The Agora

Fact vs Necessity

David Hume

An Enquiry Concerning Human Understanding

The author argues that matters of fact are incapable of logical demonstration because their negation is always conceivable and never involves a formal contradiction.

...at where there is no property, there can be no injustice_, it is only necessary to define the terms, and explain injustice to be a violation of property. This proposition is, indeed, nothing but a more imperfect definition. It is the same case with all those pretended syllogistical reasonings, which may be found in every other branch of learning, except the sciences of quantity and number; and these may safely, I think, be pronounced the only proper objects of knowledge and demonstration. 132.

All other enquiries of men regard only matter of fact and existence; and these are evidently incapable of demonstration. Whatever is may not be. No negation of a fact can involve a contradiction. The non-existence of any being, without exception, is as clear and distinct an idea as its existence. The proposition, which affirms it not to be, however false, is no less conceivable and intelligible, than that which affirms it to be. The case is different with the sciences, properly so called. Every proposition, which is not true, is there confused and unintelligible.

That the cube root of 64 is equal to the half of 10, is a false proposition, and can never be distinctly conceived. But that Caesar, or the angel Gabriel, or any being never existed, may be a false proposition, but still is perfectly conceivable, and implies no contradiction. The existence, therefore, of any being can only be proved by arguments from its cause or its effect; and these arguments are founded entirely on experience. If we reason a priori, anything may appear able to produce any...

David Hume

An Enquiry Concerning Human Understanding

Fact's Contingent Nature

This candidate extends Hume's distinction between relations of ideas and matters of fact, directly reinforcing the parent text's core argument that the contrary of every matter of fact is possible and cannot be demonstrated because it implies no contradiction.

...e is equal to the square of the two sides_, is a proposition which expresses a relation between these figures. That three times five is equal to the half of thirty, expresses a relation between these numbers. Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe. Though there never were a circle or triangle in nature, the truths demonstrated by Euclid would for ever retain their certainty and evidence. 21.

Matters of fact, which are the second objects of human reason, are not ascertained in the same manner; nor is our evidence of their truth, however great, of a like nature with the foregoing. The contrary of every matter of fact is still possible; because it can never imply a contradiction, and is conceived by the mind with the same facility and distinctness, as if ever so conformable to reality. That the sun will not rise to-morrow is no less intelligible a proposition, and implies no more contradiction than the affirmation, that it will rise. We should in vain, therefore, attempt to demon...

It may, therefore, be a subject worthy of curiosity, to enquire what is the nature of that evidence which assures us of any real existence and matter of fact, beyond the present testimony of our senses, or the records of our memory. This part of philosophy, it is observable, has been little cultivated, either by the ancients or moderns; and therefore our doubts and errors, in the prosecution of so important an enquiry, may be the more excusable; while we march through such difficult paths with...

Friedrich Nietzsche

Beyond Good and Evil

The Myth of Certainty

This candidate fundamentally challenges the assumption of 'immediate certainties' and the clarity of our ideas upon which Hume's distinction relies, arguing that even basic propositions like 'I think' involve a series of unjustified assertions. It thus disputes the epistemological foundation of Hume's argument.

...therefore, at least as regulative hypothesis, if not as heuristic principle. What? And others say even that the external world is the work of our organs? But then our body, as a part of this external world, would be the work of our organs! But then our organs themselves would be the work of our organs! It seems to me that this is a complete REDUCTIO AD ABSURDUM, if the conception CAUSA SUI is something fundamentally absurd. Consequently, the external world is NOT the work of our organs--? 16.

There are still harmless self-observers who believe that there are "immediate certainties"; for instance, "I think," or as the superstition of Schopenhauer puts it, "I will"; as though cognition here got hold of its object purely and simply as "the thing in itself," without any falsification taking place either on the part of the subject or the object. I would repeat it, however, a hundred times, that "immediate certainty," as well as "absolute knowledge" and the "thing in itself," involve a CONTRADICTIO IN ADJECTO; we really ought to free ourselves from the misleading significance of words! T...

--In place of the "immediate certainty" in which the people may believe in the special case, the philosopher thus finds a series of metaphysical questions presented to him, veritable conscience questions of the intellect, to wit: "Whence did I get the notion of 'thinking'? Why do I believe in cause and effect? What gives me the right to speak of an 'ego,' and even of an 'ego' as cause, and finally of an 'ego' as cause of thought?" He who ventures to answer these metaphysical questions at once by...

David Hume

An Enquiry Concerning Human Understanding

Belief from Custom

This candidate explains *why* we come to believe in matters of fact and existence, identifying the psychological mechanism of 'customary conjunction' and habit, which is the hidden driver for the type of reasoning Hume describes as incapable of demonstration.

...ny particular matter of fact, which you relate, you must tell me some reason; and this reason will be some other fact, connected with it. But as you cannot proceed after this manner, in infinitum, you must at last terminate in some fact, which is present to your memory or senses; or must allow that your belief is entirely without foundation. 38. What, then, is the conclusion of the whole matter? A simple one; though, it must be confessed, pretty remote from the common theories of philosophy.

All belief of matter of fact or real existence is derived merely from some object, present to the memory or senses, and a customary conjunction between that and some other object. Or in other words; having found, in many instances, that any two kinds of objects--flame and heat, snow and cold--have always been conjoined together; if flame or snow be presented anew to the senses, the mind is carried by custom to expect heat or cold, and to believe that such a quality does exist, and will discover itself upon a nearer approach. This belief is the necessary result of placing the mind in such cir...

All these operations are a species of natural instincts, which no reasoning or process of the thought and understanding is able either to produce or to prevent. At this point, it would be very allowable for us to stop our philosophical researches. In most questions we can never make a single step farther; and in all questions we must terminate here at last, after our most restless and curious enquiries. But still our curiosity will be pardonable, perhaps commendable, if it carry us on to still...

Blaise Pascal

Pensees

Heart's First Principles

This candidate redirects the epistemological discussion from Hume's framework of relations of ideas vs. matters of fact to a different axis: the heart versus reason. It reframes the source of our certainty about first principles (including matters of fact) as intuitive and foundational, not merely as non-demonstrable propositions.

...Is it by reason that you love yourself? 278 It is the heart which experiences God, and not the reason. This, then, is faith: God felt by the heart, not by the reason. 279 Faith is a gift of God; do not believe that we said it was a gift of reasoning. Other religions do not say this of their faith. They only gave reasoning in order to arrive at it, and yet it does not bring them to it. 280 The knowledge of God is very far from the love of Him. 281 Heart, instinct, principles. 282

We know truth, not only by the reason, but also by the heart, and it is in this last way that we know first principles; and reason, which has no part in it, tries in vain to impugn them. The sceptics, who have only this for their object, labour to no purpose. We know that we do not dream, and however impossible it is for us to prove it by reason, this inability demonstrates only the weakness of our reason, but not, as they affirm, the uncertainty of all our knowledge. For the knowledge of first principles, as space, time, motion, number, is as sure as any of those which we get from reasoning....

(We have intuitive knowledge of the tri-dimensional nature of space, and of the infinity of number, and reason then shows that there are no two square numbers one of which is double of the other. Principles are intuited, propositions are inferred, all with certainty, though in different ways.) And it is as useless and absurd for reason to demand from the heart proofs of her first principles, before admitting them, as it would be for the heart to demand from reason an intuition of all demonstrat...

Blaise Pascal

Pensees

Skepticism's Origin Doubt

This candidate questions the very possibility of obtaining certainty about any first principles (including those governing matters of fact) due to the skeptical problems of our origins and the state of dreaming vs. waking, casting doubt on our ability to settle the foundational issues Hume's argument rests upon.

...eat or small. And those who have said the one or the other, knew nothing about it, and guessed without reason and by chance. They also erred always in excluding the one or the other. Quod ergo ignorantes, quæritis, religio annuntiat vobis.[160] 433 After having understood the whole nature of man.--That a religion may be true, it must have knowledge of our nature. It ought to know its greatness and littleness, and the reason of both. What religion but the Christian has known this? 434

The chief arguments of the sceptics--I pass over the lesser ones--are that we have no certainty of the truth of these principles apart from faith and revelation, except in so far as we naturally perceive them in ourselves. Now this natural intuition is not a convincing proof of their truth; since, having no certainty, apart from faith, whether man was created by a good God, or by a wicked demon, or by chance, it is doubtful whether these principles given to us are true, or false, or uncertain, according to our origin. Again, no person is certain, apart from faith, whether he is awake or sleeps...

So that half of our life being passed in sleep, we have on our own admission no idea of truth, whatever we may imagine. As all our intuitions are then illusions, who knows whether the other half of our life, in which we think we are awake, is not another sleep a little different from the former, from which we awake when we suppose ourselves asleep? [And who doubts that, if we dreamt in company, and the dreams chanced to agree, which is common enough, and if we were always alone when awake, we...

John Stewart Mill

Utilitarianism

Unprovable Ultimate Ends

This candidate shifts the discussion toward practical reasoning, asking by what faculty we judge 'questions of practical ends.' It implicitly responds to Hume's description of human enquiry by focusing on the 'what should we do?' aspect, moving from description to guidance.

...called the external sanctions; and when those sanctions are wanting, or act in an opposite direction, constitutes in itself a powerful internal binding force, in proportion to the sensitiveness and thoughtfulness of the character; since few but those whose mind is a moral blank, could bear to lay out their course of life on the plan of paying no regard to others except so far as their own private interest compels. CHAPTER IV. OF WHAT SORT OF PROOF THE PRINCIPLE OF UTILITY IS SUSCEPTIBLE.

It has already been remarked, that questions of ultimate ends do not admit of proof, in the ordinary acceptation of the term. To be incapable of proof by reasoning is common to all first principles; to the first premises of our knowledge, as well as to those of our conduct. But the former, being matters of fact, may be the subject of a direct appeal to the faculties which judge of fact--namely, our senses, and our internal consciousness. Can an appeal be made to the same faculties on questions of practical ends? Or by what other faculty is cognizance taken of them?

Questions about ends are, in other words, questions what things are desirable. The utilitarian doctrine is, that happiness is desirable, and the only thing desirable, as an end; all other things being only desirable as means to that end. What ought to be required of this doctrine--what conditions is it requisite that the doctrine should fulfil--to make good its claim to be believed? The only proof capable of being given that an object is visible, is that people actually see it. The only proof...