Note: Herewith several related comments on the role of “proof” in the contemporary natural and human sciences. A critical comment on the title of a recently-published book by A. Aczel — which carries the confusing title Why science does not disprove God (2014) — is also included. The first of my comment deals with what it is that “scientific activity” produces. The heading “Science does not prove — but only declares” summarises my conclusion. In brief, that the outcome of scientific inquiries are a series of declaration on our current knowledge about “our world” which together constitute a comprehensive representation — a momentarily authentic picture of what the world is like.
What is commonly understood by *submitting a proof* and its opposite, *submitting a disproof*? When someone submits a proof they are said to demonstrate to others how a conclusion they themself (privately) reached was obtained. More specifically, how they arrived at the conclusion by entirely logical means, and not by empirically demonstrations.
If they told us that they just “felt that the vase they had unearthed” was a Greek urn which had once contained the ashes of a fallen warrior, we would call it a “guess” but not a true discovery unless the claim was supported by much more evidence or provenance! If they “show” that something they had foretold had materialized, like that a gesture made towards heaven produced a hail of manna, that is not a proof, but only a demonstration: it shows that their prediction on this particular occasion worked! Such predictions were once made routinely by reputed “wise men” but none have been recorded reliably for the past few hundred years.
A proof, on the other hand, refers to a post-facto event which states that whatever was initially said about a matter followed logically from some earlier explicitly-cited assumptions. For example, that 2 of anything added to 3 results in 5 items. In this case there is no doubt about the existence of the numbers cited, or that the number 5 can be generated in a different ways. The assumptions may not be empirically true — often they are not! What we have here is a calculation which involves abstract, not empirically true events. Two goats standing in the meadow and three sheep grazing nearby make five animals. Contrast this to the claim made that “When I put a match to this spout of a bottle a flame will emerge”. The answer to the question “how is this possible?” will require, amongst others, a reference to specific, well-attested laws of chemistry, rules about what substances are flammable and which are not.
A proof, in short, refers to the outcome of clearly-stated logical operations. Such operations are traditionally performed only by humans — although many psychologists and biologists have argued that it is also found in some non-humans, but only in those species whose nervous system have similar features to ours, containing, for example, neural circuits, a hemispheric brain, cortex, areas which have become centres of control for specific outcomes or operations.
Much has been written and speculated about the relation between the brain as an cohesive organ, as a processor of information and how such information may eventuality translate into states of awareness and also of actions — but it is an ongoing, not a completed story — part of a book with many chapters of which only the first few have been written so far. The future, we predict, will surely offer many additional surprises, and these will be related to the fact that with time and much effort we may get to know more and more about the functional and structural properties of the brains of different species.
One enduring (and thus far unsolved) problem has been to account for corrections which are made by an individual member of a species as a result of their experiences in the past — and how this could be forwarded (transferred) to their descendents to facilitate the behaviour of unborn generations. Are there some aspects of our experiences which are coded so as to become transmittable from generation to generation, just as many bird-song do? The empirical answers to such questions will most likely emerge within the foreseeable future, but in the meantime we can only create increasingly better and superior questions and suppositions of what goes on within creatures which reflect changes in their daily lives, specifically how they come to predict some future events on the basis of their earlier experience or perhaps even by virtue of cross generational transmissions. I could imagine, for example, a mechanism whereby a set of experiences could be transmitted to several future generations so that traces of former experiences would wane and disappear. One may need to exclude carry-overs from the immediate past because these changes may only reflect temporary matters, which traditionally were covered by the term *habituations*, i.e. transitional intra-organic changes which left very few — or minimal enduring residues, for transfer to off springs.
When I state — as in the title of this blog — that “Science does not prove but only declare,” I mean that the fruits and outcomes of scientifically conducted investigations take the form of declarations which one has presented to oneself. Modern science is a communal activity whose traces are found in a group of cohorts and which usually demand that anyone who makes and accepts a new claim can and will defend it publicly in person — as at a scientific conference — or by circulating a documentary report of their investigations in a publicly available journal where it can be criticized by others!
One communicates one’s claim by issuing statements, which may contain abstract formulae that summarize both what one has done to secure the information, but also what one has concluded from such earlier work. It is a declaration of the truth as seen by oneself which is made publicly known so that it can be openly viewed and, if so deemed, criticized! The declarer admits that they could be mistaken about some or even all the summary conclusions presented, but hopes that little of what they claimed has to be withdrawn or revised as a result of criticism.
The popular statement that the “proof of the pudding lies in its eating” is therefore incorrect. The proof of an argument in particular lies in the correctness of its logical derivation, something which requires that the steps taken accord to well-stated rules. The rules predate investigations, research. One assumes that all the assumptions made in an extended argument are necessarily correct, and do not contradict other explicitly made arguments. To be correct therefore assumes that what a statement declares is independently defensible, and therefore does not depend on the correctness of an individual’s perception only. It is assumed to rely on the verification by everyone involved or concerned with the argument, that what has been claimed can also be independently supported by applying common method to the claim.
For example, several claims have been made throughout the last 1500 years that the shroud in which Jesus was wrapped after his body was taken from the cross — data which is not doubted by most — was subsequently found and is now available for public display and examination. However, each shroud so far examined (there have been several) has failed to stand up to all the tests applied, including tests of their reputed age. Thus the hypothesis that the original shroud had been found has not been supported, and cannot be affirmed with confidence, but seems to be based on a wish to believe that such a shroud exists.
Of course, such wishes have no permanent place in scientific investigations but have to be abandoned regardless of their origins. (I’m sure the priests in Egypt believed their stories of the origins of humanity, just as the early priests of Judaism believed in their, may I add, fanciful account of the origin of women! Evidence cited to support a “position” is often viewed as a distraction in such cases since nothing is stronger than the wish to believe.
My preference, therefore, has been to view each declaration in Science as a temporary, time-bound claim only. All these and similar claims are ultimately disputable — and are more than likely to be. The claims may therefore need amendment(s) or may de facto be discarded under the heading, “was of one-time interest because its claim accorded with other plausible pictures or representations available at the time.”
Foremost is the notion of a *research episode*, which I view as a prolonged and systematic inquiry into one or more well-articulated problems, and where each problem studied relates to some earlier research. There are many examples which could be cited, for instance the many cited in Hawkings A Brief History of Time (1988), but my own research was heavily influenced by two newcomers in the early 1950’s, by ethology (a form of studying animal behaviour: Niko Tinbergen, A Study of Instinct, 1950) and the study of operant behaviour as advocated by B.F. Skinner in his book The Behaviour of Organisms (1938).
The implication: science is more like a soft-cover book. A better analogy would be that science has the features of a loose-leaf file which is appropriately date stamped on every page. Its pages can be removed — but not trivially discarded. Continuity is an important factor in understanding!
Living Science is like a loose-leaf folder in which our latest insights into every aspect of Nature are temporarily stored. The folder is part of our font of knowledge and therefore contains all sorts of bric-a-brac, including recently acquired knowledge and items of information which have been handed down to us over generations. They are often treasured, mainly for that reason, not because of they have much truth-value.
This creates a highly correctable collection of items, not a book of ultimate truths. Our folder has inestimable value in a world which too often is haunted and harassed by self-righteous humans touting their own brands of Truths and Virtues.

Philosophy is not Science. Most philosophers are not scientists by inclination or training. Some may have studied science subjects at school or university; others may have backgrounds in the liberal arts or mathematics, or they may have just drifted into philosophical studies and later became totally absorbed in it. It was not always thus. In earlier times there were those who called themselves natural-philosophers because their primary interest was in the study of natural phenomena: physics, chemistry, botany, anatomy, whereas others were content to be grouped with theologians, or with students of language, the law, the classics or were clerks or politicians in their daily life.
Two years is a long time to get an answer to one’s mail but it often takes even longer to think through the implication of a counter-proposal or expansion to one’s ideas. That said, let me answer Sean (March 29, 2011) who suggested that one could view the divisions within science that take place over time, and with increasing frequency as well severity, a case of zooming. *Zooming* is not a common term applied to the expansion of disciplines, but is itself a neologism. It means that when all our knowledge is taken as a whole it is possible to focus on a section of it, zooming on a speck of this to the exclusion of all else. The effect is to give this section clarity whereas other matters become in-articulated, nebulous, even frozen for the time being.
During the past 75 years departments in major universities have increasingly divided or split into separate units, a phenomenon I term “fractionation”. Fractionation is not confined to the “mature” disciplines in the natural sciences, Physics, Chemistry, or Biology, but seems to apply generally.