Hume’s "sceptical solution"

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PHI2391: Kant

Hume’s “sceptical solution”

It is because we “feel” a connection between beliefs about A and B that

We call A the cause of B (vii.2 pp. 360-361)

The “impression” of this feeling - the experience of the connection - is what gives us the idea of a cause.

Many scientists and philosophers viewed this as a disastrous outcome, among them Immanuel Kant

Kant’s Copernican revolution

Philosophical development beginning with Descartes ends in Kant’s “Copernican Revolution”

Revolution: Imagine that, instead of our thinking conforming to nature, nature conforms to our thinking!

This approach brings two significant advantages to the philosophy of science

Kant’s Copernican revolution

1st advantage: Explanation of the status of mathematics

2nd advantage: Explanation of the status of metaphysics

In the solution of the above problem there is … the answer to the questions:

How is pure mathematics possible?

How is pure natural science possible?” “Critique of Pure Reason, Introduction [B20, p.147]

How is pure natural science possible?

There is an additional question, not immediately related to the philosophy of science: “How is metaphysics possible …?” [B22, p.148]

In fact, part of what Kant calls “pure natural science”, his contemporaries would have called “metaphysics.”

So what is “pure natural science”?

Pure” natural science

Discussed in Kant’s minor work Metaphysical Foundations of Natural Science

Has a specific - technical - role in Kant’s system

But: we can understand its motivation anyhow

Attempt to redefine the scientific metaphysics of his time

Scientific metaphysics

By “scientific metaphysics” I mean, e.g. Descartes’s metaphysics

Descartes: world consists of extended (thus geometric bodies); or, e.g. Leibniz’s metaphysics,

Leibniz: World consists of energetic “monads”. They have only predicates (no relations).

Descartes and Leibniz conceive of space and matter in radically different ways

Scientific metaphysics

Even though D. and L. disagree on the metaphysics, they agree on some of the mathematical physics

Perhaps: Their metaphysical commitments are secondary

But: They are not irrelevant to the physics

Kant: “All natural philosophers who wanted to proceed mathematically in their work had therefore always … made use of metaphysical principles.” Met. Foundations [472, p. 9]

Scientific metaphysics

Related to the metaphysical questions (as quote shows) is the old phil. question:

How and why does mathematics apply to physical reality?

Descartes: geometry and algebra describe the fundamental properties of matter

Empiricists (Hume/Locke): Mathematics is a “shorthand” for describing complex relationships among things.

Like all other sciences, mathematics is developed by generalising and simplifying our experiences.
Scientific metaphysics

Kant: We need to provide a replacement to scientific metaphysics.

The replacement will also explain the status of mathematics

In general: the new metaphysics will explain and justify the use of synthetic a priori knowledge in science.

Synthetic a priori knowledge

Two fundamental distinction due to Kant:


A priori/a posteriori

These distinctions apply to judgments, and thus to propositions, and knowledge generally

Part of standard vocabulary of the philosophy of science

A priori knowledge

Kant: “We are in possession of certain a priori cognitions” CpR, Introduction II

Quine will deny just this

A priori: “if a proposition is thought along with its necessity, it is an a priori judgment” CpR, Introduction [B10, p. 141]

It is absolutely a priori if derived only from necessary propositions.

A priori knowledge

Examples (not so great): “All bodies are heavy”

For Kant, bodies are extended things (they “take up” space), but,

They could be extended without being heavy

So in saying, “All bodies are heavy”, I am saying something that I cannot know without experience

I must lift many bodies, to make the inductive generalisation

A priori knowledge

But not all knowledge is like this

Some - mathematics and scientific metaphysics - seems independent of (prior to) experience

So 2+2=4 may have been learned from experience

But it can be proven without appeal to experience


Another distinction: between “analytic” and “synthetic”

In analytic judgments “the predicate B belongs to the subject A as something that is (covertly) contained in this concept A”

In synthetic ones “B lies entirely outside the concept A, though to be sure it stands in connection with it.” [A6, p. 141]

Example: “All bachelors are unmarried men”

All bodies are extended”

We would say: analytic judgments are true by logic alone

Synthetic judgments require logic + something else


So we have 4 types of judgment:

Kant: All a posteriori judgments are synthetic [B11, p. 144]

Clearly (?) analytic a posteriori is of no interest

Leaves synthetic a priori


Mathematical judgments are synthetic a priori

Natural science contains synthetic a priori judgments

(Bad) metaphysics contains synthetic a priori judgments
Synthetic a priori knowledge

Problem of philosophy (of science) becomes:

How is synthetic a priori knowledge possible?

Kant’s answer: synthetic a priori knowledge derives from the forms of our thought

Forms of knowledge

Two principal components to our minds: intuition and understanding

intuition(s) = the given(s)

understanding = the concepts

We have knowledge when intuitions are “subsumed” (brought under) concepts

I see a red house. I have an intuition of redness in a particular region of space, structured in a house-shape

I say: “There is a red house”

Forms of knowledge

When I do, the intuition is subsumed under the concept, and the result is a judgment (proposition)

Kant: intuition and the understanding have “pure” parts:

Pure intuitions: space and time

Pure concepts: quantity, cause-effect, substance, etc.

Kant calls them “categories”, and they are more or less Aristotle’s

Forms of knowledge

Just as we get propositions when we subsume empirical data under empirical concepts

We get propositions when we subsume “pure” data under “pure” concepts

These propositions are the components of mathematics and pure natural science

Pure science

There can be 2 kinds of pure science, 1 per form of intuition:

The science of bodies (extended things)

The science of mind (temporal succession)

The latter is (according to K) trivial or degenerate

The former deals with time-space relations

Pure science

So pure natural science (non-mind) establishes the natural laws governing experience

These laws must be mathematical, because bodies are, in a sense, mathematical

So, all true science is mathematical

Chemistry and biology are not sciences!! (according to K)

Causality and Space-time

For us, two key aspects of Kant’s theory

Causality is a pure concept

Space and time are pure intuitions (forms of givens, data-structures)

As we saw, for Kant

We get knowledge when intuitions (spatio-temporal sense-data) are synthesised (brought together) by concepts (class-terms)


Kant claims that some concepts are a priori

For instance, causality, the relation x-causes-y

When we say “A causes B” we synthesise A and B with the relational concept x-causes-y

But Hume showed us that x-causes-y is not in the intuitions (raw data) A and B

According to Kant, we add it in a priori


Kant: “Hume … believ[ed] himself to have brought out that such an a priori proposition is entirely impossible.” [B20, p. 146]

Why? Because in adding in causality, we use this concept without empirical justification

Kant: We make a synthetic a priori judgment

In using the “category”, or “pure concept” of causality, we make our experiences objective


Kant believes that without causality, substance, and the other categories like quantity, etc. we would not have “objective experience” of the world

He calls the categories “conditions on the possibility of experience”

If you didn’t use causality, you wouldn’t be having objective experiences

Causality and justification

Kant argues that without causality, we wouldn’t have conscious experience.

That is why we are justified in using it

Similarly, the concept of substance (a unified entity that persists through change) synthesises intuitions (data)

We are justified in speaking of substances (horses, trees, rocks)

Without ordering our world this way, we would have no experience of intersubjective things
Hume and Kant

Remember Hume’s question:

Are we rationally justified in inferring causes from experimental observations?

Kant’s answer: we can give a “transcendental deduction” of why we must do so

Of course both agree that we do think causally, the question is

By what right do we think causally?

Kant’s Answer(s)

Kant’s answer:

Psychological interpretation:

Without the categories (causality, substance, etc.), I wouldn’t have a consciousness

The “world” would just be a mass of sensations, with no order

There would be no subject, because mind would be fragmented

Compare: “Anthropic Principle” in contemporary physics

Kant’s Answer(s)


A world that was not interpreted by means of the categories and pure mathematics would not be unified

If there is to be a unified world, then

Since all objects appear in space and time, and,

Time and space have distinct parts

They can only be unified if

The parts are filled with substances that causally interact

Kant’s Answer(s)


Time and space can only be unified if their parts are filled with substances that causally interact

Example (Einsteinian simultaneity):

When can I tell something on my video screen is live?

Only when I cause what I see to change.

How can I know that events in the Rideau Centre are happening now?

Under what circumstances is a body orbiting Pluto “part of my world”?

Science-theoretical answer

There can be no guarantee that the world will be comprehensible as a unified mathematical system

But, if there is to be a body of knowledge corresponding to the whole of nature

Then it must have this mathematical, nomological (law-governed) structure

Compare: Einstein on “EPR”

Space-time and mathematics

So far have talked about the categories that synthetise intuitions

What gets synthesised - the “intuitions” - are sensations in space and time

They are in space and time, meaning

In space their shape, magnitude, and relation to one another is determined” [B37, p. 174]

“… simultaneity or succession would not … come into perception if … time did not ground them a priori. Only under its presupposition can one represent that several things exist at one and the same time (simultaneously) or in different times (successively).” [B46, p. 178]

Mathematics is synthetic a priori

Kant claims that all mathematical propositions are synthetic a priori

Arithmetic [Introduction B15, p. 142; Axioms of Intuition B205, p. 288]]:

7+5=12 may seem analytic

Then it should be the case that the concepts 7, 5, and + parts of the the concept 12. But (says Kant) they are not

So 7+5=12 is synthetic

But we know it a priori

So it is synthetic a priori

Mathematics is synthetic a priori

Geometry [B16, p.145]:

The concepts shortest and straightest do not contain one another (one concerns distance, the other direction)

But we know a priori (says Kant) that a straight line is the shortest distance between two points

So the proposition is synthetic a priori

How is it possible that mathematics be synthetic a priori?

Kant sees a problem that his predecessors can’t solve

They believe that space exists as a property of things in themselves

One group (the “mathematical investigators”) believes that space is a thing that exists on its own (so it’s a substance)

Another group (the “metaphysicians”) believe that it is a property of things that exist on their own (substances, Leibnizian monads)

How can mathematics be synthetic a priori?

Mathematician-physicists like Newton “… must assume two eternal and infinite self-subsisting non-entities” [TA B56, p. 184]

They can explain why mathematics holds of physical objects - they are in space and time

But (so Kant) “they become confused” when attempting to explain how there could be anything beyond space and time (e.g. God and angels)

Also, they must explain in what sense these things exist, since they seem to be a pure emptiness (thus “non-entities”)

How can mathematics be synthetic a priori?

Metaphysicians like Leibniz think that space and time are human constructions

We have confused knowledge of things (monads), and we organise this confused knowledge with space and time

But, in the things themselves, space and time are not present

How can mathematics be synthetic a priori?

Leibniz (and presumably Hume) “must dispute the validity … of a priori mathematical doctrines” [B57]

Why? Because space and time are confused “creatures of the imagination” [B57], i.e. we make them up

How could we have precise knowledge of something confused?

If S&T were merely inductive generalizations of observations, how can we explain the Law of Inertia?

Don’t bodies have to “obey” (Euler) the straight lines and follow inertial paths?

How can mathematics be synthetic a priori?

Kant claims his theory solves all these problems:

Mathematics is true of things insofar as they are objects of possible experience

So: insofar as they are “represented” in pure space and time, the forms of experience

We know it a priori, because we know the structure of our own minds

NB Kant also admits that mathematics doesn’t hold of things in themselves

But he can explain why it holds of all objective experience

Importance of Kantian Doctrines

19th c. philosophy, and thus philosophy of science profoundly affected by Kant

But also science itself:

Kantian theories (apparently) lay to rest questions about absolute space and mathematics

Important assumptions: there are synthetic a priori truths

There are “intuitions” (raw data) at the basis of mathematics that are - in being spatial - essentially the same as our everyday intuitions

Importance of Kantian Doctrines

Kant gives a non-metaphysical explanation of the task of science

We are built to explain events in space-time in terms of causal relations between events

Our reason imagines a “total system” in which all events that occur could be predicted as instances on general mathematical laws

This completed system is an “ideal” (Kant’s term) towards which we strive

The ideal system has an a priori core which Kant calls [Metaphysical Foundations, p.4ff.] the “pure part” of science

Importance of Kantian Doctrines

Kant’s system lays down model for future philosophy of science

Pure logic and mathematics form the a priori core of science

They lay down basic patterns of reasoning

These patterns allow us to think about the data of our experience - to draw conclusions

And to predict

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