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Clear and Distinct

How could the intellect alone enable us to know the essential nature of things?

‘I am certain that I am a thinking thing.

Do I not therefore also know what is required for my being certain about anything?

In this first item of knowledge there is simply a clear and distinct perception of what I am asserting; this would not be enough to make me certain of the truth of the matter if it could ever turn out that something which I perceived with such clarity and distinctness was false.’

‘I now seem to be able to lay it down as a general rule that

whatever I perceive clearly and distinctly is true’

(Meditation 3)

1. I clearly and distinctly perceive that I am a thinking thing.

2. This clear and distinct perception is enough for certainty.

3. Suppose not all clear and distinct perceptions were enough for certainty about what is perceived.

4. Then no clear and distinct perception would be enough for certainty.

5. But then my clear and distinct perception that I am thinking would not be enough for certainty.

6. Which it is.

7. So #3 leads to contradiction.

8. So all clear and distinct perceptions are enough for certainty.

recall from a moment ago

How could the intellect alone enable us to know the essential nature of things?

‘I am certain that I am a thinking thing.

Do I not therefore also know what is required for my being certain about anything?

In this first item of knowledge there is simply a clear and distinct perception of what I am asserting; this would not be enough to make me certain of the truth of the matter if it could ever turn out that something which I perceived with such clarity and distinctness was false.’

‘I now seem to be able to lay it down as a general rule that

whatever I perceive clearly and distinctly is true’

(Meditation 3)

At this point we face a flood of questions.

1. What are clear and distinct perceptions?

2. Why think perceptions which are not clear and distinct do not yield knowledge?

3. Why think clear and distinct perceptions do yield knowledge?

So far: on the basis of a single case study
So far: no reason
So far: the kind involved in cogito-style arguments
Let’s see whether we can get a bette sense by thinking about a particular case ...
recall from a moment ago

How could the intellect alone enable us to know the essential nature of things?

‘I am certain that I am a thinking thing.

Do I not therefore also know what is required for my being certain about anything?

In this first item of knowledge there is simply a clear and distinct perception of what I am asserting; this would not be enough to make me certain of the truth of the matter if it could ever turn out that something which I perceived with such clarity and distinctness was false.’

‘I now seem to be able to lay it down as a general rule that

whatever I perceive clearly and distinctly is true’

(Meditation 3)

Example: the wax

‘the perception I have of it is a case not of
vision or touch or imagination
... but of
purely mental scrutiny;

and this can be
imperfect and confused
as it was before
or
clear and distinct
as it is now,
depending on how carefully I concentrate’

Option 1: ‘clear and distinct’ is a psychological property

Option 2: ‘clear and distinct’ is a lose way of talking about whatever underpins mathematical knowledge

One attraction of this idea is that it gives us answers to all the questions ...

1. What are clear and distinct perceptions?

Those involved in thinking mathematically.

2. Why think perceptions which are not clear and distinct do not yield knowledge?

Erm ... because only mathematics yields knowledge?

3. Why think clear and distinct perceptions do yield knowledge?

Because mathematics is possible.

Only problem is that physics does not reduce to mathematics. (Although Descartes might reasonably have thought otherwise.)

Option 1: ‘clear and distinct’ is a psychological property

Option 2: ‘clear and distinct’ is a lose way of talking about whatever underpins mathematical knowledge

But Euclid’s fifth postulate (the ‘parallel postulate’) ...

‘If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.’

... and the Axiom of Choice ...

... and ...

Option 1: ‘clear and distinct’ is a psychological property

Option 2: ‘clear and distinct’ is a lose way of talking about whatever underpins mathematical knowledge

Dilemma: is your perception of the parallel posulate clear and distinct?

If not, you can never know which perceptions are clear and distinct.

If it is, not all clear and distinct perceptions yield knowledge.

Option 1: ‘clear and distinct’ is a psychological property

Option 2: ‘clear and distinct’ is a lose way of talking about whatever underpins mathematical knowledge

But Euclid’s fifth postulate (the ‘parallel postulate’) ...

‘If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.’

... and the Axiom of Choice ...

... and ...

What do you think? Are either of these options viable? Is there another option?
What does Descartes himself say? Nothing much in the Mediatations. But

‘What is meant by a clear perception, and by a distinct perception.

I call a perception 'clear' when it is present and accessible to the attentive mind - just as we say that we see something clearly when it is present to the eye's gaze and stimulates it with a sufficient degree of strength and accessibility.

I call a perception 'distinct' if, as well as being clear, it is so sharply separated from all other perceptions that it contains within itself only what is clear’

\citep[pp.~207--8, AT VIII:21--22]{descartes:1985_csm1}

Descates (Principles of Philosophy)

No idea what to make of this.
Earlier I considered these questions. What have we learned?

1. What are clear and distinct perceptions?

2. Why think perceptions which are not clear and distinct do not yield knowledge?

3. Why think clear and distinct perceptions do yield knowledge?

Descartes is not super informative himself. I think you can read in what you like
Either no perceptions yield knowledge, or only perceptions of logical and perhaps mathematical truths.
You shouldn’t.

puzzle

A puzzle on Descartes’ positive views about how we acquire knowledge of the essential natures of things.
Descartes appears to hold that we have some kind of mathematical basis for knowledge of the essential natures of bodies. But he is also an early proponent of the importance of measurements. His scientific work all involves combining mathematics with observation. This is what led to the great breakthrough in science.

Hypothesis testing

1. Sensory perception alone cannot tell you which hypothesis is true.

2. Humans are disposed to accept many false hypotheses.

Therefore:

3. Your sensory perceptions and sense of what is plausible should not constrain which hypotheses you consider.

4. ... but observation (sensory perception) is essential for testing hypotheses.

xkcd.com/2115

[To illustrate that common sense shouldn’t be used in deciding which hypotheses to test.]