• Wallows
    8.7k
    Hello, @Wittgenstein, you are missed dearly.

    Best regards.
  • Pussycat
    194
    No wonder Wittgenstein was suicidal.
    My goodness, you tried to tear me into pieces.
    Wittgenstein

    Yes, well, sorry, I like to dissect to see what's inside, don't take it personally! :)

    090427heroes_sylar1.jpg

    Since we are talking about earlier Wittgenstein, this was before Godel came with his incompleteness theorem which by the way, Wittgenstein rejected even in the latter days.He couldn't have meant that when he wrote back then but you can take his wordings differently to get the accurate interpretation.Wittgenstein

    I remember reading about Wittgenstein's efforts to understand Godel and his incompleteness theorem, Wittgenstein used, as usual, a dialectical approach, like a child, and wrote his thoughts in his notebook. After seeing this, Godel exclaimed: "Has Wittgenstein lost his mind?!" :D But I don't think that we should see Wittgenstein's remarks neither as an affirmation nor as a rejection of the theorem.

    What I meant by certainty was a relative certainty in science compared to absolute uncertainty in ethics,metaphysics ( these 2 ).If you look at Wittgensteins mathematical philosophy, he considered them to be tautologies which do not belong to this world.Wittgenstein

    You know, "absolute" and "relative" do not make much sense. But there is surely a difference between scientific and ethical matters. Current situation in mathematics is that to prove stuff, a mathematician must make clear what system and what axioms are going to be employed. A theorem that is proved in one system, might be disproved or be not provable in another, and I think that most mathematicians have stopped trying to conform maths to reality, seeing their science as a game, sui generis. Whereas in physics, we are at a standstill, with all these tens or hundres of interpretations of quantum mechanics flying around, each giving its own view of how things stand, the physical reality I mean. So pretty uncertain there, not to mention the uncertainty principle. Now, ethics is something else, I doubt that we can even use "certain" or "uncertain" to describe it. And I don't think that Wittgenstein used the term "tautologies" for ethics and metaphysics, but for propositions of logic.

    Tbh, it was a complete intrepretation but it had flaws too.
    There are countless ways to read the Tractatus, I dont think any viewpoint is totally wrong.There are flaws and advantages.Can you explain how it is incomplete.
    Wittgenstein

    I think that the logical positivists paid no attention to the last few pages of the Tractatus, treating them as mere nonsense, as if they outright discarded it. Which is why I said "uninterpreted", but yes of course, you can say "misinterpreted" as well. So either "complete (and flawed)" or "incomplete", logically it makes no difference anyway, the difference is only a psychological one, it is what it is, like they say.

    On the last point, the tractatus talks of states of affairs which are essentially all the possible combinations of objects, and the possibility is written in the objects themselves.We get the picture theory from it and in my opinion, the picture theory favours taking objects as tangible things for lack of better word.He describes somewhere that we cannot think of a geometrical object without space to further elucidate his picture theory.Wittgenstein

    I will take these two propositions from the Tractatus:

    2.01 An atomic fact is a combination of objects (entities, things).
    2.0251 Space, time and colour (colouredness) are forms of objects.

    So objects are entities, things. And if their form is space, time and colour, something pretty abstract that is, then we can only imagine what objects really are. Not anything tangible anyway.

    Also:

    2.021 Objects form the substance of the world. Therefore they cannot be compound.
    2.0231 The substance of the world can only determine a form and not any material properties. For these are first presented by the propositions—first formed by the configuration of the objects.

    Substance, which is related to objects, does not have any material properties. Which is where logical positivists I think got it wrong, assuming that objects are something like elementary particles, with elementary propositions describing how these particles are and behave.

    So I see that Wittgenstein took tractarian objects as an auxilliary hypothesis, like those used in philosophy of science, dark matter, for example: "we don't know what/how they are, but we are certain that they exist, we hope that future examination will give us more insight into these". But of course Wittgenstein was forced later to drop all talk about elementary propositions, and objects too, I suppose. (a picture held us captive)

    https://en.wikipedia.org/wiki/Dark_matter#In_philosophy_of_science

    How old are you btw, it seems you are older than me.Wittgenstein

    I will tell you, since you ask, but let us see first if you can guess my age?

    If you want to know about my last statement you can check this out.Wittgenstein

    Thanks, I read it, I tried to find what your opinion is on these simple objects, but I can't say that I have.
  • Pussycat
    194
    But if it is such that God is connected with meaning, then I think that the act would have to be that of giving meaning to one's life, to find purpose, to make one's life meaningful, to make it worth and mean something, whatever that may be, and what happens afterwards, as a consequence of this act, this is not related to God's will in any case. And furthermore, a meaning-giving act is something most godly, holy and divine (good willing) that brings about happiness - a hallowing, whereas a meaning-removing act something most ungodly and unholy (bad willing) that brings about unhappiness - a wallowing. Such that the value of the action is in the act itself, like you said, the act being a meaning-creating one, in contrast to a meaning-destructive one, both acting on the ethical plane, and not on the facts of the world. Who would support the notion of a meaningless God anyway? So it would appear that Wittgenstein is telling us that it is God's will to give ourselves a purpose in life, but not specifying which.Pussycat

    Yes, a wallowing of sorts... But, there's something to be said about wallowing, coming from a professional wallower. In that to wallow is to appreciate and prioritize or value what one does already have. The act of endowing meaning onto the world is in some sense solipsistic and egotistical. As if the ant or pig, which we step on or eat, didn't have a personal life of its own, which it might as well have.Wallows

    Hey Wallows, in regard to these, have you watched the series "Hannibal"?

    https://www.imdb.com/title/tt2243973/
  • Wallows
    8.7k


    No, but I'll give it a whirl. Looks cool.

    :cool:
  • Wittgenstein
    190

    I remember reading about Wittgenstein's efforts to understand Godel and his incompleteness theorem, Wittgenstein used, as usual, a dialectical approach, like a child, and wrote his thoughts in his notebook. After seeing this, Godel exclaimed: "Has Wittgenstein lost his mind?!" :D But I don't think that we should see Wittgenstein's remarks neither as an affirmation nor as a rejection of the theorem.
    If l can recall Wittgensteins remarks
    I imagine someone asking my advice; he says: “I have constructed a proposition (I will use ‘P’ to designate it) in Russell’s symbolism, and by means of certain definitions and transformations it can be so interpreted that it says ‘P is not provable in Russell’s system’. Must I not say that this proposition on the one hand is true, and on the other hand is unprovable? For suppose it were false; then it is true that it is provable. And that surely cannot be! And if it is proved, then it is proved that is not provable. Thus it can only be true, but unprovable.”
    My humble take on this is, what is wittgenstein saying by using the word true, is he equating provable with true.He tried in the following quotations to dismantle the incompleteness theorem.
    Just as we can ask, “ ‘Provable’ in what system?,” so we must also ask, “ ‘True’ in what system?” “True in Russell’s system” means, as was said, proved in Russell’s system, and “false” in Russell’s system means the opposite has been proved in Russell’s system.—Now, what does your “suppose it is false” mean? In the Russell sense it means, “suppose the opposite is been proved in Russell’s system”; if that is your assumption you will now presumably give up the interpretation that it is unprovable. And by “this interpretation” I understand the translation into this English sentence.—If you assume that the proposition is provable in Russell’s system, that means it is true in the Russell sense, and the interpretation “P is not provable” again has to be given up. If you assume that the proposition is true in the Russell sense, the same thing follows. Further: if the proposition is supposed to be false in some other than the Russell sense, then it does not contradict this for it to be proved in Russell’s system.
    He clearly states the proposition "P is not provable has to be given up ".

    Current situation in mathematics is that to prove stuff, a mathematician must make clear what system and what axioms are going to be employed. A theorem that is proved in one system, might be disproved or be not provable in another, and I think that most mathematicians have stopped trying to conform maths to reality, seeing their science as a game.
    I don't think mathematicians have to conform to anything besides their own system of axioms and wittgenstein was strictly.I see this as a great merit and clearly ethics or metaphysics do not have such groundwork to support/prove their proposition.There is certainty in a system, it would be absurd to compare two "games" with different rules.Bertrand Russell wrote somewhere that all the worlds must conform and be according to mathematical truths, but the project failed as mathematics wasn't what they thought it was.
    ( even Kant made this mistake when he did not consider non euclidean geometry ).

    So I see that Wittgenstein took tractarian objects as an auxilliary hypothesis, like those used in philosophy of science, dark matter, for example: "we don't know what/how they are, but we are certain that they exist, we hope that future examination will give us more insight into these". But of course Wittgenstein was forced later to drop all talk about elementary propositions, and objects too, I suppose. (a picture held us captive)
    Auxiliary hypothesis can mean two things, either he was not clear in what they meant or rather it didn't matter what they referred to.Either way, it creates problems as we go further on reading tractatus.They are central to tractatus and the picture theory.

    I think that the logical positivists paid no attention to the last few pages of the Tractatus, treating them as mere nonsense, as if they outright discarded it. Which is why I said "uninterpreted", but yes of course, you can say "misinterpreted" as well. So either "complete (and flawed)" or "incomplete", logically it makes no difference anyway, the difference is only a psychological one, it is what it is, like they say.
    They did but could not make anything out of it, those propositions were central to wittgenstein refuting his earlier philosophy.I think wittgenstein was trying to show the inexpressible but he was forced to express it in the end, which led to confusion.He even referred to it as a ladder which must be discarded.

    Whereas in physics, we are at a standstill, with all these tens or hundres of interpretations of quantum mechanics flying around, each giving its own view of how things stand, the physical reality I mean. So pretty uncertain there, not to mention the uncertainty principle.
    Well let's not exaggerate the number of interpretations to a hundred, the standard one is clearly copanhagen one, but l believe physicists are clearly not impressed with philosophy these days sadly and they would rather not discuss what wave function refers to in the real world but simply its function,uses,applications in the mathematical framework of quantum physics.Uncertainity principle can be applied to real life examples such as electrons but they are deeply rooted in mathematics.I am against scientism and do not believe it can describe the world completely.
    Infact wittgenstein was really critical of it and he suggested that natural laws and the physical phenomenon are not synonymous and we can imagine a different set of system, which have different set of natural laws and each describe the world with the same accuracy.
    When I quoted science and mathematics, I wanted to demonstrate that, these fields have sorted themselves out as correction was possible but ethics and metaphysics cannot be sorted out, their problems are merely nonsense and they do not need an answer as the problems vanish once we understand the confusion.
  • Fooloso4
    1k
    On the last point, the tractatus talks of states of affairs which are essentially all the possible combinations of objects, and the possibility is written in the objects themselves.We get the picture theory from it and in my opinion, the picture theory favours taking objects as tangible things for lack of better word.Wittgenstein

    The substance of the world can only determine a form, and not any material properties. For it is only by means of propositions that material properties are represented - only by the configuration of objects that they are produced. — T 2.0231

    That there are simple objects he takes to be evident, a priori. Just what those objects are, however, he never says. It is the configuration of objects that determine material properties, that is to say, tangible properties. The the ability to picture facts is based on the transcendental logical scaffolding that underlies both the facts and our ability to picture them. It is not necessary to know the objects only their configuration.
  • Wittgenstein
    190

    . Just what those objects are, however, he never says.
    I have to disagree, he does mention what objects are in the tractatus.
    3.203 A name means an object. The object is its meaning. ('A' is the same sign as 'A'.)
    The question remains that are the names universals or particulars ?
    Can you clarify on pictorial form ?
    2.17 What a picture must have in common with reality, in order to be able to depict it--correctly or incorrectly--in the way that it does, is its pictorial form.
    2.174 A picture cannot, however, place itself outside its representational form.
    How can we know a pictorial form since it is outside the representational form, are there rules in which object combine to form a proposition ?
    There is also another important question, I hope you will give it a little attention, Can two proposition be different yet be logically equivalent.Consides this below
    ~p implies q and ~p implies q" , does that make q and q" logically equivalent, although they maybe different proposition.
    Final question, How would you describe the picture of a contradiction, consider a proposition p having a pictorial form.Can we picture or imagine a singular ~p ?
    What if we have a system of 100 propositions and we negate all of them, what does that leave for us to picture ?
  • Pussycat
    194
    He clearly states the proposition "P is not provable has to be given up ".Wittgenstein

    I think that he was just trying to clarify what the concept of "proof" really is, and what does it do. Wasn't it in this section that he wrote that squaring the circle with just using only compass and straightedge was proved impossible, or do I remember incorrectly? And that this proof stopped people from further trying? So, if I remember correctly, he said that proof ends all further attempts, this is what proof actually does to you. And my take is that he was afraid that, once people accepted Godel's theorem, taking it as a proven fact, they would stop further inquiry into the matter. oof!
  • Pussycat
    194
    cool, but what about the other series, Legion? You haven't told me.
  • Pussycat
    194
    I have to disagree, he does mention what objects are in the tractatus.
    3.203 A name means an object. The object is its meaning. ('A' is the same sign as 'A'.)
    The question remains that are the names universals or particulars ?
    Can you clarify on pictorial form ?
    2.17 What a picture must have in common with reality, in order to be able to depict it--correctly or incorrectly--in the way that it does, is its pictorial form.
    2.174 A picture cannot, however, place itself outside its representational form.
    How can we know a pictorial form since it is outside the representational form, are there rules in which object combine to form a proposition ?
    Wittgenstein

    Continuing from what I wrote before, let us take the concept of proof and treat it as a tractarian object. We have a name for it, called "proof", in english, in other languages it is called otherwise. But however it is called, the meaning is the same - the object (proof) is the name's meaning. What is its pictorial form, how do we know it, and how does it combine with other objects to form propositions?
  • Fooloso4
    1k
    [quote=
    I have to disagree, he does mention what objects are in the tractatus.[/quote]

    He does not identify anything as a simple. He never names a simple object. He never analyzes a word to determine what the simples are that it is composed of.

    How can we know a pictorial form since it is outside the representational form, are there rules in which object combine to form a proposition ?Wittgenstein

    Objects do not combine to form propositions, words do. Words are a combination of simple names but again Wittgenstein never names them.

    3.334 The rules of logical syntax must go without saying, once we know how each individual sign signifies.

    Can two proposition be different yet be logically equivalent.Consides this below ~p implies q and ~p implies q" , does that make q and q" logically equivalent, although they maybe different proposition.Wittgenstein

    Does this answer your question?:

    3.34 A proposition possesses essential and accidental features.
    Accidental are the features which are due to a particular way of producing the propositional
    sign. Essential are those which alone enable the proposition to express its sense.

    3.341 The essential in a proposition is therefore that which is common to all propositions which
    can express the same sense.
    And in the same way in general the essential in a symbol is that which all symbols which
    can fulfill the same purpose have in common.

    Final question, How would you describe the picture of a contradiction, consider a proposition p having a pictorial form.Can we picture or imagine a singular ~p ?
    What if we have a system of 100 propositions and we negate all of them, what does that leave for us to picture ?
    Wittgenstein

    4.462 Tautologies and contradictions are not pictures of reality. They do not represent any possible situations. For the former admit all possible situations, and latter none.
  • Wittgenstein
    190

    Does this answer your question?:

    3.34 A proposition possesses essential and accidental features.
    Accidental are the features which are due to a particular way of producing the propositional
    sign. Essential are those which alone enable the proposition to express its sense.

    3.341 The essential in a proposition is therefore that which is common to all propositions which
    can express the same sense.
    And in the same way in general the essential in a symbol is that which all symbols which
    can fulfill the same purpose have in common.
    Consider this proposition, "The cat is sitting on the table", can you point out the accidental and the essential feature.
    What are the particular ways of producing propositional sign ? according to ramsey, propositional sign are actually sentences but they express the essence/quality of the words of which they are composed of.
    Now to take on "the essential" since it enables proposition to express something common to all proposition which express the same sense, what part of proposition can be termed as essential, you have quoted him but l think the ambiguity here is really confusing.I don't think we can understand wittgenstein unless we apply his philosophy on practical examples to see his theory of proposition becoming alive and clear.

    What if we have a system of 100 propositions and we negate all of them, what does that leave for us to picture ?
    — Wittgenstein

    4.462 Tautologies and contradictions are not pictures of reality. They do not represent any possible situations. For the former admit all possible situations, and latter none.
    I have a made a distinction between two different types of contradiction.If we consider a world(system), where we have 100 possible propositions, how does negating one of them lead to no possible situation.Is still allows us to 99 other possible situations.

    3.334 The rules of logical syntax must go without saying,
    What are the rules of logical syntax ?

    He does not identify anything as a simple. He never names a simple object. He never analyzes a word to determine what the simples are that it is composed of.
    He never names the simple object but since he was influenced by Russell who treats objects as names, we can say that his silence was for allowing different Interpretations.Names are used in propositions but names must refer to something in the world, otherwise they would be meaningless, hence names are the meaning of objects.
  • Fooloso4
    1k
    Consider this proposition, "The cat is sitting on the table", can you point out the accidental and the essential feature.Wittgenstein

    Cat and table do not name simple objects. The names are accidental. The signs are accidental. We might say: Die Katze sitzt auf dem Tisch.

    3.1431. The essential nature of the propositional sign becomes very clear when we imagine it made up of spatial objects (such as tables, chairs, books) instead of written signs.
    The mutual spatial position of these things then expresses the sense of the proposition.

    Putting a cat on a table would express the sense of the proposition.

    I have a made a distinction between two different types of contradiction.If we consider a world(system), where we have 100 possible propositions, how does negating one of them lead to no possible situation.Is still allows us to 99 other possible situations.Wittgenstein

    I am sorry but I do not understand what you are saying. What are the two different types of contradiction? Negation is not a contradiction. A contradiction cannot be negated.

    What are the rules of logical syntax ?Wittgenstein

    We cannot have an illogical thought (3.03). Any thought already complies with logical syntax. It is not as if there is a set of rules that we can either comply or not comply with. We either say something that has sense or is nonsense. Logic takes care of itself.

    He never names the simple object but since he was influenced by Russell who treats objects as names, we can say that his silence was for allowing different Interpretations.Names are used in propositions but names must refer to something in the world, otherwise they would be meaningless, hence names are the meaning of objects.Wittgenstein

    He never names simple objects simply because he can't. This was at the basis of his criticism of the Tractatus in PI.
  • Wittgenstein
    190
    Cat and table do not name simple objects. The names are accidental. The signs are accidental. We might say: Die Katze sitzt auf dem Tisch.
    I can see them being accidental in the sense that we could easily replace cat and table with dog and chair respectively.However this depends on how does one define accidental or essential in a system.Their placeholders must be there in the proposition," x is sitting on y", in this general proposition, x and y are essential as all they denote all the possible substitutents. We can also argue in a certain world, only cats can sit on table ( it is not hard to imagine ), would that make them essential.
    To give a better example, consider this "electrons are negatively charged and are found in the atom " are the electrons an essential feature in this sentence in this world.I believe that it is not possible to distinguish essential and accidental feature, it is all relative to the the frame of reference.

    What if we have a system of 100 propositions and we negate all of them, what does that leave for us to picture ?
    — Wittgenstein

    4.462 Tautologies and contradictions are not pictures of reality. They do not represent any possible situations. For the former admit all possible situations, and latter none.

    l have a made a distinction between two different types of contradiction. If we consider a world(system), where we have 100 possible propositions, how does negating one of them lead to no possible situation.Is still allows us to 99 other possible situations
    What are the two different types of contradiction? Negation is not a contradiction. A contradiction cannot be negated.
    Actually it was a miscommunication, sorry for messing it up, l actually wanted to ask you if we can can call a proposition which negates all of the proposition in the system except itself to be a picture of the reality.
    It is interesting to note the feature which a contradiction and a negation share in this special case, ( a contradiction says nothing so we cannot picture a reality while a total negation also leaves nothing to picture reality, it is close to Russell's paradox.) The proof by contradiction and proof by negation are also similar.I disagree that a contradiction cannot be negated, suppose L is a contradiction then ~L would be a tautology.

    We cannot have an illogical thought (3.03). Any thought already complies with logical syntax. It is not as if there is a set of rules that we can either comply or not comply with. We either say something that has sense or is nonsense. Logic takes care of itself.
    How will that sit with incompleteness theorem since we have something that Is not provable in a system and there are other controversial axiom of choice,axiom of infinity in logic which cause trouble.I agree that we can not think illogically but sometimes illogical proposition can appear even in a rigorous system.Logic needs to be taken care of sometimes.

    He never names simple objects simply because he can't. This was at the basis of his criticism of the Tractatus in PI
    Well, I will look up to that, does it mean that naming simple object causes a lose of generality.
  • Wittgenstein
    190

    I think that he was just trying to clarify what the concept of "proof" really is, and what does it do. Wasn't it in this section that he wrote that squaring the circle with just using only compass and straightedge was proved impossible, or do I remember incorrectly? And that this proof stopped people from further trying? So, if I remember correctly, he said that proof ends all further attempts, this is what proof actually does to you. And my take is that he was afraid that, once people accepted Godel's theorem, taking it as a proven fact, they would stop further inquiry into the matter. oof!
    Well squaring the circle was proved to be an impossible feat by proving pi was transcendental.Wittgenstein was a an advocate of math being our creation, we cannot say what can or not be done in mathematics or in another case, he found fermet's last theorem, as not falling in mathematical realm as it was essentially saying
    a^x +b^x=c^x, there is no set of numbers (a,b,c ) which satisfy the equation for x>2.He did not believe this statement to be decidable, hence you are right in saying he thought they discouraged people from looking on but the key point was he did not consider them to be mathematical propositions.
    the object (proof) is the name's meaning. What is its pictorial form, how do we know it, and how does it combine with other objects to form propositions?
    Well it is clear a proof consist of more than one proposition, is it simple, I dont think so.Further can we l dont think wittgenstein says object and proposition are same, let alone a set of proposition and an object.I could be wrong though.
  • Fooloso4
    1k
    I can see them being accidental in the sense that we could easily replace cat and table with dog and chair respectively.Wittgenstein

    But that would not be a picture of the facts. Dogs are not cats and chairs are not tables. It is not the case that a dog is on the chair.

    l actually wanted to ask you if we can can call a proposition which negates all of the proposition in the system except itself to be a picture of the reality.Wittgenstein

    Do you mean: all propositions except this one are false? Sure, why not. First, that proposition might be false despite the claim that it is true, and in that case the truth or falsity of other propositions remains unchanged. Second, within a specified domain I see no problem with saying that every proposition in that domain except this one is false - all p's are not-p and all not-p are p.

    total negation also leaves nothing to picture reality,Wittgenstein

    No, it simply changes the truth value of the propositions.

    I disagree that a contradiction cannot be negated, suppose L is a contradiction then ~L would be a tautology.Wittgenstein

    L and ~L would be a contradiction. L and L would be a tautology.

    How will that sit with incompleteness theorem ...Wittgenstein

    I don't know enough about the incompleteness theorem to comment.

    ... since we have something that Is not provable in a systemWittgenstein

    It is not a matter of proof within a system. An illogical proposition is nonsense.

    I agree that we can not think illogically but sometimes illogical proposition can appear even in a rigorous system.Wittgenstein

    Is the problem with logic or with a formal system of logic? Wittgenstein says that logic is transcendental (6.13) - it is the condition for the possibility of the facts of the world and language. I think Wittgenstein regards set theory, along with mathematics, to be an invention, a construct. Any problems that arise within it are inherent in construct not in the logical scaffolding.

    Well, I will look up to that, does it mean that naming simple object causes a lose of generality.Wittgenstein

    I am not sure what you mean. On one hand you have simple objects and on the other names of those objects. The configuration of objects form the things of this world, the facts - cats and dogs and tables. The configuration of simple names form the words that name such things as cats and dogs and tables.
  • Pussycat
    194
    Well it is clear a proof consist of more than one proposition, is it simple, I dont think so.Further can we l dont think wittgenstein says object and proposition are same, let alone a set of proposition and an object.I could be wrong though.Wittgenstein

    I am talking about proof's form in general, a proof of something. For example, a mathematical proof like Fermat's theorem, proof about who the murderer is, proof that your wife is cheating you, whether it is raining etc. Proof can be combined with these, but it cannot combine with, lets say, what the best colour is. If you wanted to picture "proof", as a concept, how would you do it? Or if you wanted to explain it to someone ignorant, what would you tell him?
  • Wittgenstein
    190
    But that would not be a picture of the facts. Dogs are not cats and chairs are not tables. It is not the case that a dog is on the chair
    It will be a different fact but the proposition will have a sense.Since you disagree with that reason for cats,table being accidental feature.How do you determine an accidental feature and how do you determine an essential feature ?
    No, it simply changes the truth value of the propositions
    It does change the truth value of proposition.There are some problems with negation, consider the proposition
    " there is a shape which is both circle and square" , its negation is true ( correspondance to reality shows) but can you say the shape which we are talking about exists in reality.Is its picture possible.It isn't.However the negation is true.I hope l have shown that a proposition can have sense and be true yet have no corresponding picture in reality.You can claim it is not logical but since l haven't used the term "square circle", but used the term shape which is logical.I can be wrong.

    Is the problem with logic or with a formal system of logic? Wittgenstein says that logic is transcendental (6.13) - it is the condition for the possibility of the facts of the world and language. I think Wittgenstein regards set theory, along with mathematics, to be an invention, a construct. Any problems that arise within it are inherent in construct not in the logical scaffolding.
    Wittgenstein regards math as a method of logic, so if we were to take it by face value, it would mean a formal system of logic ( like maths ) has the problem.I think your point of view is closer to being correct to what wittgenstein had in mind but l would wonder where the boundary lies between formal system of logic and logic, and how would logic allow the systems to have a logical fault in their construction.

    Thanks for going at detail length on names,objects.If l understand you correctly.
    Simple names are left untouched in tractatus, their configuration forms words which name object.
    "The configuration of objects form the things of this world, the facts - cats and dogs and tables."
    Is "cat" a picture of reality- a fact.However wittgenstein claims states of affairs ( facts) are the combination of objects.So would the proposition " the cat is sitting on a table " be a complex proposition?
  • Wittgenstein
    190

    “I want you to realize that when I speak of a fact I do not mean a particular existing thing, such as Socrates or the rain or the sun. Socrates himself does not render any statement true or false. What I call a fact is the sort of thing that is expressed by a whole sentence, not by a single name like ‘Socrates.’ . . .We express a fact, for example, when we say that a certain thing has a certain
    property, or that it has a certain relation to another thing; but the thing which has the property or the relation is not what I call a ‘fact.”’ (‘Logical atomism’,41, my emphasis) [\quote]~Russell
    So do words like cats,dogs represent a fact, or did wittgenstein believe in that ?
  • Wittgenstein
    190

    Proof can be combined with these, but it cannot combine with, lets say, what the best colour is.
    If you wanted to picture "proof", as a concept, how would you do it? Or if you wanted to explain it to someone ignorant, what would you tell him?
    If you want to treat prove as an object, but l don't think wittgenstein would allow it. Wittgenstein describe objects combining with each other as in chains, he kept silent on the relations between them. Objects exist independent of each other and maybe we can determine which objects cannot be combined when we see that the proposition lacks sense. How would l picture a proof, that is a tough question, l can think of its logical form but the picture would not be possible in certain cases.Wittgenstein does not consider mathematical propositions to be a part of reality, so we cannot picture them.A proof about the wife cheating her husband can be pictured easily ( I will leave that to your imagination ) . If proof were a simple object, l would give you a definite answer.I dont think a proof is an object, when like a shirt is not a an object, it is a combination of different things, hence not simple.
  • Wittgenstein
    190

    L and ~L would be a contradiction. L and L would be a tautology
    If you are using "and" as /\, the logical operator then yes but that was not my point.What l was trying to say was if L is a contradiction, then in classical logic ,~L would be a tautology.
  • Wittgenstein
    190

    3.333 The reason why a function cannot be its own argument is that the sign for a function already contains the prototype of its argument, and it cannot contain itself. For let us suppose that the function F(fx) could be its own argument: in that case there would be a proposition 'F(F(fx))', in which the outer function F and the inner function F must have different meanings, since the inner one has the form O(f(x)) and the outer one has the form Y(O(fx)). Only the letter 'F' is common to the two functions, but the letter by itself signifies nothing. This immediately becomes clear if instead of 'F(Fu)' we write '(do): F(Ou). Ou = Fu'. That disposes of Russell's paradox.
    Is wittgenstein simply saying that in f(x) and f(f(x)) the outer f perform different function in both of them and does he imply that a proposition cannot take another proposition of the same ( logical ) order as its argument. So to avoid confusion we can write F(u) where u=f(x) , to clear up that F and f are different propositional functions.
  • Fooloso4
    1k
    There are some problems with negation, consider the proposition
    " there is a shape which is both circle and square" , its negation is true ( correspondance to reality shows) but can you say the shape which we are talking about exists in reality.Is its picture possible.It isn't.However the negation is true.I hope l have shown that a proposition can have sense and be true yet have no corresponding picture in reality.
    Wittgenstein

    2.202 A picture represents a possible situation in logical space.
    2.203 A picture contains the possibility of the situation that it represents.
    2.21 A picture agrees with reality or fails to agree; it is correct or incorrect, true or false.
    2.221 What a picture represents is its sense.
    2.222 The agreement or disagreement of its sense with reality constitutes its truth or falsity.
    2.223 In order to tell whether a picture is true or false we must compare it with reality.
    2.224 It is impossible to tell from the picture alone whether it is true or false.
    2.225 There are no pictures that are true a priori.

    You are not negating a proposition. It is not a proposition. A shape which is both circle and square does not represent a possible situation in logical space. It is not a picture that can be true or false, hence it is not a picture that can be negated. We do not have to compare it to reality to determine whether it is true of false. We can determine that it is false a priori.

    An aside: spin a square from its center and the shape you see is a circle.

    Is "cat" a picture of reality- a fact.However wittgenstein claims states of affairs ( facts) are the combination of objects.So would the proposition " the cat is sitting on a table " be a complex proposition?Wittgenstein

    All propositions are complex. They are combinations of names. It does seem odd to say that "cat" is a proposition. But objects are unalterable (2.0271) and cats are not. Cats are complexes and can be divided into parts that can be named. Wittgenstein at that time thought that the division could not go on ad infinitum. There must be a terminus, some indivisible simple objects.

    It will be a different fact but the proposition will have a sense.Since you disagree with that reason for cats,table being accidental feature.How do you determine an accidental feature and how do you determine an essential feature ?Wittgenstein

    The proposition will have a sense but not the same sense. "It's raining" has a sense but the sense has nothing to do with cats and dogs, unless it is raining cats and dogs.

    I answered the question about accidental and essential features in an earlier post.

    What l was trying to say was if L is a contradiction, then in classical logic ,~L would be a tautology.Wittgenstein

    4.464 A tautology’s truth is certain, a proposition’s possible, a contradiction’s impossible.

    4.466 What corresponds to a determinate logical combination of signs is a determinate logical
    combination of their meanings. It is only to the uncombined signs that absolutely any combination corresponds.
    In other words, propositions that are true for every situation cannot be combinations of signs at all, since, if they were, only determinate combinations of objects could correspond to them.
    (And what is not a logical combination has
    no combination of objects corresponding to it.)
    Tautology and contradiction are the limiting cases—indeed the disintegration—of the combination of signs.
  • Fooloso4
    1k


    There are probably others here more competent to give you an answer about this. Or, I am sure that a search will yield results.
  • Pussycat
    194
    If you want to treat prove as an object, but l don't think wittgenstein would allow it.Wittgenstein

    Sure as hell Wittgenstein wouldn't allow it, at least the early one, but I am not so certain about the late, I think he would allow any kind of game.

    It is because you said:

    I don't think we can understand wittgenstein unless we apply his philosophy on practical examples to see his theory of proposition becoming alive and clear.Wittgenstein

    Well, I gave you just that, I think, why won't you take it? But if you want to be loyal to the Tractatus, like Fooloso4 does, who is loyal in general, then what sort of examples can we give? I don't think the Tractatus, carried out strictly, leaves much room for play. Loyal or renegade, what say you?
  • Pussycat
    194
    Well! Wittgenstein, being in dire straits and not making head or tails of the situation, not knowing his way about and not relying upon anyone, started writing his thoughts in his little diary, as his own means for clarification. But later, after all his friends' betrayals, and no matter how clearer things got - fighting with the dirt and all - he realized that this was not some private investigation, just like there is no private language, and after all it brought him no pleasure knowing anything unless this knowledge is somehow shared, as in the dictum sharing is caring, or it is no gift unless it is shared. And so he decided and tried to open his thoughts to the public, turning it into a public investigation. 'Cause what have you got at the end of the day, when the curtain falls, what does it all matter anyway?

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