Tractatus Logico Philosophicus

Facts

1. Total facts determine what is case and not case. All that is case is world. Thus facts in logical space constitute world.
2. case is existence of atomic facts.
3. Atomic facts are combinations of objects.
4. Configurations of objects form facts. Hence facts with variable form.
5. Existence and non existence of atomic facts is Reality
6. Atomic facts independent of another.
7. the propositional sign is a fact. A picture is a fact. Elements in definite way, that is structure. Thhat is to have a sense alternatively.
8. Only facts can be articulated sensibly. Names have no meaning on their own.
9. fact such as of relations between spatial objects , the mutual spatial objects ort positions represent the sense of a proposition.

Objects

1. There are no logical objects as logic talks of possibilities which are facts.
2. Objects have names
3. objects contain possibility of facts, the possibility is form of object
4. Objects in world have fixed form, which is determined via substance. Substance doesn't determine attributes of objects.

Names

1. The meaning of the name is the object.
2. Names empty are signs, with meaning are symbols.
3. Names are talked of, cannot be asserted since not facts.
4. Names are like points in space, meaningless dimensionless whereas propositions are like vectors.
5. The only analysis of names possible are in definitions.
6. Name have meanings then only in the context of propositions

Thoughts

1. Thoughts are logical picture of facts.(conscious thoughts)
2. Thus what is thinkable can be made explicit and stated in logical form.
3. Totality of true thoughts is thus a picture of the world.
4. THought contains possibiklity of State of affairs which it thinks.
5. Thus what is thinkable is imaginable and is possible, though can be true/false. One can't think of impossibilities, that is contradictions.
6. A thought is true a priori when its possibil;ity itself guarantees its truth, that is, a thought such as free will is known be true or cartyesian by the virtue of its existenmce.
7. Thoughts are expressed vai propositions through perceptory senses sound and writing.

Propositions

1. Sensible if derived from other true propositions.
2. Propositions are in projective relation to the world. They contain the projection not the p[rojected.
3. THat is to say the possibility of the projected, not itself.
4. The content of the proposition is that of the significant(which signifies), to repeat, in the proposition, the form of its sense contained, not the content.
5. aRb does not imply a stands in relation to b where a and b are objects. it implies "a" stands in relation to "b" where a, b are names.
6. When the constituent of proposition changed to a variable then we get a class of propositions. if all constituents of a compount proposition changedm we still have a class of propositions.
7. thus p1p2p3 to xyz, then xyz is corresponding to a logical form, with values p1,p2,p3
8. p1,p2,p3 here are expressions of the proposition p, the general form of xyz which take the symbols p1,p2,p3, then the determined values p1p2p3, the essence lies in the description of symbols, and asserts nothing of the symbolized(explain)
9. thus propositions is a function of symbols/expressions contained in it.
10. thus in logical syntax, the proposition cannot talk about itself. This is because the propositional; sign cannot be contained in itself - theory of types
11. that is to say a function cannot be its own argument F(F(x)) here since F but one outer one inner they have different meanings and hence redundant. Thee F kletter by itself signifies nothing. then if F(F(x)) and F(F(F(x))) here one is \(\phi(F(x))\) and other is \(\psi(\phi(F(x))\)
12. thus we can write the resolution of russells paradox as \[F(F(u)) : (\exists\phi:F(\phi u).\phi u = Fu\]
13. Propositions have accidental and essential features, the former is how particular signs make it up where as the latter expresses its sense. The particular configuration that is to say unimportant but the possibility of every possible is revealing of Reality.
14. Propositions have a sense independent from facts. Say if that were not the case, then T/F relations exist between signs too. p signifies T !p signifies F, such that understandiung by the way of !p(negative teaching) is completely valid. But this cannot be so since p is T if it asserts the case where "p" = !p[is the case]then !p is T[ !p is tyhe case] and we have a contradiction.
15. This is to say that p and !p can assert the same assertion only means that the not operator ! is not in reality. Negation doesn't add to the sense of proposition such that !(!p) = p. p and !p have opposite senses but coreespond to the same reality.
16. For example a black spot on a white page where each pixel takes a 0 to 1 value indicating black or white, the point here is that cfor any pixel to have a black or white value, it first needs to be known under what conditions is it judged as either Black or white. In a random pixel, even where there exist T/F values but not the judgment conditions,c the proposition is rendered without sense as they coresspond to nothing.
17. This is to say that "The present king of france is bald" cannot be taken at false value since there is no present king of france so that it can neither be judged T or F whil;e in logic which is not rid of colloqial elements has this problem and incorrectly judged as false. Thus for a proposition to exist it must have sense. It's possibility stems from thabt, and hence sense precedes proposition and cannot be judged a posteriori that sense or senseless.
18. Thus !p = T is wrong as the sense is in denial, and a denying proposition is logically different from a proposition denied. the proposition denied in fact determines the denying proposition. Thus to deny the the denied proposition are two different proposiitons.
19. \(\sum P:P==T\) is Totality of Natural Science. Thus Philosophy cannot be a natural science. Philosophy object in elucidation or clarification of arguments/thoughts, and hence is an anctivity. Thus there are no philosophical propositions.
20. Proposiitons represent Reality, cannot represent what they share in common with reality. Since that is akin to the logical form which provides the possibility of representation.
21. To represent the logical form one needs to go outside that logic, the world that is to display it. A 2d plane's geometry logic can only be displayed with the existence of a 3d space.
22. The sense of a proposition lies in its agreement(disagmt) with the existence of atomic facts. The simplest propon that is asserts the existence of an atomic fact. The simple propon is then just a connection of names where if names x0,y0,z0 then a function of names is the simple propon
23. say p: a=b where = implies sign a is replaceable by b, then a and b are two signs of same meaning, and are just presentations which say nothing about the meanings of a and b. So say you don't know that a and b signify the same object. Then do you understand the names? Of course not.
24. the proposition a=a is neither a simple proposition nor significant signs, since a simple proposition if T implies that the atomic fact exists.

Signs and symbols

1. sign must be sensibly perceptible used for projecting possible state of affairs
2. projection here is tantamount to thinking of the sense of proposition.
3. sign which carries the proposition is the propositional sign.
4. definitions are primitive signs
5. names are simple signs
6. primitive sign signifies through signs by which it is defined.
7. thus primitive signs are the named, the rest which are derived and are not primitive are defined with primitive signs.
8. unlike the proposition the derived sign though cannot be taken apart, the primitive signs which form then are unique and independent or atomic./
9. primitive signs meaning in ostentation or elucidation, what is not already expressed in primitive or derived signs applied by the existents to express that unexpressed.
10. Elucidation is a proposition of primitive signs, where the existent sigmns meanings are already known.
11. expressions are symbols, that is signs with sense. expressions are parts of propositions which characterize its meaning.
12. the proposition is a symbol or expression and characterizes a form and content.
13. symbol presupposes the forms of all propositions in which it can occur. that is the propositions a symbol characterizes represent that symbol in their general form where in this form. the expression or symbol is contant and everything else is variable.
14. that is a common charachteristic mark of proposiitons.
15. The symbol is presented as variable, which when valued are propositions various which contain the sense of that symbol. that is Lt var-> constant Expn = propon - this is thus a propositional variable.
16. 2 symbols can have a common sign, the sign is the sense perceptible part of the symbol, but then those 2 signs signify differently, that is same signs but different symbolisms.
17. Let \(x : (x_{1},x_{2},x_{3},...)\) then the variable \(x\) is the sign of the concept-object(objects as variables in logical symbolism). The point is that the object belonging to a formal concept cannot be expressed by a proposition. It is shown in the sign(name) of that object. These formal concepts just like proper concepts cannot be presented by functions(primitive signs analoggy). Expression of a formal concept is a propositional variable. Thus the propositional variable signifies the formal concept where the values the variable holds are objects under the said concept.
18. \(\exists (x,y)\) if this is used as a proper concept then arise from it senseless propositions.
19. For example "There are objects" is not valid(LIKE PYTHON) "there are books" is valid.
20. For example \(\exists y\in Y\) then the objectsare underlied with macros so to say, the keywords in a programming language, which then cannot be used as variables, as that would lead to recursion. Similar problematic uses of words like compllex, facts, objects, functions, number - is a must to be resolved in PL. Here these formal concepts can be treated as variables only where values are taken, not as functions or classes which is error.
21. Thus to say 1 is a number is a senseless proposition as it is a recursion, akin to saying There is only one 1 or more evidently "2+2 at 3'o'clock is equal to 4". The senselessness in all of these aret he same, however it may not be appartent in some which leads to paradoxes.

Language

1. In colloquial language multivalued signs is prevalent, 2 symbols with same signs.
2. For example "is" - equality, existence, verb, adjective(identity)
3. Colloqial confusions - applicable symbolism "Green is green" where proper noun and adjective same sign
4. In development of perspicious language such symbolism is to be avoided. The symbolism needs then a logical grammar.(syntax)
5. In the logical language(perscipious) symbol through use of sign where unecessary signs rendeered meaningless.
6. Thuys Russell's paradox is resolved that is every set which is not a member of itself -
7. Talking about the meanings of sign themselves that is the sign x is empty but not in russell's case, in the logical syntax, a sign itself has no meaning, it is only in the description of expresisons.
8. The propositional sign is the thought or alternativelky the thought is significant proposition.
9. Language is \(\sum P\)
10. Natural language hides within it the logic of language, just as we produce sounds without knowing how we do the process via the vocal cords. Natural language thus expresses sense despite the confusions within it.
11. Natural language like the clothes that ornament the clothed, where the body parts are implicit in the cloth for that particular limb.
12. NL are words like Wittgenstein box which hides the thought, and hence propositions in NL are prone to senselessness(not true or falsity)
13. What is good, or is that beautiful - an example of a pseudo philosophical problem merely the problem of NL and hence a senseless assertion.
14. That what appear to be deep problems nothing but word play since the apparent logical form from NL is not the logical form of the PL. (The clothes themselves without the body)

Case, States

1. state of affairs can be described but not named.
2. b
3. c

Pictures

1. objects form the elements of a picture of facts
2. picture of fact itself a fact.
3. elements related to all other elements in a picture. This is structure.
4. The possibility of this structure is the form of representation.
5. There are relations which make the picture. This relations belong to the picture of connection between elements and objects. This is intuition.
6. PIcture is thus a snapshot/model of reality.
7. picture is a fact, fact not necessarily a picture.
8. fact to be a picture, the picture needs to be true in the logical space, that is a correspondance between the picrture and the pictured. This correspondance is the form of representation.
9. Picture does not represent form, it shows it implicitly. This is because picture cannot be placed outside its form of representation(to show it that would be a requirement)
10. What is common between the reality and the picture is itself the form which is implicit in the picture
11. A picture is a logical picture if logical form. The logical picture can depict the world then. The logical form underlies the picture and pictured.
12. Pictures represent thus aa possible state of affairs in logical space. The picture within it the possibility of state of affairs it represents.
13. Since logical, pictures agree or disagree with reality. A picture nedds to be faithful, that is it represents the represented, which is independent of T/F values
14. What a picture presents if faithful as its SENSE
15. Thus truth or false of whether sense that is if the picture independent of T/F is faithful to reality, thus two sets of T/F
16. A true picture thus necessarily need be faithful ie sense and hence its truth cannot be stated independently.
17. THUS there can't be a priori TRUe picture.
18. A picture of state of affairs is a proposition iff logically expressed.

Logic,Language,Propositions

1. proposition determines poition in logical space. The existence of logical space guaranteed via existence of the proposition itself(form) though space can be empty. Thus a proposition gives us the whole logical space
2. proposition is a picture of reality.
3. Example - A musical piece, say beethovens 9th symphony. We have the musical sheet music or score, vinyl, cd's cassettes, 0s and 1s, analog waves, phonetic signs via singing.This is akin to the relation between language and the world.
4. The logical structure/form is common to all of these isomorphisms/manifestations. One can change among them, is like a translation of language.
5. Thus if a proposition is understood, being a faithful picture of reality, one knows the state of affairs presented by it, here then the proposition is understoiod, without having the sense of the proposition be known,c thius is because the proposition itself reflects the sendse.
6. A proposition expresses the what, but it doesnot express but implicitly shows the how, and hence is a description of a fact - description of objects being its external properties whereas description of reality being the internal properties.
7. in a true proposition then one can see the logical properties of reaslity, this is because propositions construct a reality through logic.
8. Therefore if one understands a proposition that implies if true it implies what is the case, hence understanding precdes truth and falsity of the proposition.
9. THere are logical signs yes, but they are not representative since only objects can be named, hence the logic of facts cannot be represented.
10. Lets suppose we have \[x:f(x)\]then a) Is \(f(x)\) general?, No, because we can't answer what is generalized. b)\(f(x_{g})\) then there is no scope for generalization. c) \((G,G).F(G,G)\) here we cvant determin4e the identity of variable. These methods fail because they don't have the necessary mathemnatical multiplicity.
11. thios is all to say that proposition elements and the different state of affairs have the same multiplicity, but that this multiplicity cannot be represented.
12. In Idealism spatial relations gathered through spatial spectacles, but they cant exzplain the multiplicity of those spatial relations, assumes without spectackles and with spectacles but those spectacles are necessarily always on.
13. Just like the musical piece, the logical form shows itself in language, cannot be isolated or made explicit.The vinyl disk with grooves is the proposition with the form of that musical piece. Thus the propositions exhibit the logical form of reality, so if fa propn for object a and ga another propn and if fa and ga contradict one naother this is shown in the structure, and what can be shown cannot be said.
14. The properties of these structures is then called internal property and the relations as internal relations which are iumplicit.
15. If this internal property since by definition is unthinkable(in the thought sense) then the object doesn't posess the internal property like it posesses the external attributes.
16. To distinguish then forms via properties cannot be done as iot would assume we can assert properties of forms.
17. Thus the internal relations between possible state of affairs express themselves via internal relations the propositions presenting them.
18. For example a series of numbers orderedd via an internal relation or a series of propositions aRb then \(\exists x: aRx.xRb\) or equivalently \((x,y): aRx.xRy.yRb\)
19. The logical form is anumeric, that is there ate noi numbvers in logic - then to say of Monism, dualism in logical form is senseless.
20. Specification of all True simple propositions then describes the world. if n atomic facts then kn possibilities that is \[k_{n}= \sum_{0}^{n} \small n\large C\small v ={^n}C{_0}+{^n}C{_1}+{^n}C{_2}...{^n}C{_n}\]
21. Since the propositionis expression of agreement disagreement with the truth possibilities, T or F coresspond to no objects, and hence there are no logical objects.

Constructing the Perspicious/logical language from Natural Language

1. Since the formal concept is given in the object which falls under the said object, then one cannot introduce concept of a function as well as special functions as primitive concepts(say concept of a number and definite numbers)
2. For example - p - b is successor to a, here \(aRb,\exists x:aRx.xRb,\exists(x,y): aRx.xRy.yRb\) Here we are going in a vivious circle and hence it's not valid since the general term is through a variable.
3. This is to say this - No proposition can answer on the question of existence of formal concepts - The following question is thus senseless "Are there unanalyzable propositions?"

The meat - Logic** Technical

Operations

1. a

Tautologies and Contradictions

Philosophical Implications

1. The limit of my language means the limits iof my world