Tutorial #1. The Status of Morality. Hume on Ought-Is

The "is-ought gap" (see David Hume, ‘Moral Distinctions not Derived from Reason’):

1. All claims that can be known by reason are either empirical matters of fact or conceptual truths (e.g. "All bachelor are married", "All triangles have three corners").
2. Moral claims do not represent empirical matters of fact.
3. Moral claims do not represent conceptual truths.
4. Therefore, reason cannot give moral knowledge.

Any valid argument for an ought claim must have at least one ought-claim among its premises.
Ethical claims about what is right or wrong are ought claims.
A valid argument for an ethical claim must have some other ethical claim among its premises.
Therefore, no number of facts about how things are deductively entails that they ought to be one way or another.

NOTE
- Hume was an empiricist:
In general, empiricism is the thesis that:
We have no source of knowledge (or for the concepts we use) other than sense experience.

Hume maintains that all the materials of thinking, which he calls "perceptions", can be divided into two categories:
1) impressions, which are called sensations.
2) The less forceful, remembered copies of our immediate experiences, which are called ideas.
All ideas come from impressions.
Ideas can be combined.

Relations of ideas include mathematics.
Mathematical claims are true by virtue of the meaning of the terms, and to deny them is to assert a contradiction.
But these do not tell us what the world is like.
Matters of fact are based on sensory experience.
There is no contradiction in asserting that they are false.
They do not enjoy certainty but can be known only with varying degrees of probability.