Thanks.

Ya, well, we would disagree there.

Yes, that's true, and I mentioned this above to Harry. You can always rephrase a question and turn it into a statement. However, the question by itself is not true or false.

You should start your own thread on why questions should be considered propositions. The question is settled for me, I'm not going to debate it.

Logic Post 11

Before I go any further, I should give some of the symbols used in logic, and their meanings. I don't want to assume that everyone knows the symbols. I'm going to use the symbols used in the Principia Mathematica. However, Hilbert's symbols are probably used more often by mathematicians.

Negation (not) ~
Conjunction (and) ·
Disjunction (or) ∨
Material Implication (if, then) ⊃
Material Equivalence (if and only if) ≡
Therefore ∴

Why are symbols used? Logicians probably wanted a language that was free (as free as possible) from the abiguity, vagueness, and some of the defects of language. It was also a way for logicians to demonstrate the logical structures of statements/propositions.

To designate statements abstractly we will be using p and q as markers, i.e., p and q mark the position of statements. Next, we need symbols for truth-functional connectives, which I gave above. For example, "We will be buying a home and we will be buying a car next week." The individual statements are:

We will be buying a home. (We symbolize the first statement using p.)
We will be buying a car next week. (We symbolize the second part of the statement using q. If there were more statements involved, we would continue using r, s, t, etc.

The truth-functor: and
The statement form: p and q
It's symbolized using the symbol for and. p · q

Logic Post 10

There are two kinds of arguments in logic, deductive and inductive arguments. We will first discuss deductive arguments.

Deductive Arguments

A good deductive argument must be

(1) valid
(2) sound
(3) cogent

As I mentioned already, validity is a quality of good deductive arguments. Validity means that the form of the argument forces you to the conclusion. The correct form is crucial. Therefore, if the evidence is accurate, then the conclusion must follow. Note the following forms:

Premise 1: All X are Y.
Premise 2: b is an X.
Conclusion: Hence, b is a Y.

An argument of this form will lead you to a conclusion that is true provided the evidence, which is in the form of premises, are true. The following is an argument using the above form.

Premise (1) All cats are animals.
Premise (2) Morris the Cat is a cat.
Conclusion: Hence, Morris the Cat is an animal.

The following are more examples of valid deductive argument forms.

Modus Ponens: If X, then Y.
----------------------X.
----------------------Therefore, Y.

The following is an argument using this form:

Premise (1) If George is human, then George is a person.
Premise (2) George is a human.
Conclusion: Hence, George is a person.

Modus Tollens: If X, then Y.
-------------------- ~Y.
---------------------Hence, ~X.

Example:

Premise (1) If Harry is a cat, then Harry is an animal.
Premise (2) Harry is not an animal.
Conclusion: Hence, Harry is not a cat.

There are other deductive forms. For instance,

Hypothetical Syllogism: If X, then Y.
---------------------------------If Y, then Z.
---------------------------------Hence, if X, then Z.

Transposition: If X, then Y.
--------------------Hence, if not Y, then not X.

So, again, validity has to do with the structure or the form of the argument


The next criteria of a good deductive argument is soundness, which means that the argument is valid, plus the premises are true. The following argument is valid and sound.

Modus Ponens:

If I think, then I exist.
I do think.
Hence, I exist.

The next argument is valid, but not sound.

Modus Ponens:

Premise (1) If humans are dogs, then dogs are humans.
Premise (2) Humans are dogs.
Conclusion: Hence, dogs are humans.

This is a valid argument, but is it sound? No. It is not sound, because the premises are not true.

Our third criterion is cogency.

Now there are going to be some that disagree with this criterion. However, I believe it is very important.

Cogency means that the premise's of a deductive argument are known to be true by the person to whom the argument is given. What this means is that not only is the argument sound, but the premises are known to be true. There are proofs, i.e. deductive arguments that are sound; however, you don't know they are sound, because you don't know if the premises are true. The following is an example:

"The base of a souffle is a roux.
This salmon dish is a souffle.
Hence, the base of this salmon dish is a roux.
(Dr. Byron Bitar)"

Therefore, in order for a proof to work for you, you have to know the premises are true. If you do not know the premises are true, it will not convince you, even if the argument's conclusion is true.

These posts may help some of you with the basics in logic, but it's not like taking a course. However, you don't need to take a course in logic to become good at evaluating arguments, you just need a lot of practice. Logic isn't difficult, at least the basics aren't difficult, you just need lots of practice. Moreover, reading a logic text isn't enough, no more than reading a math book is enough to learn math.

Logic Post 9

Logical vs Non-logical Material

One of the problems in analyzing many arguments is separating the logical material from the non-logical material. Keeping in mind that logic is concerned with the informative side of language, i.e., with what is being asserted. You need to be able to distinguish between the emotive content and factual assertions; and to be able to translate emotive content into neutral content. Consider the following two propositions:

1) "Trump is a liar!"

2) "Trump was mistaken."

The first statement is likely to be from someone with a negative attitude, while the second one might be from someone with a more positive attitude. We are not concerned with the attitudes of people. We are more concerned with the factual content. Expressions of attitude indicate a positive, negative, or neutral evaluation of someone or something. As we said earlier in the discussion we want to focus on the cognitive use of language as opposed to the evaluative use.

You should get some practice reading articles and picking out and separating propositions into the five general categories that we have discussed.

I will conclude this section with the three basic kinds of disagreements.

There are disagreements in attitude, in belief, and verbal disagreements.

Ones attitude has more to do with one's state of mind or feeling about an event or fact, and less to do with what is claimed or asserted.

Disagreements about beliefs, on the other hand, are arguments over the supposed facts. These can be classified in two ways. First, the disagreement can be a real disagreement, in that there is a logical inconsistency in one of the arguments. Second, there can be an apparent disagreement, i.e., both arguments are consistent, which means the arguments can be resolved, at least in theory.

Finally, there can be a verbal disagreement. That is to say, the people arguing are using words or phrases with different meanings.

Buy a used logic book, that should help. Here is a cheap used one.

https://www.thriftbooks.com/w/introduction-to-logic_jacquelyn-ann-k-kegley_charles-william-kegley/2627456/item/2242315/?mkwid=%7cdc&pcrid=395840866446&pkw=&pmt=&slid=&plc=&pgrid=83212263032&ptaid=pla-439650351594&gclid=CjwKCAjwnIr1BRAWEiwA6GpwNVPQBkzwqUEAh8VRv7zy1SrcrnRWQ5SsxUCsrNwIFoyhPzE8pHi4HhoCv8MQAvD_BwE#isbn=0675083583&idiq=2242315

Logic Post 8

The five general categories of language are the following:

1) Cognitive (Informative) Function.

Language is used to convey information. As the following statements demonstrate.

"There are two desks in my room."

"The Japanese bombed Pearl Harbor on December 7th, 1941."

"Triangles have three sides."
(That triangles have three sides is also an example of an analytic statement. An analytic statement is one in which concept of the predicate is included in the concept of the subject.)
"Bachelors are unmarried men."
"All bodies are extended in space."
"All wives are female."

The one characteristic of these statements is that they can be spoken of as either true or false, i.e., they declare that something is or is not the case. That is not to say that other criteria cannot be applied to statements of information, since one can also ask if the statement is significant or not, or one can ask if it is useful or not.

Logic is not concerned with establishing truth or falsity. Logic simply asks if the conclusion follows from the truth of the premises. Another way to put it is that logic is concerned with the internal relationship between or amongst propositions.


2) Expressive
In these examples language is used to express feelings or emotions.

"I am having a great time at the beach."

"The portrait is beautiful."

"You idiot."

The important point here is that these statements express a feeling, emotion, or an attitude. These phrases are also considered evaluative, i.e., they reveal a positive or negative judgment by the speaker.



3) Evocative or Directive
Language is also used to arouse feelings, emotions, attitudes, and certain kinds of responses or actions in others. Examples of these kinds of statements are as follows:

"Duck!"

"Attention!"

"Please wash your hands before eating."

"Brush your teeth three times a day."

"John Doe for president."

These statements are a bit different from the ones I gave earlier, in that they are designed to produce an effect or an action from two perspectives: First, the purpose or purposes of the user of the sentences, and two, the effect the user of language wishes to have or not have ( Introduction to Logic, Kegley and Kegley, p. 34).

It is important in the study of logic to distinguish between informative statements and evocative statements. After all logic is concerned with what is being asserted, not with how it is being asserted. As Spock might say, emotional appeals are irrelevant.

Now I am not saying that we should eliminate all emotion from our language, but only that we should be careful when formulating an argument that we do not include appeals to emotion, and that we stay away from personal attacks.


4) The Evaluative Use of Language

The complexity of the language used to make 'value judgments' is mind-boggling. The contexts of such language includes just about every context imaginable. As you can imagine there is still much disagreement over how to characterize such language. In this brief introduction I cannot even begin to do justice to this use of language, so I will only make a few remarks.

As you probably already know evaluative language makes judgments of what is of value, i.e., what is good, just, and beautiful. All you have to do is to look at some of the arguments on the internet, and you will see the wide variety of views in relation to ethics, religion, politics, language, etc. Some people believe that value judgments are subjective, while others believe they are objective, and still others hold some middle ground. Some examples are as follows:

"Knowledge is good in and of itself."

"Trump is stupid."

"This is a good book."

"This song is beautiful."

"The Iraq war is just."



5) Finally, the Ethical and Aesthetic (pertaining to a sense of beauty, or having a love of beauty) use of language.

This use of this kind of language raises very important questions about how to interpret statements like, "Torture is wrong." Is it merely expressive, which translates into something such as, "I do not like torture" or "Torture - yuck!" Can it be that these statements are simply directive in nature - for example, "Do not torture!" And finally maybe statements like "Torture is wrong" are assertive-type statements that require us to give good reasons for accepting them.

These are very controversial topics, and will not be settled in my short musings.

I came across a brilliant paper published in a philosophical journal. I was thinking of the reasons behind philosophical disagreements and why there isn't some sort of consensus among philosophers regarding philosophical ideas. For anyone interested, l have attached a link to the article written by Prof Christopher Daly. — Wittgenstein

This problem has always fascinated me. The answer, I believe, lies in the complexity of language, the complexity of the human condition, psychology of belief, causes versus reasons for belief, intelligence (ability to reason), etc, etc. I don't think there is a way to solve this in the near future, maybe in the distant future. if we gain the ability to communicate mind-to-mind, it might clear up some of the fog.

Logic Post 7

Dimensions of Language

Since logic is concerned with both communication and understanding it will be important to sort through some of the functions of language. This will enable us to focus on the actual argument being presented; and it will help us to seek clarity and precision.

Formal analysis of an argument is not an easy task, since arguments in everyday life are rarely put in a form that is easy to analyze. However, if we want to think rationally we need to be able to think clearly about what we intend to say; and once we know what we intend to say, then we can concentrate on saying it well.

Keep in mind that language can also be used to persuade without concern for rational arguments. We see this all the time. Sometimes people will appeal to opinions, prejudices, and emotions without concern for rationality.

Remember some of the distinctions that I have already pointed out about sentences, and the different ways in which they can be used. Not all sentences make statements. For instance,

1. Is your name John?
2. Stand there!
3. Please don't do that.

These interrogative (sentences that ask a question) or horatory (sentences that exhort or encourage) sentences are not the kind of sentences we will be concerned with. We will be concentrating on statements or propositions that are declarative. For example, "The moon is approximately 240,000 miles from earth", or "It is snowing." What sets these sentences apart from the ones listed above is that you can properly ask about their truth or falsity.

Hence, logic again is concerned with statements or propositions, and thus with sentences that assert or deny something.

Language is very flexible, and in spite of the fact that language has many functions it can probably be classified under five general categories. The philosopher Ludwig Wittgenstein identified many of the uses of language in the Philosophical Investigations. The following are some examples:

Giving orders, and obeying them.
Describing the appearance of an object, or giving its measurements.
Constructing an object from a description (a drawing).
Reporting an event.
Speculating about an event.
Forming and testing a hypothesis.
Presenting the results of an experiment in tables and diagrams.
Making up a story; and reading it.
Play-acting.
Singing catches.
Guessing riddles.
Making a joke; telling it.
Solving a problem in practical arithmetic.
Translating from one language into another.

We are not talking about meaning, but whether the sentence can be said to be true or false. A question just isn't considered a proposition that asserts that something is or is not the case.

It seems that we can assert that something is the case in each of these examples:
1. That the person doesn't know who the third president of the United States is.
2. That the person wants us to be seated.
3. That the person wants us to keep quiet. — Harry Hindu

The point is that the question "Who is the third president of the United States?" is not a true or false statement/proposition. It doesn't make sense to say it's true or false. All you're doing is drawing an inference based on the question. That inference, may be true or false, but you're changing the sentence in order to do that.

Logic Post 6

Here are five steps to help you analyze an argument.

1) First find the conclusion, that is, what is the point of what is being claimed.
2) Once you have located the conclusion, then locate the supporting data - the reasons or evidence given in support of the conclusion.
3) Next rule out repetitious statements and emotional content.
4) If there are missing pieces of evidence, then supply what is needed to make the argument a good one. Ask yourself what additional evidence is needed for support. You may also need to ask yourself - what must be assumed in order for the conclusion to follow.
5) Finally, you may also what to look for additional arguments within the context of the main argument. That is, there may be smaller arguments within the larger context of the statements.

Logic Post 5

Logical Analysis

To properly analyze an argument the argument must be stated clearly and precisely. One must be able to identify the data used to support the conclusion; and if you do not understand the data that supports the argument, then it is generally considered unwise to criticize it. However, one must not only understand the argument - one must also be able to identify the structure of the argument. In later posts we shall come to see that the structure of an argument is what makes it valid. Hence, structure and validity go hand-in-hand.

Although arguments can be very complex, they can all be put into two basic forms.

1) This is true, therefore, that is true.
2) This is true, because this is true.

Premises (evidence, grounds, reasons), therefore, conclusion.

Because Bob went to the dance last night with his girlfriend, [thus] Mary, who is Bob's girlfriend, went to the dance also.

I saw a black bird on the first house I passed on Washington street, and on the second, third, fourth, and fifth house, [so] the sixth house will also have a black bird on it.

Keep in mind that arguments given by people in our daily lives are rarely so easy to follow. They tend to be very complex pieces of discourse that are presented with any number of irrelevant pieces of information.

Good writing will provide you with clues that let you know that an argument is present. For instance, words like because, for, since, in view of, etc., indicate that what follows is probably a premise; and words like therefore, so, thus, it follows that, and hence, etc., are words that indicate that what follows is a conclusion.

When analyzing arguments one must also be able to tell the difference between a causal explanation, which seeks to answer the question why, and arguments, which seek to establish the truth of the conclusion based on the evidence.

The following explanatory statements are in the form 'S because R:'

The man fell off the cliff, because his rope broke.
The litmus paper turned red, because it was put into acid.
The ice on the sidewalk melted because of the salt.

None of these are considered arguments, because they merely offer explanations. However, that is not to say that we could not put them into argument form. For example...

If litmus paper is put into acid, then it will turn red.

The litmus paper was put into acid.
Therefore, it turned red.


In these instances, we took an explanation and put them into an argument form.

Again, we gave causal explanations intended to show a causal connection between events. So, rather than asserting a logical connection between statements, we are offered a non-argument in the form of 'S because T.' The intention of an argument is to establish the truth of S, and the truth is established by citing evidence. If S is true, then T is true.

Why is this important? It is important because we want to be able to distinguish non-arguments from arguments. How do we know when an argument is present? We know because the purpose is to try to establish the truth of other statements. Explanations are given to answer the question why. Again though, keep in mind that even explanations can be asserted in argument form as we saw above in the litmus example.

What I'm saying is, basic logic is much broader in scope than that.

There is the Law of Identity, which states that A is A or anything is itself.

Logic Post 4

Arguments

An argument uses one or more statements to support a conclusion. The conclusion is supposed to follow from, or be justified by the other statements. These statements are called evidence, reasons, grounds, or premises. So, every argument is made up of two parts - the premises and the conclusion.

For example, I enjoyed the first three movies that Harrison Ford starred in, therefore, I will probably enjoy his fourth movie.

I did well in algebra, geometry, and trigonometry; therefore, I will probably do well in calculus.

These two examples are called inductive reasoning, I will talk more about these kinds of arguments later.

In a very rudimentary sense (practical or pragmatic way), one can think of logic this way: Being reasonable requires one to treat like cases likely; different cases differently. That simple axiom is used all the time in everydayness. — 3017amen

That's not much of an axiom. If you're saying that X=X and X is not Y, then yes, but you're not saying much. Logic covers a wider spectrum of propositions/statements.

Logic Post 3

Statements, propositions, and sentences

Since logic is concerned with assertions that are justified, logic therefore deals with statements and propositions. I will use the terms statement and proposition interchangeably, since their meaning is nearly the same.

A statement or proposition is a claim that something is or is not the case. For example, "George Washington was the first president of the United States" asserts that something is the case, whereas the proposition "Abraham Lincoln was not the second president of the United States" denies that something is the case. When these kinds of statements are made, we can specifically ask about their truth or falsity. Furthermore, we can ask what grounds or reasons one has for making the assertion.

Keep in mind that statements or propositions are all sentences. However, not all sentences are statements or propositions. Consider the following examples:

1. Who was the third president of the United States?
2. Will you please be seated.
3. Keep quiet!

Each of these are sentences, but none of them assert that something is or is not the case.

Well, only that there are different kinds of logic, viz., formal logic, informal logic, symbolic logic, and mathematical logic to name a few. However, that's going beyond the scope of this thread, which is just a guide to basic logic.

Just keep posting whether people respond or not. When I start a thread I usually have something to say regardless of the responses.

Logic Post 2

It is important to understand that logic is not concerned with the thinking process. Thinking processes themselves are the subject of psychology. Psychology studies how people think; whereas, logic is concerned with how people should think, if they want to think rationally.

What is an argument? An argument is a set of statements or propositions, in which one, called the conclusion is supposed to follow from the premises or the evidence. The act of drawing a conclusion based on the evidence is called the act of inferring, or the act of formulating an inference. Therefore, argumentation is discourse (communicating by writing or talking etc) containing inference. It should never be confused with the popular notion of the term argument meaning dispute (to argue vehemently; wrangle or quarrel - it is not shouting and fighting - it is not egotistical).

Logic is concerned with what is being asserted (to maintain or defend), not with emotional content or attitudes. It is irrelevant how you feel about the argument in question, or how you feel about the person giving the argument. For instance, if I say "William is lying" or "Jackie is ignorant" I am expressing attitudes about people. Hence, it is important to distinguish between attitudes and factual assertions. If I say, "Abraham Lincoln was the sixteenth president of the United States," we can ask if this statement or proposition is true or false. It is a cognitive (of or pertaining to the mental processes of perception, memory, judgment, and reasoning, as contrasted with emotional processes.) use of language, and as such, it expresses a belief. When someone expresses a belief we often want to know what reasons or evidence they have to support that belief. Attitudes (For instance," I don't believe what he/she is saying, because he/she is an idiot," or you reject him/her because of their color, religion, or political affiliation.) often just express positive, negative, or neutral evaluations toward someone or something.

Did he have anything to say about the Halting Problem? I have a sudden, strong hunch that it's related to this. Maybe I'm just seeing things, but grasping that a Turing machine goes on forever without doing any calculations seems to be a case of grasping a rule in Wittgenstein's sense. — Pneumenon

I don't know Pneumenon.

How can you even say that one follows from the other - that one gets a sense of infinity from finite signs expressed by finite beings? — Harry Hindu

Where do you think our sense of infinity comes from? It comes from us, i.e., finite beings, we create the concepts using finite signs. We extrapolate based on the continuation of 1,2,3.. that it goes on ad infinitum. There's no mystery here.

One could argue, probably successfully, that Wittgenstein was not a finitist, i.e., he never held to the idea that the finite character of language meant that there weren't infinite processes or methods. He was mainly interested (at least it can be argued) in the problem of the grammar of the infinite method or procedure. In other words, how is it that finite signs, as expressed by finite beings, have a sense of infinity. This has more to do with Wittgenstein's later philosophy, i.e., what it means to master a technique or practice.

Are letters objects? Are ink scribbles on paper objects? — Harry Hindu

You tell me, do you or we refer to marks on a piece of paper as objects? I think not. Some might say that they refer to objects.

, here is a quote from Wittgenstein in the Philosophical Remarks that might have some bearing on the subject.

"We can ask whether numbers are essentially concerned with concepts. I believe this amounts to asking whether it makes sense to ascribe a number to objects that haven't been brought under a concept. For instance, does it mean anything to say 'a and b and c are three objects'? I think obviously not. Admittedly we have a feeling: Why talk about concepts; the number, of course, depends only on the extension of the concept, and once that has been determined, the concept may drop out of the picture. The concept is only a method for determining an extension, but the extension is autonomous and, in its essence, independent of the concept; for it's quite immaterial which concept we have used to determine the extension. That is the argument for the extensional viewpoint (p. 123)."

We have a concept (a mathematical concept), and we use the concept to refer to things, but the things do not reflect the concept, i.e., it is not as though the concepts are intrinsic to the things. We group things together under the rubric of the concept, and we extend this concept to group other things under the same umbrella. "The extension is autonomous." The extension reflects a certain state-of-affairs that is brought under the mathematical concept.

Have you considered an exposition on Remarks on the Foundations of Mathematics? — Banno

I have read some of his Philosophical Remarks, which I believe was written in 1931, it contains the seeds of his later writings on mathematics. I have an interest, but I am not sure I have the will.

Do you have an opinion on the changes to W.'s views on mathematics between the Tractatus and PI? — Banno

I haven't studied it enough to make an intelligent assessment.

I'm in the middle of WoW I've lost interest in philosophy. :lol: I need a break. People in here take themselves to seriously, including moi.

I don't remember him saying anything about it. I don't think there is much to it. It seems silly to me.

Oh, the motto, that's a strange motto. :gasp:

After he dedicates the book to his friend Pinsent, then comes the preface written by Wittgenstein, is that what you're referring too?

What specifically are you referring too?

After writing the Tractatus Logico-Philosophicus Wittgenstein abandoned philosophy for a few years, and in 1920 he became an elementary school teacher in Austria until he resigned in 1926. There is evidence that this period of time had an affect on his thinking. Apparently he taught children reading, writing, and arithmetic, and also compiled a dictionary of several thousand words for young children.

How do we know if a child has learned to use a word correctly - is it because they can define the word? No, we observe how they use the word. It seems that this time of teaching brought Wittgenstein's philosophy down to earth, i.e., his observations of the way children learn words probably played a part in his later view of language.

In the late 1920's Wittgenstein attended a lecture in Vienna on the Foundations of Mathematics, and this apparently began to stir his thinking once again. He returned to Cambridge early in 1929 and registered as a student. It seems he wanted to work toward his PhD. However, as it turns out, he was allowed to present the Tractatus as his thesis, and if I remember correctly, he presented it before Russell and Moore.

Soon after he returned to England he wrote a paper for the Aristotelian Society called Some Remarks on Logical Form, and in this paper it is clear that he still subscribed to many of the doctrines of his earlier work. However, there is a short remark in the paper that seems to point in a new direction ("...we can only arrive at a correct analysis by what might be called, the logical investigation of the phenomena themselves, i.e., in a certain sense a posteriori, and no[t]: by conjecturing about a priori possibilities."). This seems to hint at a new method of inquiry (an a posteriori method of analysis), which is reflected in his later work.

This methodological turn in his mind is what differentiates the early Wittgenstein from the later Wittgenstein. It is not that he repudiates all of what he wrote in the Tractatus, but his method of analyzing propositions shifts; and it is this more practical or pragmatic approach that becomes the hallmark of his philosophical inquiry until his death in 1951.

Anything to add about truth tables? — Banno

I tried to sum up the Tractatus into what I thought was important. Obviously there is a lot that I left out, and his use of truth-tables was one of those things. Wittgenstein is credited with developing truth-tables.

We know that Wittgenstein thought that all propositions were truth-functions of elementary propositions. Therefore, if a proposition X is analyzed into elementary propositions p and q, and they are connected by the truth-functional connective and, then the truth-value of X is determined by p and q. If you took logic, then you should remember truth-tables. For example...

P-------Q---------X
_______________

T-------T---------T

T-------F---------F

F-------T---------F

F-------F---------F


So, if X is true, both p and q have to be true. If not, then it is false. X is dependent upon the truth-values of p and q, i.e., its component parts. So X qualifies as a genuine proposition - X has sense. Wittgenstein demonstrated using truth-tables, that for any proposition, when analyzed into elementary propositions, we can determine whether it has sense or not (T. 4.31).

According to Wittgenstein there are two extreme cases amongst the possible groups of truth-conditions. In one of these cases, the proposition is true for all truth-possibilities of elementary propositions; and thus, we say that the truth-conditions are tautological. In the second case the proposition is false for all truth-possibilities, which then yields a contradiction (T. 4.46).

"Propositions show what they say: tautologies and contradictions show that they say nothing.

"A tautology has no truth-conditions, since it is unconditionally true: and a contradiction is true on no condition.

"Tautologies and contradictions lack sense.

"(Like a point from which two arrows go out in opposite directions to one another.)

"(For example, I know nothing about weather when I know that it is either raining or not raining.) (T. 4.461)."

"Tautologies and contradictions are not, however, non-sensical. They are part of the symbolism, much as '0' is part of the symbolism of arithmetic (T. 4.4611)."

Wittgenstein goes on to say that tautologies and contradictions are not pictures of reality, since they do not represent possible situations or states of affairs. Tautologies show all possible situations or states of affairs; and contradictions show us no possible situations or states of affairs (T. 4.462). These are not propositions in the strict sense, but are degenerate propositions; and any proposition that is not subject to truth-value analysis is considered non-sense, or a pseudo-proposition.

"Summarily then, language consists of propositions. All propositions can be analyzed into elementary propositions and are truth-functions of elementary propositions. The elementary propositions are immediate combinations of names, which directly refer to objects; and elementary propositions are logical pictures of atomic facts, which are immediate combinations of objects. Atomic facts combine to form facts of whatever complexity which constitute the world. Thus language is truth-functionally structured and its essential function is to describe the world. Here we have the limit of language and what amounts to the same, the limit of the world (K. T. Fann, p. 21)."

Maybe some of you can see why the Logical Positivists latched onto Wittgenstein's theory, and tried to make it support their own view of reality.

Hopefully I didn't leave too much out. Maybe this will give you some understanding of how his picture and truth-function theory works.

I'll debate anyone who wants to, on the subject of whether there is evidence that consciousness survives death. I'll debate them formally in the debate thread with a moderator.

He said the world is made up of facts or states-of-affairs. A true proposition is one that pictures states-of-affairs in the world. All propositions, whether they are known or unknown, true or false, imaginary or not, represent pictures, and we can understand them because they are pictures.

Of course what is unknown is part of reality, unless you're referring to that which is outside the world, the metaphysical, this goes beyond the world, or beyond what can be said. However, there is that which is unknown in the world, and this can be pictured too. All the facts in the world, known or unknown, are what we can talk about. Wittgenstein mapped out what can be talked about (at least in theory).

So can we conclude that Wittgenstein's description, or definition of "the world" is unacceptable, and "the world" as we know it is quite different from this? — Metaphysician Undercover

I don't find his idea of the world a problem, but his ideas of how language connects to the world. Moreover, his idea that there is a limit to language, this idea is not only a part of the Tractatus, but also the PI.