Inductive Logic

It doesn’t give the same certainty that deductive arguments give us

Inductive arguments

  • For inductive arguments

    • The truth of the premises make the conclusion more probable than it otherwise would be.

    • The conclusion is not contained within the premises but follows from the premises for some other reason.

    • Inductive arguments are strong if all the premises support the conclusion in some way, and they are weak if the premises fail to provide that support.

      • Some inductive arguments can be “stronger” than others

    • Inductive arguments are cogent if they are strong and the premises are true.

Inductive arguments: examples

  • Many inductive arguments are based on assumptions about the human senses, e.g.:

    • I perceive this object as red

    • Therefore, this object emits or reflects light with a wavelength between approximately 625 and 740 nanometers

  • This argument makes the assumption that the human eye distinguishes different wavelengths of light and interprets them as colors, at least with some high degree of accuracy and probability.

  • Cogent arguments must be based on true (or very probably true) assumptions.

  • Many inductive arguments are based on assumptions about the reliability of nature, e.g.:

    • The sun has risen every day since the beginning of recorded history.

    • Therefore, the sun will rise tomorrow.

  • This argument makes the assumption that natural processes observed for long periods of time will continue to operate according to recognized laws, all things being equal.

Heuristics for good reasoning: Analogies

  • One very important type of argument is the argument from analogy.

    • Take two or more objects

    • Note their similarities

    • Conclude that they must have an additional similarity

  • Analogies are common in medicine and the legal world

    • “Because mice possess a genome similar to our own, if a medicine affects mice a certain way, it will likely affect humans in that way, as well”

  • One common kind of analogy is extrapolation: analogizing from the small-scale to the large scale

    • Cases of COVID-19 rose exponentially on campus in the first weeks of class

    • COnditions on campus will remain stable throughout the rest of the semester

    • Therefore, we can confidently assert that cases of COVID-19 will rise exponentially throughout the entirety of the semester

  • Is this argument strong? Is it cogent? What weakness does it have if any?

    • It’s weak

    • new people and new exposures

    • not consistently mixing new people at this rate for the whole semester

    • people drop

    • too many conditions that change as time goes on

Heuristics for good reasoning: Analogies

  • Decision procedure for creating strong analogies

    • Ask: what are the most important feature(s) of a given thing we’re trying to explain, or what features of a given thing are most pertinent to our argument?

    • Look for known processes/cases/arguments in which THESE FEATURE(S) plays the same role

    • Make sure there are few or no relevant differences

    • Analogize

Heuristics for good reasoning: Abduction

  • Abduction, or “inference to the best explanation” is one of the cornerstones of the scientific method

    • Consider all the explanations for a given fact

    • Rule out impossible or absurd explanations

    • Of the remaining explanations, choose the best one

  • For example: I can not find my keys

    • Consider all explanations: perhaps I misplaced them, perhaps my wife is hiding them, or perhaps someone snuck into my home and stole them without disturbing anything else

    • The last explanation is clearly ridiculous

    • My wife is unlikely to hide my keys

    • We are left with one best explanation, which we should accept

Abduction: what makes an explanation the “best” one?

  • It’s not always obvious what the best explanation is

    • Often, we jump to the first explanation we think of and believe that to be the best, without justified reason.

    • When we want is the most “likely” explanation - but what explanation is most likely will probably be quite context-dependent

  • Two general criteria

    • Simplicity parsimony (“Ockham’s razor”)

    • Coherence with established knowledge

Some general words on argumentation

  • Goal of argumentation is not winning — it’s truth

  • Philosophical argumentation proceeds best when two principles are kept in mind:

    • Charity: always assume that an author/speaker is offering the strongest possible argument for their position

    • Clarity: always present your and others’ arguments in as formally clear a manner as possible

      • Put them in a standard format

      • Alert your audience as to what general forms you are using

      • Singal how you would deal with any obvious objections