PHIL 415 Lecture Notes - Lecture 11: Isomorphism, Ordinary Language Philosophy, Barber Paradox
12 Jun 2018
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-Isomorphism: sameness (iso) of “shape” (morph-), i.e. structure
-A picture depicts by means of a (logical) isomorphism, the picture and what it depicts
-Therefore, a picture shows but does not depict (“say”, express, represent) its own
structure
2.11 “A picture presents…”
A picture is a model of reality
The imagery we’re supposed to have here as map, in the ordinary sense as 2-dimensional
Model, sometimes 3-dimensional
A picture will pick out certain aspects of reality that it wants to model
A map is a map that we care about
EX: A metro map for people who want to travel
Different maps will pick out different aspects of reality
It gives partial information
This is the same way with models
2.13 The way that a picture depicts is an isomorphism (sameness of structure)
The picture has elements in it where each element corresponds to the thing in the state of
affairs
The picture depicts by virtue of sharing some logical structure with the state of affairs
2.131 Further specification
2.14 A picture is a fact
We depict fact by means of other facts
Why? It’s a fact that a certain state of affairs
A picture depicts a fact but it’s also itself a fact because it is elements or objects related in
certain ways
The relation between the object and the picture and the object in reality are supposed to
mirror each other, the sameness of structure, that the picture depicts what it depicts
Pictorial space = special kind of fact
2.151 Pictorial form
A picture is a logical picture – it depicts by virtue of sharing logical structure
Pictorial form is the possibility of the form in that picture
He’s using the notion of form to talk about your shape in logical space
2.1511 Specifying 2.151
“It reaches right out to it” – this is very strange
It is laid against reality like a measure
EX: Let’s say you’re putting a ruler up against an object to measure it
You line up the ruler up against the tip of the object
I don’t need to the rest of the ruler
I just need the surface point
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We’re asked to imagine an insect that perceives the world through feelers
Imagine that they work by touching the things
It tells you that something is there because something is touching it
So the contact is really the end points
The picture is attached to reality because it reaches right out to it
2.16 Language is also a thing in the world
Propositions are either written, or spoken, however it works in the brain, it’s still part of
the world
Facts depicting facts should be ok (as something to understand)
We’ve shifted the terminology but we haven’t said anything more significant (besides
logical isomorphism – this is a innovative concept)
2.17 For something to be a picture, for a fact to be a picture (propositions will also be
pictures – this is what we’re leading up to), it must share logical structure with that with
which it depicts
A spatial picture can depict spatial states of affair
2.172 A picture cannot depict its own pictorial form, it displays it – this is important
Things that can say versus things that can only be shown
A picture can depict a state of affairs, but it cannot depict it’s own pictorial form
It cannot depict its own structure – it makes it apparent, manifest, it shows it…
Why?
The claim is not that the pictorial form of a picture cannot be represented
The claim is that the picture cannot depict it’s own logical structure/pictorial form
By virtue of what is a picture a picture of anything? By virtue of isomorphism, by virtue
of sharing a logical structure
There’s a fact and there’s a picture
For each fact, we need a picture of the fact, for each relation, there is a representation of
the relation = isomorphism
Everything is represented – this is why it’s a picture
The picture cannot represent its own structure
2.182 Every picture is a logical one, but not necessarily a spatial structure
A picture necessarily has a logical structure
Logic just is
Logical picture of facts is a thought
Wittgenstein will want to ultimately argue that language, thought, and world, all share a
structure and this is how the limits of language will also be the limits of the world
The limits of meaningful language will also be the limits of meaningful thought
Comment: there’s a recurrent theme that we find in religious/philosophical contexts: idea
of isomorphism between two or more realism
EX: the microcosm and the macrocosm, whatever happens in heaven will reflect on earth
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Document Summary
Isomorphism: sameness (iso) of shape (morph-), i. e. structure. A picture depicts by means of a (logical) isomorphism, the picture and what it depicts. Therefore, a picture shows but does not depict ( say , express, represent) its own structure. The imagery we"re supposed to have here as map, in the ordinary sense as 2-dimensional. A picture will pick out certain aspects of reality that it wants to model. A map is a map that we care about. Ex: a metro map for people who want to travel. Different maps will pick out different aspects of reality. 2. 13 the way that a picture depicts is an isomorphism (sameness of structure) The picture has elements in it where each element corresponds to the thing in the state of affairs. The picture depicts by virtue of sharing some logical structure with the state of affairs. We depict fact by means of other facts. It"s a fact that a certain state of affairs.
