Hume in logic and philosophy of science i

6th November 2020

all the objects of human reason or enquiry may naturally be divided into two kinds […], Relations of Ideas, and Matters of Fact

Hume, An Enquiry concerning Human Understanding, Sect. IV, Part I, 20

Relations of ideas

every affirmation which is either intuitively or demonstratively certain

Hume, An Enquiry concerning Human Understanding

Mathematical or theoretical operations: they are characterized by the fact that they are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe.

Relations of ideas can be demonstrated to be false, they can be

Matters of fact

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

Hume, An Enquiry concerning Human Understanding, Sect. IV, Part I, 26

Matters of fact imply existence; the above is valid only in the case the Sun exists. There is no logical connection between these two sentences.

Matters of fact are impossible to be logically placed in a context since:

  • there is no logic contradiction in two alternate occurrences;
  • a proposition about an entity automatically implies the existence of such entity, and it has no meaning whatsoever without that entity.

Existence isn’t a matter of logic reasoning; any a priori knowledge of matters of fact is impossible. What is

the nature of that evidence which assumes us of any real existence and matter of fact, beyond the present testimony of our senses, or the records of our memory.

Hume, An Enquiry concerning Human Understanding, Sect. IV, Part I, 23

Use induction to conceive as infallible his statement

Only some of our factual knowledge is based on what we perceive or what we remember.

Most of our factual knowledge concerns things or events which actually are quite remote from us.

All our reasoning regarding matters of fact relies on a connection between a present fact and some other fact from which the other is inferred from.

How do we reason?

We reason in the same way of when we think in the context of cause and effect. Can we apply actual knowledge on this connections?
We actually do this, but how do we do it, and why?

12th November 2020


Hume’s model of reasoning is the cause and effect, a connection between between a present fact and another one, in order to infer one from the other. Connecting an effect to a cause.

??? We start from the effect or from the cause?
A: from the effect

How are we able to make such an inference?

Of course starting entirely from experience: it will also make us state that under certain conditions we can always project events in the future. Experience can make us expect the connection even before events to actually happen.

Experience of repeated connection creates some sort of expectation in us, which consolidates in a habit, a custom. We take cause and effects for granted, and it’s partly deceiving: we pretend we’re making an inference, which is a logical process, while we’re experiencing a psychological attitude, expectation.


Hume comes up with counterarguments to prove his thesis.

How the mind would proceed if we analyzed an event without consulting past observations:

  1. The mind has to invent or imagine some event as an effect, arbitrarily
  2. Tie between cause and and effect is then arbitrary, too

We need to think these observations as events, not as objects. When a rock breaks a window, it’s not about the rock, but about a rock hitting a window and therefore hitting it.

Hume’s example

Imagine a billiard table. Nothing gives us the slightest hint that when a ball hits another ball the other one will go in a certain direction: anything can happen if we don’t consider what we experienced previously. By reasoning only, we’ll never be able to choose an outcome rather than another.

Contiguity, priority, regularity

Here is a billiard ball lying on the table, and another ball moving towards it with rapidity. They strike; and the ball which was formerly at rest now acquires a motion. It is evident that the two balls touched one another before the motion was communicated, and that there was no interval betwixt the shock and the motion. Contiguity in time and place is therefore a requisite circumstance to the operation of all causes. It is evident, likewise, that the motion which was the cause is prior to the motion which was the effect. Priority in time is therefore another requisite circumstance in every cause.

Using our mind alone we can’t affirm what is going to happen unless we have previous knowledge

Thus, there’s an arbitrary tie between cause and effect, and only experience can help us, in this way.

when we reason apriori, and consider merely any object or cause, as it appears to the mind, independent of observation, it never could suggest to us the notion of any distinct object, such as its effect; much less, show us the inseparable and inviolable connexion between them. A man must be very sagacious who could discover by reasoning that crystal is the effect of heat, and ice of cold, without being previously acquainted with the operation of these qualities.

Hume, An Enquiry concerning Human Understanding, Sect. VII, Part II, 27

Deductive vs Inductive reasoning

Statement 1:

Either it is raining ($p$) or it is snowing ($q$)
It isn’t snowing ($!q$)
------------ It is raining ($p$)

which corresponds to: \((p \vee q) \wedge !q \rightarrow p\)

Statement 2:
there is a flash of light (event A) ------------ There will be a clap of thunder (event B)

As it’s evident, statement 1 is logical, where the second one is not.
So, we may reformulate S2 in such a way it may be logically interpreted:

There is a flash of light if there is a flash of light, there will be a clap of thunder ------------ There will be a clap of thunder

The added premise is not known itself apriori, but it comes from experience.

How can we logically infer that just because past A-events have been followed by B-events, future A-events will be followed by B-events?
How do we logically justify that what we’ve experienced up to now will repeat in the same way in the future?

Structure of inductive argument

How do I go from the first to the second statement?

The connection from an event to a conclusion isn’t direct nor immediate. A medium, an additional premise, is needed. Hume is quite skeptical about this medium and he points out several times that such a medium can’t be rationally justified, it passes his comprehension.

Of course we do know what this medium is, but it has to be logically justifiable.

The premise has to be that the future will be conformable to the past; that the laws of nature that held in the past, will hold in the future.

The Principle of the uniformity of nature

the same pattern of relations between kinds of events —the same laws of nature— will hold in the future as have held in the past

By adding this medium, this inference from experience becomes logically acceptable.

This, according to Hume, can’t be safely accepted (logically).

A solution would be to focus on the matters of fact, nevertheless we’d be introducing a “vicious circularity” because we’re taking for granted the exact type of reasoning the validity of which we’re trying to understand. All inductive inferences are valid only because the premise c holds

all our experimental conclusions proceed upon the supposition that the future will be conformable to the past. To endeavour, therefore, the proof of this last supposition by probable arguments […] must be evidently going in a circle and taking that for granted, which is the very point in question.

Hume, An Enquiry concerning Human Understanding, Sect. IV, Part II, 30

It is impossible, therefore, that any arguments from experience can prove this resemblance of the past to the future; since all these arguments are founded on the supposition of that resemblance.

Hume, An Enquiry concerning Human Understanding, Sect. IV, Part II, 32

This becomes a question-begging argument

??? isn’t it the same thing as the demonstration of Aristotelian first principles?

Inductive circularity

c is the missing link, and we need to make it explicit, yet it’s itself an inductive inference: it says exactly the same thing.

Circularity is vicious here because we’re using induction to justify induction. Any experimental demonstration actually requires that the future has to resemble to the past.

if there is a suspicion that the course of nature may change, and the past may not be a rule for the future, then all experience becomes useless, and can give no rise to any argument or inference.

Hume, An Enquiry concerning Human Understanding, Sect. IV, Part II, 32

The appeal to custom

Why do we keep using inductive reasoning?

To Hume, there’s no logical reason; the psychological explanation is the only reasonable one we can give.

For wherever the repetition of any particular act or operation produces a propensity to renew the same act or operation, without being impelled by any reasoning or process of the understanding, we always say, that this propensity is the effect of custom.

Custom is the great guide of human life. It is the principle alone which renders our experience useful to us, and makes us expect, for the future, a similar train of events with those which have appeared in the past. Without the influence of custom, […] we should never know how to adjust means to ends […]. There would be an end at once to all action […]

Hume, An Enquiry concerning Human Understanding, Sect. V, Part I, 38

“Natural instinct”

If we can’t set goals, expectations for our future, what would give us some sort of confidence about our purpose in the future?


  • Inductive reasoning can’t be logically justified
  • Inductive reasoning is instinctual, thus inevitable
  • Inductive reasoning is at the basis of our beliefs about the future
  • Inductive reasoning informs both scientific inquiry and purposive action
  • Inductive reasoning is indispensable both scientific inquiry and purposive action

Further questions


If induction can’t be logically justified —with no necessary reasons to support it— is induction not rational, or even irrational?

If we use an irrational way of thinking, then it would mean we are irrational. We are questioning the very foundation of the way we interpret the world.
This is a radical skepticism which intuitively appears as quite implausible

We’d start questioning several beliefs based on inductions, such as memories and the durability of objects and most of all science itself


If an inductive inference still makes a certain conclusion look at least ‘reasonable’, can reasonableness be at all justified?


Next topic: Bertrand Russel



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