RoR: Forum

The reason that a single instance, in some cases, is sufficient for a complete induction is because it refutes: either a contradiction of the proposed hypothesis (thereby proving the hypothesis true via reduction ad absurdum*) or a sole contrary to the proposed hypothesis.

Maybe, but I don't see how your elephant-flea example fits.

I offer this. Suppose a lot is known about X's. A new fact F about one X is discovered, F is strongly connected to other facts about X's, and F implies R. Inductively then F implies R in all cases.

I offer the discovery of isotopes as an example. (Isotopes are variants of a particular chemical element such that, while all isotopes of a given element share the same number of protons and electrons, each isotope differs from the others in its number of neutrons.) Many decades ago scientists were puzzled that the atomic weights of some elements were not integer values. Particularly puzzling was chlorine's atomic weight of 35.45. Then it was discovered to have two stable isotopes that explained the non-integer atomic weight (link). That immediately gave a sound explanation of non-integer atomic weights for all other elements as well.

I wonder what an anti-inductionist and champion of falsification would say about this example. Deny that induction exists? Deny that it is induction? Test every other element to try to falsify that isotopes explain atomic weights? :-)
(Edited by Merlin Jetton on 7/15, 3:16am)

Post 21

Sunday, July 14, 2013 - 4:46pm

Merlin,

A problem I have with the isotope generalization is that it does not have to be true (i.e., it's empirically falsifiable). The reason I like the elephant-flea generalization is that it has to be true -- future empirical investigation will reveal that you have to change the context in order to escape the necessity of the generalization, as is. An example might include putting fleas into an oxygen tank -- so that they could breathe even if their size increases dramatically (something which is, normally, impossible).

Ed

Post 22

Sunday, July 14, 2013 - 10:39pm

We all have our areas of interest. I just re-read The Decipherment of Linear B by John Chadwick. On the one hand, it could not have been done without all of what is commonly called "induction" but the insight was intuitive, beyond the accumulated evidence -- which in fact had been overlooked by other scholars.

However, that said, verification, validation, and proof, came from the accumulation of just such niggling little data points.

Induction is "problem" only if you expect all of human experience to be explained in twenty-five words or less.

Post 23

Monday, July 15, 2013 - 3:14am

Ed, I didn't see your elephant-flea example as "a single instance sufficient for a complete induction", i.e. "an inference from one to all".

Post 24

Wednesday, July 17, 2013 - 6:06pm

Merlin,

The single instance comes from the counter-factual thought-experiment. In your imagination, you can go ahead and try to imagine just one elephant smaller than a flea (or just one flea bigger than an elephant). Analysis of flea and elephant nature, however, limit the absolute size that either of them could ever become. So, in just imagining a single case -- a recognizing the contradiction in the imagination (making it not just imagination, but fantasy) -- you can go ahead and generalize to the entire species.

It's kind of a reverse-engineered induction, but you do use a single instance of one of your perceptual powers of awareness (i.e., your imagination) to arrive at the generalization.

Ed

Post 25

Thursday, July 18, 2013 - 5:49am

Ed, your elephant-flea example seems more like deduction to me.

Post 26

Thursday, July 18, 2013 - 6:29am

Merlin is right. Ed is wrong.

We have all written about this at length. My two posts on my blog are nice (I think), but Merlin and Rowlands here were more productive, more positive. I only criticiized and praised David Harriman's The Logical Leap: Induction in Physics, a book we all know inside and out.

The Supernova of 1054 was an excellent opportunity for "the miracle of abduction" if such mentalism were what Ed claims it to be. No one had an answer or a theory or a fact. All we had was an observation. It was astonishing -- and ignored as an inexplicable event.

Now, we are having other discussions on induction in the "Popper" topics in Dissent. The radical claim from Elliiot Temple (icting Popper) is that induction does not exist at all, that people come to conclusions via other methods entirely. He never answered me on Stonehenge, a momument to the productive success of the inductive process.

We do, indeed, have the ability to generalize from a single instance. Most often, that produces superstitions. Sometimes those false beliefs keep us alive long enough to have children.

Post 27

Thursday, July 18, 2013 - 5:48pm

Merlin,

Ed, your elephant-flea example seems more like deduction to me.

Yes, I know. It is like a deduction regarding empirical things -- a limitation on the kinds of things that you will experience now or even in the future. A similar question could be asked that, if some fire is hotter than ice, is all fire hotter than ice? Will fire always be hotter than ice?

The answer will involve only looking at one fire (and at one ice cube) -- and then generalizing to all fire and to all ice cubes from there.

Ed

Post 28

Thursday, July 25, 2013 - 7:23pm

To be coy, it is like an ampliative deduction -- a deduction that transcends experience.

Ed

Post 29

Monday, September 2, 2013 - 9:08am

When Induction Was About Concepts is by John McCaskey. He says that what was meant by induction has changed over the centuries. There is a link to a draft here. The article is scheduled to appear in a book next year, Concepts, Induction, and the Growth of Scientific Knowledge.
(Edited by Merlin Jetton on 9/02, 9:16am)

Post 30

Monday, September 2, 2013 - 1:34pm

Merlin,

This will be a good read, when finalized. From the link:

The first part of this paper summarizes the history of induction. The second part explores three cases in the history of science where an inductive inquiry concluded with universal statements that were true by definition. The statements were both true by definition and true by induction.

This is sort of like what I was saying. It is almost by-definition true that fire is hotter than ice (even fire in the future, or in far-away lands never visited before by humans), or that elephants are bigger than fleas (even elephants in the future, etc.) -- even though you have to engage in generalizing from particular instances (you have to engage in induction) in order to arrive at the truth of the matter.

Ed

Post 31

Monday, September 2, 2013 - 5:26pm

Ed, Ice is well defined: solid H2O. But fire isn't... Do you mean oxidation? Do you mean oxidation particularly by oxygen (you can oxidize with other elements too)? You can increase ice's pressure, and its melting point will increase, increase the pressure high enough that it stays solid even at the temperature that pure hydrogen gas burns in atmospheric (20%) oxygen: H2 + 2O2 -> 2H2O.

Post 32

Monday, September 2, 2013 - 5:50pm

Dean,

As an former scientist, I'll look into it. Specifically, I will look into 2 things:

1) whether it is imaginable for ice as we know it to be hotter than fire as we know it
2) whether it is acceptable/relevant to think in those terms

Sometimes, in your mind's eye, you can envision contradictions to things -- but sometimes it's dishonest to do that (as when it involves dropping context, etc).

Ed

Post 33

Monday, September 2, 2013 - 8:25pm

Dean,

Good question. When I said "fire" I meant "organic-fuel" so that a fuel is organic (e.g., methane, propane, etc.) and I meant that it is getting combined with oxygen. The lower-limit temperature of such a thing is at the tip of a flame, and is about 300 degrees C (~570 degrees F). Temperatures rise dramatically as you go into the body of the flame. Also, there seems to be a shaky line of reasoning in your example of pressurized ice and hydrogen fuel.

It would appear, at first glance, that on the one hand (with the ice), you are asking for a lot of atmospheric pressure -- but I am not so sure that you could carry over that kind of pressure to the other side of the ledger, and still witness the burning of hydrogen (at room temperature). So, making the assumption that you have to witness both things in the same system (e.g., either in your back yard, in a pressure chamber in a lab, on the surface of the moon, at the bottom of the ocean, etc.), I'm pretty sure that it wouldn't hold up.

Incidentally, if you take "ice" to mean any substance that hasn't yet melted, then tungsten is "ice" until about 3410 degrees C (6170 degrees F). This means that you can have something that is much hotter than fire, but which is still not even melting, let alone boiling.

Ed

(Edited by Ed Thompson on 9/02, 8:28pm)

Post 34

Tuesday, September 3, 2013 - 9:06am

Can induction mislead? Yes.

Does induction always mislead? No.

Can induction be useful? Yes.

Is induction always useful? No.

Is the alternative question "What never misleads and is always useful?"

Or is it, "What seldom misleads and is often useful?"

Suppose we had a scoreboard, and kept score: "Induction has mislead in Xi instances, has been useful in Yi instances, whereas Deduction has mislead in Xd instances and has been useful in Yd instances."

Would examining that scoreboard and reaching a conclusion about the relative efficacy of induction over deduction not itself be an example of "Some Swans are White?"

If so, then 'uh-oh...'

regards,
Fred

Post 35

Wednesday, September 4, 2013 - 5:19am

Merlin wrote: "When Induction Was About Concepts is by John McCaskey. He says that what was meant by induction has changed over the centuries."

The word "experiment" also meant an _observation_ in earlier times, not just a casual looking about while on a walk, but a purposeful investigation, such as Aristotle's embryology of the chick. Today, our definition of experiment is narrower.

Ed and DMG went around on fire and ice.

I have a banknote here from Iceland that celebrates their historic literacy. It shows people indoors reading. They are wearing mittens. Here in Austin, it is still about 100F outside and we turn on the air conditioning when it gets to 85 inside. That is the melting point of gallium. As I understand it, Ed wants to leap from his own common experiences to universal truths and, like Dean, I hesitate to do that.

Also, I found it curious that Ed called himself a "former scientist." I understand that he meant only that his job title has changed, but, really, to me, it is like the way that Marines feel about having been in the Corps. When do you stop being a scientist?
(Edited by Michael E. Marotta on 9/04, 5:22am)

Post 36

Saturday, September 7, 2013 - 8:57am

Mike,

All I was saying is that I used to perform science in a lab as part of my daily routine -- but that now I merely philosophize about science, almost by-definition the science performed by others. What's funny is that you claim I'm too quick to take personal experience and generalize all the way up to a universal truth, but here and now, that is precisely what you are doing (e.g., "When do you stop being a scientist?") and it is precisely what I am refraining from doing.

Go figure.

Ed

Post 37

Wednesday, September 11, 2013 - 1:55am

The two arguments against induction are 1- circular reasoning ala David Hume and 2-infinite regress ala Sextus Empiricus (Popper wrongly attributes this position to Hume.) Both are basically the dictionary fallacy that everything is defined by everything else in a soup of floating abstractions - when in fact things are defined either by direct reference to what you can observe in reality ("That, my child, is a star") or by reference to lower-level concepts that eventually resolve to direct references to reality.

On Popper and induction: He doesn't quite "solve" Hume's problem in the realm of science; he merely does an end-run around it by claiming that induction is not needed/ does not have any cognitive status/irrelevant. Basically universal scientific theories can be corroborated without appealing to induction but if you follow Hume's position consistently then that is not feasible. My impression is that he was just a confused post- Kantian mess.
(Edited by Michael Philip on 9/11, 4:03am)

Post 38

Saturday, September 21, 2013 - 5:55am

Here is a recent book about Aristotle's account of induction.

Post 39

Tuesday, October 1, 2013 - 4:36am