All other propositions are contingent. For example, it is not necessarily true that your treatment should be a cure for cancer of the albondigas yet it might be contingently true that it does. It is not necessarily true because there is no chain of argument, as there is for (say) a mathematical proof, that lands on indubitable axioms which taken as a whole proves that it cannot be other than that your treatment cures.
Here is an example from Lewis Carroll. It is contingently true that C = “Some chickens are creatures understanding French” if we accept as true for the sake of argument the (compound) proposition “All cats are creatures understanding French and some chickens are cats.” Our C is not, however, necessarily true because the premises which we assumed true are not true in fact. That means the chain of argument eventually leads to a falsity (no chickens are cats).
Leading to an uncertainty would amount to the same thing, in the sense that we would know we are dealing with a contingent proposition. Thus “working”, scientific, and observational propositions are uncertain and contingent.
A corollary to this is that a contingent truth is easily transformed into a contingent falsity or into a proposition which is uncertain. Keep C above and change the premises/evidence to “No cats are creatures understanding French and all chickens are cats” then it is contingently false that “Some chickens are creatures understanding French.” (Homework: why the two modifications?)
It should be obvious how to make any contingent proposition true, false, or in between by a simple choice of evidence. Since the evidence of contingent statements is rarely universally agreed upon, it should come as no surprise that disagreements can always exist about the truth or uncertainty of contingent propositions.
The real difficulty is in failing to monitor our language and the resultant over-confidence. We often speak loosely of contingent propositions, that they are “true” or “false” or “everybody knows that…” These are always strictly mistakes; but in everyday speech the consequences are trivial or insignificant. These are the “true enoughs” or propositions which have a chain of evidence sufficiently strong that they may as well be necessarily true, but aren’t quite: “I’m reading these words on an electronic device” (you may be deceived), “We’re having hamburgers for dinner,” “My car is in the driveway,” “Mars is the fourth planet from the sun,” and so forth almost endlessly.
But there are other examples much farther from true, most of which occur in politics, the edges of science, popular morality, etc. Example: “It is beyond doubt that ‘Mankind is causing harmful climate change.'” The speaker of this evidently has premises in mind which, if accepted, leads to the contingent truth “Mankind is causing harmful climate change.” What the speaker doesn’t realize is that his evidence does not have to be accepted, indeed unequivocally cannot be, for his opponent can supply different evidence which makes the proposition close to false.
Yet both sides argue about the probability the proposition is true—“95%!” “10%!”—forgetting the real battle is over the evidence. Because once the evidence is settled and agreed upon by all, the probability the proposition is true follows deductively (it may not, of course, be a number).
Short recap, since this subject is not easy. Any proposition depends for its degree of truth on specified evidence, or premises. Anybody is free to supply or change these (for a fixed proposition of interest). Even “1 + 1” does not have to equal 2 conditioned on premises other than the normal ones. Yet for some propositions (like “1+1=2”), called necessary truths, there is a chain of evidence which is obviously correct and not “substitutable” and which, taken as a whole, shows that the proposition must be true, that it cannot be false or in-between.
Contingent propositions, which are most in life, do not have a chain of evidence which proves the proposition of interest is necessarily true or false. Contingent propositions may, like necessary truths, have a chain of evidence on which everybody agrees but which only show the proposition has some non-extreme probability (which may be a number or interval or no number at all). Sometimes truth is denied us. This is Tough Luck.
On the other hand, the largest class of contingent propositions have no premises on which all agree. Hence disputes, acrimony, indigestion. But there are usually clues. Evidence accepted for one proposition may also figure as evidence for a second and third proposition, which themselves have significant support. This makes it more likely the evidence for the first proposition will be accepted, as long as the propositions taken together are said to be in a “class.” Susan Haack thus likens our knowledge to an enormous crossword puzzle, where entries have to make sense in more than one direction—but where some of the clues are missing! More on this another day.
So what does all this have to do with the Bobs and cancer and of the albondigas? Everything.
Matt:
I’m sure you’ve encoundered over the years the old saw that, “I know that 50% of my advertising budget is a waste. I just don’t know which half.”
Given your stated desire to get as much work for yourself as possible, suppose the CEO of a large retail chain wanted to engage you to determine what parts of their advertising budget were effective and which were not, would you take the engagement? How would you approach it?
I recall Dick van Dyke once memorably demonstrated that 1+1=11 which, under the operation of string concatenation, it is. Indubitably.
Mike B,
Excellent question, as always. Answer is “It depends.” The question is too large: that is to say, I don’t know how I’d answer until I heard a lot more details about the situation. However, it may be possible, and I have done this in the past, for me to say “What you want cannot be answered. I’d love to take your money, but it would be wasted.”
The challenge with such honesty Herr Briggs is that the honorariums become further and further apart.
The correct answer is always “YES! We can calculate that for you” followed with a contract with lots of verbiage to remove any liability…
Okay, how about this: We currently spend about $10 million per year putting weekly fliers in the local newspapers of the 40 largest markets in the country. If we just stopped, would we loose more than $10 million in sales?
Or put another way, is there a way for us to determine, through experimentation, that would we lose more sales than the cost savings if we stopped the inserts?
Do Godel’s ideas have any bearing on this Prof Briggs?
My understanding is that the truth and falsity of many proofs cannot be found in a set of contingent premises.
I admit my understanding of Godel is weak, and I am not sure how esoteric his ideas are, but they seem quite corrosive to ideas that all truths can be packed up into axiom and train of logic conclusions.
Your thoughts on this would be most interesting.
Mike B,
Even better. Do you mind I hold off answering until Part IV? It leads right into it. But sure, it’s possible.
Chinahand,
Yes. You can always have a proposition for which no set of evidence (premises) exist to show the proposition is true.
Briggs, you show what is wrong. What is right? Can experiments be used to answer questions in healthcare/marketing etc.? If not, how do you propose we find answers to healthcare/marketing questions?
Cheers
Francsois
What think you of Herman Kahn’s “Orders of Agreement”?
http://www.jerrypournelle.com/mail/2008/Q2/mail520.html#Kahn
Rich,
my computer operates under the principle that 1+1=10.
Sure, I can hold off.
BTW, any particular reason you don’t go by W. Matthew Briggs? Would look better on certificates, honoraria, etc. Is it because of your stint in the military? (my dad was a “middle name” guy, except for the two years he was in the army — “too hard to explain” he said).
But just another thought on this thing. Even if we cannot, for philisophical reasons, give a precisely knowable answer to some of these questions I’ve posed, surely that can’t mean we’re better off throwing up our hands and relying on organizational inertia and superstition to guide decision making? As long as we understand the limitations of our results, we can certainly learn something useful about how to (in this case) effectively use resources.
Mike B
What are “certificates” and “honoraria”?
It’s my mom’s doing. Too many Bills and Willies in the family, but tradition demands firstborn son is William. My first is William James, and I can him James (his friends call him Will).
No need to throw up hands. Your questions can be answered, though perhaps with less confidence than previously thought.
Francsois,
But we are being positive! One step at a time.
Rod,
I’ll take a look.
The primary purpose of language is to think. It’s secondary purpose is to communicate.
Communication is not necessary for effective thinking, but thinking is necessary to effectively communicate.
Think about it.
“The primary purpose of language is to think. ”
Well then I’ve gotten it wrong my whole life. I think in images not sounds or words. The only time I use language is when I’m communicating or thinking about communicating. I guess my lack of constant practice shows.