance. (Of greatest importance: the similarities cited between X and Y, Z etc. should be relevant to q.)
    5. Number of dissimilarities. (These, if relevant, can undermine the argument.)
    6. Modesty of conclusion. (The conclusion about q should not be too specific. We cannot expect X to be exactly like Y, Z, etc. just because it bears some similarities.)

  7. Prediction: From information about what has happened in times past, we make an inference to the future. So, predictions are a type of generalization or statistical generalization.

All argument by these informal, inductive means is holistic. One attempts to render the best all-things-considered judgment. One might call this the best account or best interpretation of the data. Sometimes this is called "abductive" thinking = inference to the best explanation. But I think that "best interpretation" is more general. So, when rendering a conclusion, it may be best to have an 8th, overall category:

  1. Best Overall Interpretation of the Evidence: But this is to say very little. To give an theory of interpretation would involve something like a theory of how to do science and detective work together. That is not possible, at least not from this author.
          So, 8 in not the preferred characterization of reasoning: We will try first to analyze a bit with 1 - 7.Sometimes we can only say that "on balance" the best conclusion is C. It is usually best, though, to be able to describe and analyze this weighing of the evidence in terms of 1 through 7. And only use 8 when we are confident that nothing we know is left out.