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.

And the afterlife is one of many imaginaries. To say personal experience is evidence for it (as per Sam26) is no more coherent than saying my memory of my dream is evidence my dream really happened. — Baden

This is what someone would say who never examined the evidence. First, dreams, hallucinations, or delusions don't describe real events as do NDEs. One can verify the accuracy of NDE testimonial evidence by talking to doctors, nurses, and family members who can verify or corroborate the evidence. This kind of response also shows a particular bias, because they don't respond to the arguments, they just give their uneducated opinions.

Post 10 (Final post of summary, as incomplete as it is.)

To conclude this basic summary of the Tractatus is to conclude that philosophy is not one of the natural sciences. Philosophy is above or below the natural sciences, but not beside them (T. 4.111). This follows from 4.11, "The totality of true propositions is the whole of natural science." This conclusion is was arrived at long before the publication of the Tractatus in 1918. It goes back to 1913 in his Notes on Logic given to Russell.

Wittgenstein is saying that philosophy gives us no truths. "Philosophy aims at the logical clarification of thoughts. [It] is not a body of doctrine but an activity (T. 4.112)."

Even in the Philosophical Investigations Wittgenstein is still aiming at the logical clarification of thoughts. Albeit, a different logical method is used. His later method in the PI isn't as rigid as that of the Tractatus, but is more flexible, which is more in conformity with how language works.

"Without philosophy thoughts are, as it were, cloudy and indistinct: its task is to make them clear and to give them sharp boundaries (T. 4.112).

"Philosophy settles controversies about the limits of natural science (T. 4.113).

"It must set limits to what can be thought; and, in doing so, to what cannot be thought. It must set limits to what cannot be thought by working outwards to what cannot be thought (T. 4.114).

"It will signify what cannot be said, by presenting clearly what can be said (T. 4.115)."

Understanding what Wittgenstein is doing should clarify what he means in 6.54, i.e., he has shown us what cannot be said, by setting a limit to language, so, you can throw away the ladder that reaches beyond the world of sense into the world of the senseless, and even further into the realm of nonsense.

For Wittgenstein the only facts are the facts in the world, there are no metaphysical facts for language to grasp hold of. If someone tries to say something metaphysical, you would show him using Wittgenstein's picture theory and his truth-function theory that he has not managed to say anything; they've gone beyond the boundaries of the world, beyond the boundaries of language. This is why Wittgenstein says, "What we cannot speak about we must pass over in silence (T. 7)."

No, this isn't about religion. I'm not religious, but I do think there is plenty of testimonial evidence that supports the idea of an afterlife. If you have the time read all of my posts.

I wrote a thread on this very subject. There is plenty of evidence of an afterlife.

https://thephilosophyforum.com/discussion/1980/evidence-of-consciousness-surviving-the-body/p1

Perhaps that is what is nascent in ↪Gregory. — Banno

Perhaps.

Okay that should be enough for now.

Post 9

As we've said the other central idea presented in the Tractatus is the truth-function theory. It goes hand-in-hand with the picture theory. "A proposition is a truth-function of elementary propositions (T. 5)." Therefore, if you are given all elementary propositions, then you can construct every possible proposition, which fixes their limits (T. 4.51). My understanding is that this sets the limit of language, or sets a limit to what can be said.

A full appreciation of this thesis requires an understanding of truth-functional logic. It suffices for our purpose to point out merely that a compound proposition, compounded of the propositions P1, P2,....,Pn, is a truth-functional compound of P1, P2,..., Pn if and only if its truth or falsity is uniquely determined by the truth or falsity (the truth-values) of P1,..., Pn. In other words, the truth-value of a compound proposition is completely determined by the truth-values of its components--once the truth-values of is components are given, the truth-value of the compound proposition can be calculated. Wittgenstein claims that all propositions are related to elementary propositions truth-functionally (K.T. Fann, p. 17).

Therefore, what follows is this: "If all true elementary propositions are given, the result is a complete description of the world. The world is completely described by giving all elementary propositions, and adding which of them are true and which false (T. 4.26)."

In the Notebooks Wittgenstein says the following: "In the proposition a world is as it were put together experimentally (Nb, p. 7)." This idea apparently occurred to Wittgenstein when he observed or read about a model of a car accident that was used in a Paris court of law, that is, they used dolls and other objects to represent the facts of the case. The model was a picture of reality; and so it is with the proposition, it is a model of reality as we imagine or picture it (T. 4.01).

Before I end this post, I just want to say that I believe that many of our propositions are pictures of reality, but again, this is not the only way propositions state the facts. Many people think Wittgenstein repudiated this idea, but I think he merely was saying that language does more than this. Just as language does more than use the ostensive definition model.

If propositions can only picture facts in the world, then it would seem to make sense that propositions of metaphysics, which go beyond the world of facts, can't picture anything. There is nothing for the proposition to picture. Right?

Post 8

In previous posts I talked about names being the simplest component of elementary propositions, and that names referred to objects, and objects make up atomic facts. The question came up about how we could make sense of a proposition if there were no corresponding objects, and thus, no corresponding facts. According to the Tractatus a proposition pictures reality, so if we are to understand a proposition that refers to unicorns, it is because the proposition displays a picture, and that picture either matches up with reality or it does not. If it correctly mirrors reality, then it is true, if it does not mirror reality, then it is false. So, to understand the sense of a proposition it is a matter of picturing the proposition, and this occurs quite apart from there being a corresponding facts in reality.

A picture or proposition presents a fact from a position outside of it, or separate from the fact it is displaying. Just as a picture of the White House presents the White House from a position outside it, or quite separate from reality or the state-of-affairs. Any picture either accurately or inaccurately presents a certain state of affairs (T. 2.1). And as we keep repeating, propositions are pictures according to the Tractatus. For example, consider any painting that displays a picture, the picture may or may not actually match up with a corresponding state of affairs (shown in the picture), and yet whether it does has no bearing on whether we understand the picture.

"The fact that the elements of a picture are related to one another in a determinate way represents that things are related to one another in the same way. Let us call this connexion of its elements the structure of the picture, and let us call the possibility of this structure the pictorial form of the picture (T. 2.15)."

The pictorial form is the form a picture shares with a fact. The form of the picture has to do with the arrangement of the elements in the picture. "What a picture must have in common with reality, in order to be able to depict it--correctly or incorrectly--in the way it does, is its pictorial form. A picture can depict any reality whose form it has. A spacial picture can depict anything spacial, a coloured one anything coloured, etc. A picture cannot, however, depict its pictorial form: it displays it (T. 2.17 - 2.172)."

There is a shared logic between the picture and the fact (T. 2.18).

How does a proposition correspond with reality? "Pictorial form is the possibility that things are related to one another in the same way as the elements of the picture.

"That is how a picture is attached to reality; it reaches right out to it.

"It is laid against reality like a measure (T. 2.151-2.1512)."

Each person, truck, bridge, house in the picture represents those things in the world.

So how do we tell if a proposition is true or false? We must compare it with reality (T. 2.223).

The sense of a picture is the arrangement of the things in the picture, which supposedly correspond to the arrangement of things in the world (T. 2.221).

The way one verifies the correctness of a proposition is by inspecting the proposition to see if it indeed reflects reality (T. 2.223).

According to Wittgenstein a thought is a logical picture (Wittgenstein does not believe that we can think illogically), it uses the form of logic to represent a fact (T. 3 and 3.03).

"In a proposition a thought finds an expression that can be perceived by the senses (T. 3.1)." So the logical picture is made by logical units, such as, visual marks or auditory marks.

Therefore, a proposition says that 'a' is in a certain relation to 'b', i.e., 'aRb'. For instance, Sam is standing next to Jane.

I guess I should get busy and post a little more.

Banno quit making things up. :joke:

We haven't even scratched the surface of all that is in the Tractatus, not that I'm going to go into that much depth.

Is there anything praiseworthy? Yes, its originality, and based on Wittgenstein's premises it follows logically. It also led to Wittgenstein's critique of the work, and to a better way of looking at how language functions. I also like the idea of propositions picturing facts or states-of-affairs, because I think it is true of many propositions (although not in the way of names connecting to objects). There is much in this work, i.e., many novel ideas, besides his picture and truth-function theories, that could be thought through. What I mean is that there are a lot of side issues that he touches on that might deserve a look at. What I find interesting, is where his thoughts led him in the end. And, ya, we might find some of his ideas silly today, but that's true of many subjects that are over 100 years old.

Is everyone bored, like MU? :wink:

This phrase seems to have two possible interpretations: attempts to say things about what kinds of things are not able to be said, vs attempts to say things which attempts are doomed to fail because the things one is attempting to say cannot be said. — Pfhorrest

In other words, it attempts to go beyond the world of language. Language, in terms of making sense, is language that describes the world. So ya, your latter interpretation.