# Unproven premises leading to true conclusion imply valid premises

Suppose that we have a bunch of premises which are unproven but lead to a valid conclusion, how much of a leap of faith it is to assert that the premises can now be seen as valid?

I have said "a bunch of" so as to eliminate the coincidence effect. This on its own leads me to another question, is it possible in this case to disregard the possibility of coincidence?
In general, and if my first question has a positive answer, would an extensive number of premises nullify the coincidence possibility?
And if so, what would be considered as an extensive number?

• It would make more sense to plausibly infer one premise when it leads to "a bunch" of confirmed conclusions than the other way around, that is how science works. If one is allowed to multiply premises one can accommodate any conclusion whatsoever:"With four parameters I can fit an elephant, and with five I can make him wiggle his trunk", as von Neumann said. Not to mention that the "number of premises" is ill-defined, any number can be rolled into a single one by using conjunction, or a single one can be split into any number by using disjunction. Jun 30 '19 at 9:34
• You're mixing up terms. `valid conclusion` --> true conclusion? or valid argument? Jun 30 '19 at 10:07
• If the premises are true and the argument (i.e. the rules of logic used in the deduction) is valid, then the conclusion is true. Jun 30 '19 at 11:41
• The "proof direction" in deductive inference is from premises to conclusion. Jun 30 '19 at 13:20
• In empirical science we can assume hypotheses and derive testable conclusions from them. Then we check the conclusion against facts and if they agree we can say that the facts "support" the hypotheses. But we cannot assert that we have proved them: further tests may falsify them. See Popper. Jun 30 '19 at 13:22

## 3 Answers

Suppose our world stands still on the horn of a cow. That`s clearly a problematic assumption, at least under the light of scientific evidences proven during the last millenium. But this assumption implies that, once our cow moves its head, our world will get shaked like it does when an earthquake occurs. One can conclude legitimately just following this unrealistic assumption of world standing at the top of a cow that earthquakes are inevitable, and this conclusion is true. Does the truthfulness of conclusion verify the assumption? Clearly not in this case.

Most of the time, however, finding a set of assumptions that are 100% true is either imppossible, or it makes things unnecessarily complicated. Let´s take economic theory. Almost at all times economic models assume a kind of sociopathic agent who always tries to maximize her material wellbeing using whatever means are present to her. Is this assumption of narrow minded utility maximizer agent a reasonable assumption? Of course not, even I myself can disprove its validity since I´m currently wasting my time writing these lines over here. But theoratical conclusions that we can reach using that assumption approximate the observable reality well enough. Even though not all people are perfect utility maximizers at all times, at least a considerable portion of them actually are. In one of his great books, Essays in Positive Economics, Milton Friedman also affirms that unrealistic assumptions don`t make the conclusions less reliable:

Truly important and significant hypotheses will be found to have "assumptions" that are wildly inaccurate descriptive representations of reality, and, in general, the more significant the theory, the more unrealistic the assumptions (in this sense) (p. 14).

• Thank you for your answer!
– Luyw
Jun 30 '19 at 19:05

Here are two unproven premises:

1. Socrates is a cat
2. All cats are greek philosophers

from 1 and 2, it follows that Socrates is a greek philosopher, which we know to be true.

Therefore, can we say that propositions 1 and 2 are true ?

• Thank you armand!
– Luyw
Jul 2 '19 at 12:07
• Special prize for specially succinct answer😆 More seriously good counterexamples are as important to logic as sound deductions. Jul 5 '19 at 14:11

Consider one hundred premises from P1 to P100. Is that enough of a bunch? Suppose we know P100 is true. Now, as it happens, the following inference is perfectly valid:

P1 and P2 and ... and P99 and P100; therefore, P100

Yet, this definitely doesn't suggest to us that P1 to P99 are probably all true or even that most of them are true.

That we happen to know that P100 is true is of no use to infer anything about P1 to P99.

EDIT

Also, the following argument is valid:

Donald Trump is a non-existent Martian; All non-existent Martians are mortal; Therefore, Donald Trump is mortal.

I hope we know the conclusion "Donald Trump is mortal" is really true, but I don't expect any of the premises to be true at all.

And we could make literally an infinity of such arguments with the same valid conclusion.

• I had this as an afterthought. In fact, the more premises you have that lead to a true conclusion, the more likely each of them is to be false separately for the reason you explain. On the other hand, the more true conclusions you can deduce from one single unproven premise, the more likely it is that the premise is true. Jul 5 '19 at 14:45
• @armand The only premise showed to be true, possibly, is the conclusion itself if it happens to be also a premise as is P100 in my example. I'll add another example to reply to your suggestion here. Jul 5 '19 at 17:53