Internai an d external properties

an object. The best way to approach this issue is to consider again the idea of the form of an object.

The possibility o f its occurring in states o f affairs is the form o f an object. (TLP

2.0141).

If two objects have the same logical form, the only distinction between them, apart from their external properties, is that they are different. (TLP 2.0233)

As we saw in part III, two objects can have the same form, and yet be different. The form of the object is a matter of the object falling under a particular formal concept.

When something falls under a formal concept as one o f its objects, this cannot be expressed by means o f a proposition. Instead it is shown in the very sign for this object. (A name shows that it signifies an object, a sign for a number that it signifies a number, etc.)

Formal concepts cannot, in fact, be represented by means o f a function, as concepts proper can. [...]

The expression for a formal property is a feature o f certain symbols.

So the sign for the characteristics o f a formal concept is a distinctive feature of all symbols whose meanings fall under the concept.

So the expression for a formal concept is a propositional variable in which this distinctive feature alone is constant. (7ÏP4.126)

It is now possible to use the Ontological Model presented above in order to clarify this issue further. If there were simple properties, as our Model suggests, then, according to our Model, they would fall under the following formal concept: a simple property is that which is capable of serving as an argument for p in the fully generalised form of elementary propositions ( p , x , y , z ,

r j . In other words, the form of a simple property would, given this Model, be its ability to combine with three simple spatial locations and a simple point in time so as to produce a state of affairs complying with the fully generalised form: property p is instantiated at the point in three- dimensional space fixed by three simple spatial locations x y z time This would be the simple property’s form, the ‘possibility of its occurring in states of affairs’ (TLP 2.0141).

That an object possesses a particular form is not however something that can be expressed by means of senseful propositions, since statements to this effect would not be bivalent and bipolar. Since objects are necessary, if an object possesses a particular form, it will possess it in all possible worlds, whereas, if it doesn’t, it won’t in any possible world. A statement to the effect that an object possesses this particular form would thus be either true in all possible worlds or false in all possible worlds, and could not be a genuine proposition. The fact (in a non-Tractarian sense) that an object has a specific form is not asserted by means of propositions, but shows itself in the type of signs that we use to designate it. Thus, for instance, ‘(Ex,0). 0 x’ shows that 0 is a property (cf. TLP 5.5261).

The form of a simple property does not however pick out any simple properties in particular. It cannot pick out their content, which is distinct from their form. And to know an object cannot be just to know its form. We cannot know an object if we only know the logical place it will occupy in states of affairs. Knowing an object must also involve knowing its content, which is distinct from its form. Consider the example of redness which, in spite of not being a Tractarian object, serves to illustrate this point (since it possesses a distinct form and content, as we saw in Part II): to ‘know’ redness cannot exclusively consist in knowing that redness is a property, or even in knowing that it is a colour property. It must involve knowing that it is a particular colour property, a colour property possessing a particular content which is different, for instance, from that oigreenness. Indeed, although a colour-blind person could grasp the idea that redness is a colour property, she or he, being unable to distinguish between redness and , would be unable to grasp the content of redness. A colour-blind person could not therefore be said to genuinely know redness-, in order to know redness, it is imperative to know both its form and its content, and this remains true of all things possessing a distinct form and content. Hence, to know a simple object must involve knowing both the form and the content of this object.

If I know an object I also know all its possible occurrences in states o f affairs. (Every one of these possibilities must be part o f the nature o f the object.)

A new possibility cannot be discovered later. (JLP 2.0123)

If I am to know an object, though I need not know its external properties, I must