Home > Andre Ariew, Lectures, Seth Kurtenbach > Lecture 10/11: IBE

Lecture 10/11: IBE

We looked at a non-deductive argument technique called “inference to the best explanation” (IBE).  Gregor Mendel’s famous experiments on peas are great examples of IBE.

Gregor Mendel (19th century)
Discoverer of GENES although, he never saw any?

Step 1 the experiment:
pea plants (what I’m about to say isn’t necessarily accurate, but captures the basic ideas.)
————-

Pea Variations:

purple vs. white petals.
smooth vs. wrinkled peas
tall vs. short stems

To begin, Mendel identifies a particular trait on which to experiment.  He breeds each purple plant with a white plant, and gets:

generation 1: (purple vs. white petals)
all purple petals.

Thus, because he has a large, unbiased sample size, he concludes that every time you breed a purple pea plant with a white pea plant, you get a purple pea plant.  Next, he breeds the members of generation 1 with each other, and gets:

generation 2: selfed the purple plants.
3:1 purple to white petals.

Time to get your science on!  Mendel is freaking out, wondering, “How did the white petals return?  Are they ghosts?” (no citation available).    From all purple petal (people eaters) in generation 1, a ratio of 3:1 purple to white resulted.  Again, due to his large unbiased sample size, he concludes the general claim:  Every time you mix (what we now call ‘heterozygous’) pea plants with other heterozygous pea plants, you get a ratio of 3:1 on the traits.

Step 2: asks “why do I get 3:1 ratios?”
hypothesis (H1): suppose transmission ranges over particles (suppose there are genes) and they obey laws (L).
hypothesis (H2): traits in offspring are the result of a blending process of the parents’ traits.
[which hypothesis best explains what I just saw? i.e. 3:1 ratios]?

What sort of inference did Mendel do?

Deduction (nope, not deduction).

Ratio of purple to white is 3:1
—–
Therefore, there are genes that obey L.

that is akin to arguing as follows:

O: lock is broken, lots of valuable in your room are missing.

H: I was robbed!             [invalid]

Deduction, take 2:

(1) If there are genes and they obey L, then I
would expect to see 3:1 ratios.
(2) I see 3:1 ratios.
(3) Therefore, there are genes and they obey
L.

if p then q
q
therefore, p.
——–
Bahhhh, Invalid.

Deduction, take 3

Modus tollens

if p then q
~q
Therefore, ~p

(1) If there are genes and they obey L, then I
would expect to see 3:1 ratios.
(2) I do not see 3:1 ratios.
(3) Therefore, there are no genes that obey L.

Whoa, that can’t be right.  Mendel’s conclusion was that there ARE genes that obey L.

Is it induction?

While maybe the discovery of 3:1 ratios in crosses of pea plants is an example of induction, the discovery of GENES is not based on induction. Why? Because he didn’t observe any.

“postulating unobservables”: proposing the existence of something that has not been observed, or cannot be observed directly.
• deduction can’t do that.
• induction can’t do that.
• inference to the best explanation can.

See how inference to the best explanation
(IBE) works:

Step 1, mundane example.
O: lock is broken, lots of valuable in your room are missing.
H: I was robbed!

If H is true then O is likely to be true.

Strength of an inference to the best
explanation is how likely the observation is
given the truth of the hypothesis.

H1: I was robbed!
H2: the cops raided your place!
H3: your friend played a joke on you!

If H2 were true, then is O likely?
If H3 were true, then is O likely?
If H1 were true, then is O likely?

H1 is the best explanation for O.

Step 2: Mendel revisited.

O: 3:1 ratios of dominant to recessive features (purple vs. white petals, tall vs. short
plants, etc.).

H1: there are genes and they obey L
H2: Blending theory (like paint).

If H1 were true, is O is likely?
If H2 were true, is O likely?

H1 is a better inference than H2 given O.

So, Mendel is using the IBE, and IBE does some cool stuff, which we’ll learn about in the next lecture post.

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