Hypotheses as acts of the imagination.
Augustus De Morgan (1806 — 1871) was a British mathematician and logician. He formulated the well-known De Morgan’s laws and introduced the term “mathematical induction”.
De Morgan was influenced Sir William Rowan Hamilton and George Boole. His important work, Formal Logic (1847), developed — among other things — a mathematically precise syllogism.
More relevantly to this piece, De Morgan made contributions (even if neglected later) to the history of science and to explaining the nature of hypotheses.
Scientific Hypotheses and Induction
The word “hypothesis” comes from the ancient Greek word ὑπόθεσις, which literally (or etymologically) means “putting [or placing] under” [i.e., for later evaluation]. In this Greek sense, the word “hypothesis” is closely related to the word “supposition”. In everyday terms, a hypothesis is a provisional idea which will need to be evaluated, tested and/or scrutinised at some later point.
As for Augustus De Morgan.
De Morgan believed that hypothesis formation (see also hypothesis) is a creative act. Primarily, it relies on the scientist’s imagination just as much as it relies on logic, facts, observations or data.
(De Morgan even held this view — at least partly — about mathematical reasoning. As quoted in Robert Perceval Graves’ book, The Life of Sir William Rowan Hamilton (1889), De Morgan said: “The moving power of mathematical invention is not reasoning, but imagination.”)
The traditional (or common) view is that a hypothesis is the end result of some kind of inferential and observational process. A process according to which we arrive at a hypothesis which can then work as a basis for further inferences, reasonings or a full-blown scientific theory. (Basically, a scientific theory is very unlike a hypothesis.)
De Morgan, on the other hand, argued (if in circumlocutory 19th-century prose) that hypotheses come before observations, not after. He wrote:
“The question now is, not whether this or that hypothesis is better or worse to the pure thought, but whether it accords with observed phenomena in those consequences which can be shown necessarily to follow from it, if it be true.”
De Morgan is more explicit in his following words:
“Wrong hypotheses, rightly worked from, have produced more useful results than unguided observations.”
Despite the words above, it’s not clear if there can be “unguided observations” in the first place. That’s primarily because genuinely and completely unguided observations wouldn’t really (or actually) be… well, observations. That is, the observer would have literally nothing to go on in order to make his observations. An observational (as it were) blank slate (or tabula rasa) would simply be a stream-of-unrelated-experiences without either definite form or definite content.
To repeat: De Morgan believed that the hypothesis comes at the beginning of all observations and reasonings. (This chicken-and-egg scenario will be tackled in a moment.) This roughly means that his position isn’t the standard (or traditional) account of a hypothesis, as the following definition shows:
“A hypothesis is a proposed explanation for a phenomenon.”
The definition continues:
“Scientists generally base scientific hypotheses on previous observations that cannot satisfactorily be explained with the available scientific theories.”
The problem here is one of distinguishing which came first: the chicken or the egg. That’s because even if a hypothesis (as it were) bounces off “a phenomenon” or off “previous observations” (as in the definition above), then that phenomenon might itself have been singled out because of a previous hypothesis (or, more likely, previous hypotheses). And so on and so on.
In any case, if a hypothesis were a logical result of previous reasonings and previous observations, then according to deductive logic itself, that hypothesis would be at least partly “contained” in the sources of those logical reasonings and observations (i.e., even if the scientist — or whoever — didn’t know this or recognise it to be the case). This means that whatever is derived from such a set of empirical premises and observations must somehow have been there from the very beginning. In this, then, such a logic would be no different to mathematics.
Deductive logic (as already hinted at) has traditionally been seen as more or less the unpacking of what’s already contained in the premises, logical truths, principles, axioms, or laws that one begins one’s logical reasonings with. Or in Platonic terms: the whole of mathematics and deductive logic is already there waiting to be discovered. Thus as many mathematicians have said: if, in any given mathematical system, there is information contained in the derived theorems which isn’t implicitly (or explicitly) contained in the axioms, then the mathematician must have gone wrong somewhere.
A hypothesis, on the other hand, doesn’t articulate what’s already there. It often tells us that if thus and thus is the case, then such-and-such (i.e., the hypothesis) may explain it.
Again, if a hypothesis were just a logical result, then, in a strong sense, science would never have moved forward to new and interesting discoveries.
On the other hand, if the process which resulted in a hypothesis were an inductive inferential process, then the hypothesis would still not be strictly logical in nature. It would be a probable hypothesis (see inductive probability). That is, if induction — at least partly — deals with probabilities, then inductive logic isn’t what has been called a “true logic”. Traditionally, true logic was deemed to deal with truth, certainties and necessities, not with probabilities. And inductive inference may well use necessary and certain truths as its premises, and even the inferences found in deductive logic, but it doesn’t thereby become a deductive logic. That’s primarily because its main task is still to generalise from given phenomena and assert certain probabilities about such phenomena. Thus induction is more a case of if…then…, than it’s a case of this is derivable from that.
Finally, if a hypothesis were certain, necessary or even highly probable, then, by De Morgan’s lights, it wouldn’t thereby be a hypothesis.
No comments:
Post a Comment