How do philosophers of various schools* explain the difference (if any) between demonstration and mere description? Are they synonymous, or are they different? How so?

My first impressions:
To demonstrate, one needs to know causes, but to describe, one needn't know causes. However, it seems description can lead to knowledge of causes, and thus the distinction between demonstration and description is less clear.

*(e.g., Kantians, Thomists, Aristotelians, Cartesians, positivists, nominalists, pragmatists, et al.)

  • It doesn't seem to apply to the same objects. You demonstrate a theorem (an abstract entity) and you describe concrete objects. You don't demonstrate from causes, but from premises. Jul 18, 2015 at 7:00
  • @quen_tin I don't think there's universal consensus among all the philosophical schools on what you say. For example: Mathematical theorems are not all that are demonstrable. Physics makes valid demonstrations from causes (not from abstract entities).
    – Geremia
    Jul 20, 2015 at 8:04
  • physicists demonstrate conclusions from physical premises (assuming laws of nature etc.). They're mathematical demonstrations like theorems. They don't "demonstrate" from causes. It's a question of vocabulary, not philosophical school: cause is not the right category to demonstrate from. Causes are in the world. Jul 20, 2015 at 11:42
  • The fact that some theorems cannot be demonstrated is irrelevant to the point. Jul 20, 2015 at 11:43
  • 1
    @quen_tin Geremia is working from a thomistic background. There, "demonstration" has a specific Aristotelian meaning. The meaning for contemporary math is most probably derivative from that account. But I take it that's part of the OPs question -- how these terms work in other philosophical schools.
    – virmaior
    Jul 23, 2015 at 3:53

2 Answers 2


First, Deduktion, a term that Kant uses in his first Critique, gets translated in English as Deduction which misses the sense of this word in German; which is juridicial, and is better translated as Justify.

Deduction in English is closely associated to Logic, and from there to mathematics; and then from both, the notion of proof; but this sense, in German, is better translated as Schluss.

In Kants work, he uses the word Transcendental in a technical sense; native to him; which is that it argues for the conditions of the possibility of experience; which in the form of a syllogism is:

if only A makes B possible

B exists, happens or is

then A is true

This is quite different from the usual sense of Transcendent, which has the sense of going beyond experience, and more to the point - the divine.

There is nothing of this sense in Kants use of it; one might say that his philosophy transcends that of the Dogmatists or that of Wolff-Leibniz as it overcomes every philosophy know up to that particular point in time; but it's generally named as his Critical philosophy; as he grounds it in reason.

Thus Kants

Transcendental Deduction of the Categories

is better translated as

How to justify the categories from reasoning about the possibility of our experience to a condition of it

And secondly, description and demonstration form a dialectic pair: there are elements of demonstration in description; there are elements of description in demonstration. They are not an identity, but not are they seperable from each other.

For can I describe this tree before me without at the same time demonstrating its existence, even though this is not my intention?

And can I demonstrate or carry through the proof that there is an infinity of primes in your minds eye, without first describing a prime?

Thus, there is no demonstration without some aspect of description, and there is no description without some aspect of demonstration.

A further example: in a book of set theory, the theory has to be described: the axioms need to be listed, as well as the rules of inference; as in fact so do the theorems; but this book is only one moment in the dialectical progression of mathematics: the theory outlined in this book certainly wasn't discovered in this fashion, and nor justified in this fashion; the book represents an ideal moment of discovery: of demonstration and description.


One of my first steps to analyze any possible terminology (or problem of words in general) is etymology. This method is not without pitfalls, but some of the age-old assumptions ported along by the words can be illustrative.

The word demonstrate translates vaguely into "to utterly show" (a "monster" is a thing seen—interesting, no?) The prefix de- sometimes being an intensifier.

A "description" is primarily a "write up"—or we could roughly say, a report of something. Usually containing details that help us identify it. Thus, we can see that they both have an overlap in the general area of sense experience. A description that contains no details that a primary experience would reinforce, is rather useless as a "description", and we can demonstrate it's raining by pointing to the sky: "see with your own eyes."

So they have an overlap, and as such, I would guess no easy separability. Would a positivist-to-verificationist accept that you can describe anything that cannot be in some way demonstrated? To part the two, however, "description" would remain closer to the sense of something somebody wrote down on paper, effluvia of somebody's state of brain.

However, I would say that in general there is some irresistible sense that a description is less committal than a demonstration. I can describe rain outside--even if your phone says no sign of rain--but I can't demonstrate it unless I show you it is. If I commit to get you up from your card game (or whatever) to come out to look at the weather, then—if it's not a lame prank—if better bear the debt to settle the matter.

However, I would say that we retain a sense of demonstration that does not require the causes—if my claim is "I will demonstrate rain"--not just demonstrate that it is raining, then yes, obviously what one demonstrates, one has, in most cases, to reproduce, which means that you're trying your hand at the pull levers of phenomena, not simply giving an account of them.

Also, in mathematics, I would expect that instructions to "demonstrate" I would have to prove something, where as in the unfamiliar case of "describe", I wouldn't.

However, still, if I'm a cunning sort I can demonstrate something that I can't necessarily describe in that much detail that would outlast my age. There have been charismatic people who can demonstrate that they can cause other people to do things for them, knowing only an intuitive path from intention to effect. This doesn't make them terribly insightful into the psychology of other humans. The simply know how to pull levers. But they will "demonstrate" feats of human manipulation to their friends as the subject of bets.

Also any primitive can demonstrate that trees will burn, without knowing the details of Lavoisier could have described.

So I go back to etymology: I show you something with "demonstrate"; I simply give you an abstract of an experience with "description", probably as writing became to be known for uninterrupted stream of detail, writing became more apt for the concept of describing (akin to how "logic" seems to come to us from the Greek logos as "word-stuff".)

So I should think that the domain of description is all schools that use words, and the domain of demonstration, carrying with it the implications of empiricism--through the school's own filter of what an empirical experience is.

The reason that I put this qualification on is that some reductionists referring to Benjamin Libet's experiments doubt that we can even demonstrate that we can intend to move our wrists in a circle. In a number of interpretations, our wrists move and we interpret that move through the delusion of intentionality that our beast self demands upon reality--possibly to increase the feeling of power(??). Thus if the beast cannot set up a simple wrist move, the epiphenomenon of intent-to-cause needs not be reliable as well, it simply joins the other epiphenomena we associate with empirical activities.

Overall, however, I'm wondering where the (pardon the use) fixation over these two words came from? I think the value to words is that they mark a set of expectations--a sort of social contract--that we invoke when we use them.

  • Good answer. I'm not so sure that I agree with your views on demonstration as it relates to mathematics. For example, one could demonstrate the power of a mathematical theorem by applying it to solve a difficult problem with apparent ease. This is distinct from proof.
    – nwr
    Dec 20, 2015 at 3:17
  • @NickR, I don't know that I doubt your point. However, how could you demonstrate that x solves a problem without proving--not necessarily proving x, but "proving" that x, taken as a given, can be applied to solve a problem? To be reliable that relatively-computable problems can be solved with a UTM that can solve the halting problem may not prove the halting problem, but should "prove" that a Halting-UTM can solve the problem as a demonstration. Perhaps I'm missing some exact mathematical term of demonstration.
    – Axeman
    Dec 20, 2015 at 3:31
  • @NickR, still though, Goedel proved Incompleteness in a sense that math students would only be required to demonstrate, by regurgitating some semblance of the proof in an assignment or test. I'm not a practicing mathematician, but just a Math minor who took some senior level courses, so my relation to Mathematics will always be as a regurgitating student. I know that at some point, should I take an unmotivated leap, I have neither demonstrated nor replicated a proof.
    – Axeman
    Dec 20, 2015 at 3:39
  • Yes, that's true. I guess the point I was making is that proof does not entail demonstration just as demonstration does not entail proof, though as we both agree, there is some overlap. I'm not aware of any exact mathematical term for demonstration, or if one is needed for purely mathematical activity.
    – nwr
    Dec 20, 2015 at 3:39

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .