November 11

Lecture Notes: November 18

References herein to Hume's work are via page numbers in the Hackett.

Hume

Hume makes a distinction between matters of fact and relations of ideas (p 15)
Relations of ideas are an exception to his empiricist rule that every object of knowledge must trace back to sense impressions.

'Matters of fact' are a posteriori, and contingent.

(Be careful not to confuse Hume's use of this term with our current idiom.)

'Relations of ideas' are a priori, and necessary.
We can demonstrate relations of ideas using the law of contradiction (p 11)

If the denial of a statement leads to a contradiction, the original statement must be true.

Earlier we called this 'proof by reductio ad absurdum'.

Examples of contradictions:

'p and not-p', for any proposition p
'x = not-x', for any object x

Hume says that we can generate mathematical (and logical) truths using such proofs.

These require no empirical support, or justification.

Compare Hume's position with Descartes'.

Descartes called a priori propositions 'innate ideas' and extended the range of these ideas.

For Descartes, anything we know has to be derived from pure reason.

This included all knowledge of the physical world.

Hume accepts this sort of reasoning (he calls it demonstrative) but limits its range to logic and mathematics.

Knowledge of the physical world will have to arise exclusively from the senses.

Review the items listed in Part I of the handout. (See Nov. 11)
1-4 are all matters of fact, trace to impressions.
5 is a relation of ideas, whose denial is a contradiction.

What about the last three? - Are they relations of ideas?
Compare A) 2+2=5; and B) the sun won't rise tomorrow.
Consider the difference between the reasons that each are wrong.

A) is false because of the way the terms are related.
B) is still possible; we can't have certainty that it's false. (See p 22)
We can't find out B) is wrong by mere process of thought.
Hume would call 6) and 7) matters of fact, since we learn them via inductive reasoning on sense experience.

How about 8)?

Compare to 'all bachelors are unmarried'.

This we might say is 'analytically' true, and so is a relation of ideas.

It's the meanings of the terms which make the statement true.

It's a truth which arises from the logic of the language.

So 6) and 7), and all scientific laws, are matters of fact.

Are they true matters of fact?
Hume argues that we don't know these, because empiricism can't establish the truth of laws of nature (p 19).
The "secret powers" (the connections) are hidden from us.
Effects are distinct from their causes (p 17).
We have no experience of the cause.
We only see the conjunctions of certain events.
Consider unknown objects: we can not reason to their natures, but only learn from experience of them.
So, all beliefs about the world are based on experience, and experience only tells us what was, not what has to be.
That is, we have no access to the causes.
So we have no access to the laws of nature.

How do we know that the sun will rise tomorrow?
We can't.
It's not about a big (law-like) explosion of the sun, but our inability to project from past experience into the future.
This is generally known as the Problem of Induction: How do we get knowledge of the unobserved?
Induction is how you know 6, 7, and how the person next to you has a beating heart

Hume's Skeptical argument about induction:

1) Our beliefs about future events and unobserved objects are matters of fact.
2) Beliefs about matters of fact are based on experience.
3) Experience tells us how things were, not how they will be.
:. Our beliefs about the future and the unobserved are uncertain.

For example, consider billiard balls:

1) I have seen one ball strike another many times.
2) Each time the ball which was struck has moved, motion was transferred.
:. The struck ball will move this time.

But the conclusion doesn't follow.
What more do we need?

We can add, as a third premise, the principle of the uniformity of nature (PUN): The future will resemble the past. (See p 22)
This would render the argument valid, but what could justify the PUN?
We have no basis for inference.

We can't, for example, bootstrap: claim that it is itself inductively justified.
Yet all inductive inference presupposes it.

If we had knowledge of cause and effect relations, we could establish the PUN.

But we only have experience of constant conjunction, not the connections. (See p 46)
We can't find effects in causes.

So why do we believe the connection?
Why do we exit through the door, not the window?
We do feel like we have the connections but this is just habit (p 50)
We make a mental leap, unjustified by evidence.
Consider the man suddenly brought into world. (p 27-8)

It is only experience which gives us knowledge of matters of fact, and this can only provide knowledge of past events, and can not justify the PUN.

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