or better, but more difficult,

https://archive.org/details/g.-e.-m.-anscombe-an-introduction-to-wittgenstein-s-tractatus

3.04 An a priori true thought would be one whose possibility guaranteed its truth.
3.05 We could only know a priori that a thought is true if its truth was to be recognized from the thought itself (without an object of comparison).

Thought, as the logical image of events defined earlier, contains only the possibility for that thought to be true. According to Wittgenstein's system, a fact can be either right or wrong, true or false; there is no middle ground, the principle of bivalence holds. Thus, thought, by itself, cannot determine the truth of its events. Within logical space, everything appears - and is - logical; everything exists as possibilities in logical space. What thought knows is that something will either be correct or incorrect, true or false. If thought wants to see which of these possibilities holds true, it needs to leave logical space and go to some other space, the space of geometry or of natural science. There, it will discover what happens in relation to the new space it finds itself in. The object of comparison is already in these new spaces. In the case of geometry, it could be a coordinate system or coordinates, while in the case of physics, it could be the various physical laws presupposing the physical system, such as the law of energy conservation.

In summary, the hierarchy of these spaces, as presented by Wittgenstein, is as follows:

a. Logical space, logical image, logic, science of logic
b. Geometric space, geometric image/shape, geometry, mathematics/geometry
c. Physical space, physical image, physics, physical sciences

The lower spaces contain the forms of the higher ones: geometric space includes logical forms/possibilities, while physical space includes both geometric and logical forms. Altogether, they exist under the dominant and primary sphere of logic, the all-encompassing logic.

Below, we see inspector Gadget doing his thing, perfectly logical, albeit somewhat paradoxical, in his attempt to apprehend his counterpart, Dr. Claw, and his organization, MAD.

I am sorry Banno, I am on a mission :grin: to finish this, won't take long.

Therefore, as long as the various spaces are distinguished and hierarchically arranged as defined above, we can say that geometric space is constrained by its dimensions, physical space constrained by the aforementioned geometrical space, as well as of all the properties of physical reality, while logical space is the only unlimited one that encompasses all those possibilities expressed in the other two spaces plus anything imaginable. Mathematicians explore geometry by creating spaces with any number of dimensions and different curvatures, while physicists have their theories, attempting to explain the interaction between bodies with various field theories. When it comes to logical space, one way to study it, is when it is examined independently of physical sciences and mathematics. This is done, for example, by science fiction authors, comic creators, poets, and artists. According to our analysis, what we call fictional or imaginative must directly draw its examples from logical space. Like it happens in dreams, where natural and geometric laws are lifted.

But also, the consciousness of someone with, say, a vivid imagination, who ponders all imaginable possibilities, it is in logical space where it floats. Similarly, individuals on the autism spectrum, for whom it is said that they have an inability to focus on something specific, their minds may well constanlty contemplate logical space, unable to do anything else, overwhelmed by information.

And finally,

From all of the above, it seems that in the realm of logic, there is an unrestricted freedom of movement, or at least much greater than in any other space. This freedom is constrained and restrained, like (in) a funnel, the opposite of the Big Bang, as we move "down" to the other two spaces, while the mouth and end of the funnel can be considered as physical reality. Because many of the things that logic encompasses, ie whatever we can think of, do not exist in the natural world, just as many of the things described by geometry about the nature of space do not. However, logic, much like geometry, can examine everything, all possible states of affairs, without commitments and limitations, as long as it is bound only by itself, which doesn't tell us much, or rather, absolutely nothing.

And so, if anything conceivable is logical, anything we can think of, then the illogical has no place in our world; since we cannot think of anything illogical, but if we can conceive it, it automatically becomes logical. With such a broad definition of logic, no person is illogical, ever. But then, what about all those people that are confined, or not, to institutions, that seem to have lost their minds? Are they illogical? By our previous analysis, certainly not.

If we were to make an assumption in accordance with the above, we would say that their problem is not the lack or absence of logical thinking, but rather an abundance, or rather an overabundance of it: they are overly logical. Similar problems are faced by individuals with autism. Just as an autistic person absorbs a huge volume of information from the natural environment without being able to process it adequately to be what we call functional, similarly, someone labeled as "crazy" absorbs a massive amount of information from the realm of logic but cannot correlate that information received there to things and situations seen and felt in the realm of nature. Thus, they are not functional either, but rather constantly confused. Essentially, the confusion arises from the movement of thought as it moves between logical-geometric-physical space. But not only confusion, but all other feelings and emotions, such as fear and security, joy and sorrow, hate and love, interest and indifference, etc., can be explained in the same way. For example, when faced with the unlimited choices and possibilities as mentioned in the case of someone considered "crazy," they may feel fear at the prospect of this boundless freedom, a fear at some existential level, from which other things arise, such as a kind of mania. Therefore, we could say that they are not ultimately becoming illogical, but rather they are thoroughly logical, although I do not know how much this would help them. Laughter might also arise from the mixture of different logical forms among themselves or with natural forms, the result of which appears funny as they blend together. Art and music effectively does the same for us sane people, however under (some) control, because they both have the ability to move our thoughts to anything that can be conceived, along old or new paths, offering e-motions, thereby expanding our world.

Now, the mechanism or mechanisms behind all this, do not fall under, and are neither the scope of the science of logic, to find and expose them, but rather of other sciences. For instance, psychology will talk about how what is called the human psyche is influenced when thought moves from one object to another, what happens within us, what is the psychological relationship between what we say, what we think, and what we mean, why and how various psychological compulsions are created, etc. Or a biologist/pharmacist will search to find the materialistic mechanism/organ in the human body that makes people think, sometimes more or less logically, constructing substances and drugs to address problems. Such inquiries do not concern the logician, at least not in its pure form. For this reason, Wittgenstein, in the Tractatus, did not delve into psychology, biology, or the theory of evolution because he wanted to insist and remain in a purely logical analysis of phenomena, considering it rather the most important, and that anything else follows this or can be reduced to it, as if it doesn't make much sense to explore secondary issues. In his later work, Philosophical Investigations, however, he leads the reader to the same or different ideas through a psychological experiment conducted there. The therapeutic character, both of his early and later work, has been highlighted many times, by many thinkers, because, as they say, many of the problems that humans have, are ultimately dissolved, with his method, into being pseudo-problems. Through philosophy and the critique of language, as he uses them, functioning as therapy, a kind of speech therapy.

Mythical creatures like dragons also constitute a reality, a logical reality, and not a physical one And usually, dragons are admired, as in the song from the movie "Flight of Dragons" performed by the renowned artist Don McLean, for being free and unencumbered, undisturbed to fly in the skies and go wherever they want. The form presented here is similar to the form sought by the logician when he says that he wants to explore all possibilities of thought within the realm of logic, dissolving any illusions or pseudo-problems, restoring certainty and order where confusion and chaos reign. Thus, the dragon, as the pilot of imagination, carries this symbolism.



Or for a more instrumental version



I feel that the logician wants to put herself in the eye of the dragon. But what is the dragon, really?

Wow, that was quite a ramble! :smile: What on earth was I thinking, where was my consciousness at? Lots of it is was not even readable. Also co-pilot didn't do well in translating.

Anyway! Maybe it goes to show the effects of being out of tune.

6.5 For an answer which cannot be expressed the question too cannot be expressed.
The riddle does not exist.
If a question can be put at all, then it can also be answered.
6.51 Scepticism is not irrefutable, but palpably senseless, if it would
doubt where a question cannot be asked.
For doubt can only exist where there is a question; a question
only where there is an answer, and this only where something
can be said.
6.53 The right method of philosophy would be this. To say nothing
except what can be said, i.e. the propositions of natural science,
i.e. something that has nothing to do with philosophy: and then
always, when someone else wished to say something metaphysical, to demonstrate to him that he had given no meaning to certain signs in his propositions. This method would be unsatisfying to the other;he would not have the feeling that we were teaching him philosophy;but it would be the only strictly correct method.

This is like the Gordian Knot, that Alexander the Great thought untiable, and so he just cut through it with his sword, problem solved. Same is with philosophical problems. Just as some may not see Alexander as truely untying the knot, just the same many may feel that the problem was not really solved.

Hello guys, new to this discussion. I don't know if you have already discussed this but I am having a hard time to understand what a symbol is. All I know is that it is the same thing as an expression, which is what characterizes a proposition's sense (3.31). So for example "x is y" taken altogether is an expression, I guess. But when Wittgenstein starts to discuss the relationship between signs and symbols, he says that , for example, "is" is a sign for the symbol of copula. But "is" itself does not characterize any sense in a proposition such as "x is y". I tend to identify symbols with names, and a sign is just a physical expression of a name, but names have no meaning without being a part of a proposition.

Also, since I brought up names, can anyone tell me what a simple word, such as "cat" is? Is it an atomic fact or a name, because on the one hand its definition seems to consist of other signs thus is not a primitive sign, and on the other hand "cat" alone doesn't seem to mean anything.

Thanks a lot.