I agree that the expression "logical objects" may be read in two ways. It can be referring to either 1) objects that are logical or 2) logic can be an object. — RussellA
As concepts can be simples, the concept "grass" could be a simple, and as words such as "grass" logically picture an object such as grass existing in a logical space, this suggests that objects such as grass are also simples. — RussellA
At 4.126 Wittgenstein introduces the term "formal concepts".
— Fooloso4
In the function T (x), where T is on a table, the function T (x) is true if the variable x satisfies the function T (x). For example, T (x) is true if the variable x is a book.
As I understand it, the variable x is what Wittgenstein is defining as a formal concept. — RussellA
An unhappy apple is an illogical proposition not an illogical object. An apple on the table or inside the sun is not a combination of objects it is a relation of the objects apple and table (on) or apple and sun (in). — Fooloso4
I don't know if you are attempting to interpret the Tractatus or argue against it. He makes a distinction between proper concepts such as grass and formal concepts such as 'simple object'. — Fooloso4
Book is not a formal concept. — Fooloso4
.For example, if an apple was a logical object in logical space, it would have the necessary properties such as weight, colour and taste. — RussellA
There are proper concepts such as "grass" and formal concepts such as the variable "x". — RussellA
I'm suggesting that in the expression "grass is green" is true iff grass is green, objects such as grass are not referring to actual objects, which are divisible, but must be referring to logical objects, which can be indivisible, and are simples. — RussellA
As part of a propositional analysis apples and tables can function as simples. Whether they do does not depend on their being possible, but on whether further analysis is needed in order for the proposition to make sense, that is, to know what is the case if it is true. — Fooloso4
Book is not a formal concept.
— Fooloso4
I agree. The variable x is the formal concept, not the book. — RussellA
In the function T (x), where T is on a table, the function T (x) is true if the variable x satisfies the function T (x). For example, T (x) is true if the variable x is a book.
As I understand it, the variable x is what Wittgenstein is defining as a formal concept. — RussellA
4.1271 – Every variable is the sign for a formal concept — RussellA
You're close, but this isn't quite right, I don't believe.
In the function: "T(x)", both "T()" and "x" show that to each corresponds a different formal concept. — 013zen
This is to say, that there is a formal concept associated with it, but "x" is not itself a formal concept, nor does it name a formal concept — 013zen
If, as Russell stipulates, x is a book, then there are no formal concepts in "T(x)". I don't know what () on the table means. — Fooloso4
A formal concept defines how the variables "T" and "x" are to "behave" or perhaps a better way to say it, is how they are to be understood. These aren't like "proper concepts", such as "red", "hard", etc. which settles the external properties of complex objects. — 013zen
We cannot, for example, input a proper number to which corresponds the formal concept of number for say, a simple object. — 013zen
So, while we can say: "There are two red fruits" this analyzes into:
∃x(P(x)) ∧ ∃y(P(y) ∧ (x≠y)) There is no sign corresponding to the formal concept "number" despite what appears to be a number presented in the proposition. — 013zen
See 4.12721. The concept of a number is a formal concept. Particular numbers are not. They fall under the concept of a number. — Fooloso4
Why do you think that particular numbers, such as the number 1, are not formal concepts? — RussellA
(4.12721)A formal concept is given immediately any object falling under it is given. It is not possible, therefore, to introduce as primitive ideas objects belonging to a formal concept and the formal concept itself. So it is impossible, for example, to introduce as primitive ideas both the concept of a function and specific functions, as Russell does; or the concept of a number and particular numbers.
I think Wittgenstein is saying that an "object" like the number 1 has a sense if it is an object or a description. — schopenhauer1
It follows from this that we cannot make such statements as “there are more than three objects in the world”, or “there are an infinite number of objects in the world”. Objects can only be mentioned in connexion with some definite property. We can say “there are more than three objects which are human”, or “there are more than three objects which are red”
It seems that an object like the number1 is a formal concept, and being a formal concept, can never be the sense of a proposition and can never be described by a proposition, but only shown. — RussellA
(4.12721) "A formal concept is given immediately any object falling under it is given. It is not possible, therefore, to introduce as primitive ideas objects belonging to a formal concept and the formal concept itself. So it is impossible, for example, to introduce as primitive ideas both the concept of a function and specific functions, as Russell does; or the concept of a number and particular numbers." — Fooloso4
In their monumental Principia Mathematica, Russell and his co-author Alfred North Whitehead attempted to create a logically sound basis for mathematics. In it their primitive proposition ∗9.1 implies that at least one individual thing exists. It follows that the universal class of things is not empty. This is stated explicitly in proposition ∗24.52. Whitehead and Russell then remark: “This would not hold if there were no instances of anything; hence it implies the existence of something.” (Principia Mathematica, Volume I, 1910, ∗24). Here then, logic seems committed to the existence of something.
If, however, I say: "There are three horses" then the number of horses is not expressed as the variable 'x', which could mean any number of horses, but as '3'. — Fooloso4
Thus, it seems to be the case for Witt’s theory, 1 + 1 = 2 is formal as it is not a state of affairs per se, but a description of a category of sets that may occur as a state of affairs. It’s a description of a class not of a particular state of affairs that could be true or false. — schopenhauer1
As numbers are formal concepts, I think I am right in saying that Wittgenstein would call this proposition meaningless. — RussellA
(4.126)When something falls under a formal concept as one of its objects, this cannot be expressed by means of 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.)
(4.1271)Every variable is the sign for a formal concept.
For every variable represents a constant form that all its values possess, and this can be regarded as a formal property of those values.
'Number' is the constant form. 1, 100, and 1,000 are variables that have as a formal property this formal concept. — Fooloso4
Yes, but Kant would simply classify it as analytic a priori. It is a truth that can be grasped through purely reasoning and not experience (equivalent to Wittgenstein's "state of affairs in the world"). But I am perplexed why with all this epistemological history he could have drawn from, he ignores it. — schopenhauer1
(6.2)Mathematics is a logical method.
The propositions of mathematics are equations, and therefore pseudo-propositions.
Yes, but Kant would simply classify it as analytic a priori. It is a truth that can be grasped through purely reasoning and not experience (equivalent to Wittgenstein's "state of affairs in the world"). But I am perplexed why with all this epistemological history he could have drawn from, he ignores it. — schopenhauer1
4.1272 - "The same applies to the words "complex", "fact", "function", "number" etc. They all signify formal concepts"
4.1274 "To ask whether a formal concept exists is nonsensical"
6.22 "The logic of the world, which is shown in tautologies by the propositions of logic, is shown in equations by mathematics.
4.21 - "The simplest kind of proposition, an elementary proposition, asserts the existence of a state of affairs.
What falls under a formal concept is not another formal concept..................If '3' was a formal concept then every number would be a formal concept. — Fooloso4
Mathematical equations are pseudo-proposiitons , but this does not mean the equation is a concept, either proper or formal. 1+1=2 is not concept, it is a calculation. — Fooloso4
'Number' is the constant form. 1, 100, and 1,000 are variables that have as a formal property this formal concept. — Fooloso4
4.1272 "The same applies to the words "complex", "fact", "function", "number" etc. They all signify formal concepts"
4.1274 "To ask whether a formal concept exists is nonsensical"
4.1272 "This the variable name x is the proper sign for the pseudo-concept object.
4.126 "the confusion between formal concepts and concepts proper"
4.21 "The simplest kind of proposition, an elementary proposition, asserts the existence of a state of affairs.
4.123 "A property is internal if it is unthinkable that its object should not possess it"
4.124 "The existence of an internal property of a possible situation is not expressed by means of a proposition: rather it expresses itself in the proposition representing the situation, by means of an internal property of that proposition".
"Objects can only be mentioned in connexion with some definite property."
"It follows from this that we cannot make such statements as “there are more than three
objects in the world”.................the proposition is therefore seen to be meaningless.........We can say............“there are more than three objects which are red”"
4.1272 "The same applies to the words "complex", "fact", "function", "number" etc. They all signify formal concepts"
4.126 - "When something falls under a formal concept as one of its objects, this cannot be expressed by means of 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.)"
4.1272 "Whenever it is used in a different way, that is as a proper concept-word, nonsensical pseudo-propositions are the result"
5.535 "This also disposes of all the problems that were connected with such pseudo-propositions"
6.22 "The logic of the world, which is shown in tautologies by the propositions of logic, is shown in equations by mathematics.
4.0312 "My fundamental idea is that the "logical constants" are not representatives; that there can be no representatives of the logic of facts."
4.126 "A name shows that it signifies an object, a sign for a number that it signifies a number, etc"
4.1271 "For every variable represents a constant form that all its values possess, and this can be regarded as a formal property of those values."
@RussellAMathematical equations are pseudo-proposiitons , but this does not mean the equation is a concept, either proper or formal. 1+1=2 is not concept, it is a calculation. — Fooloso4
It has been said that Wittgenstein never studied philosophy as such, although he may have learnt from certain other philosophers he was in direct contact with, such as Bertrand Russell. So he did ignore epistemological history as he was not interested in the history of philosophy as a field of knowledge. — RussellA
There may be a difference between Kant's analytic a priori and Wittgenstein's formal concept, in that Kant's analytic a priori is knowledge prior to any knowledge about the world, whereas Wittgenstein's formal concept straddles on one side language and thought and on the other side the world. — RussellA
In the Tractatus, the formal concepts existing in language, which cannot be described but only shown, are mirrored by formal concepts that also exist in the world
4.21 - "The simplest kind of proposition, an elementary proposition, asserts the existence of a state of affairs. — RussellA
IE, within the Tractatus, the number 3 cannot be a pseudo-object as it doesn't make up the substance of the world, but because it is part of the logical structure of both elementary propositions and state of affairs, it must be, as with all particular numbers, and as with all logical constants, a formal concept. — RussellA
The Tractatus mentions three kinds of concepts: formal concept, concept proper and pseudo-concept. — RussellA
Objects are pseudo concepts because they exist in the world and make up the substance of the world. — RussellA
The number 3 is a sign that signifies a number. Numbers are formal concepts. Therefore, the number 3 is a sign that signifies a formal concept — RussellA
Why is "One is a number" a formal concept and "1 + 1 = 2" not a "formal concept"? — schopenhauer1
"It follows from this that we cannot make such statements as “there are more than three
objects in the world”.................the proposition is therefore seen to be meaningless.........We can say............“there are more than three objects which are red”"
That was what I said, that numbers (or rather equations) are formal concepts because they are not abouts states of affairs of the world. Again, Kant is informative here, it is an analytic a priori statement. — schopenhauer1
4.21 "The simplest kind of proposition, an elementary proposition, asserts the existence of a state of affairs.
One difference between Kant and Wittgenstein is that Wittgenstein's Picture Theory in the Tractatus does not engage with the possibility of knowing that 1 + 1 = 2 prior to observing the world (as I understand it). — RussellA
Wittgenstein seems to not care to discuss mind, but language limits. — schopenhauer1
===============================================================================Now it is becoming clear why I thought that thinking and language were the same. For thinking is a kind of language. For a thought too is, of course, a logical picture of the proposition, and therefore it just is a kind of proposition.
If signs are not signifying a possible states of affairs, they are not picturing anything, and thus cannot be communicated with any sense. — schopenhauer1
1 +1 =2 is not derived from empirical evidence, but as a functioning of how numbers work — schopenhauer1
Surely I can point to these processes that account for object formation in the mind, and how we attach meaning to objects — schopenhauer1
The picture theory of meaning was inspired by Wittgenstein’s reading in the newspaper of a Paris courtroom practice of using models to represent the then relatively new phenomenon of auto-mobile accidents (Grayling 40). Toy cars and dolls were used to represent events that may or may not have transpired. In the use of such models it had to be stipulated which toys corresponded to which objects and which relations between toys were meant to represent which relations between those objects (Glock 300).
'3' signifies the value of the concept number. A particular number falls under the concept number in a way analogous to 'table' falling under the concept 'object'. That does not mean that 'table' is a pseudo-concept. — Fooloso4
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