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Occidental culture
LOGIC AND MATHEMATICS

Gauß contributed significantly to many fields, including number theory, algebra, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy, and optics.

Sometimes referred to as the Princeps mathematicorum or “the foremost of mathematicians” and “greatest mathematician since antiquity”, Gauß had a remarkable influence in many fields of mathematics and science and is ranked as one of history’s most influential mathematicians.


Carl Friedrich Gauß was the greatest mathematician of all time.


For 2150 years Euklid had been the greatest mathematician of all time, but then - at the end of the 18th century - Gauß replaced Euklid on his throne, because Gauß became the greatest mathematician of all time!


If you will „square the circle” someday, then those who have the power to determine or even dictate the relations between humans and their language, especially its semantics, will probably change the definition of “circle” and the definition of “square”.

**

But „someday never comes“, said John Fogerty (**).

Impossible?


Geometry

The figure in that picture moves, but geometric figures are actually immobile. So, it is a question of definition, of definional logic. If you want to describe a geometrical figure, then you actually do only consider that that figure is static, thus that that figure is immobile.

If we also want tz talk about the philsophical meaning of physics and about physics itself, then moving bodies are one of the main physical premises; but moving bodies are not the main geometrical premises (this does not mean that it is impossible to have also moving bodies as a premise in geometry); so we have to be careful and should not combine physics and mathematics too much. Combining physics and mathematics too much has been being a problem of the physicists for so long - since the 20th century, especially since the second half of the 20th century. Another example is the problem of combining economics and mathematics too much, and this problem has been existing since the second half of the 20th century (we can talk about it in another thread). I do not say that we should not do it, but we should be careful with that. I argue not against the mathematics but against the domination of the megalomania in physicis, economics, and some other scientific disciplines.


According to the mathematical and logical definition of probability and thus to the probability calculation itself it is not possible to know what would or will happen - otherwise the mathematical and logical definition of probability and thus to the probability calculation itself would be superfluous, redundant.


I think that the complete understandability of the universe, especially of its beginning and of its end, is more an issue of philosophy or/and theology than of physics or/and mathematics, because especially the question of the physical beginning and the physical end of the universe can merely be answered, if the framework conditions are defined and not merely calculated / computed. Mathematics allows too much, even the calculation of things humans can never completely understand by using other scientific disciplines than mathematics. I think the humans are not able to completely understand such things, although they are able to calculate / compute them.


If scientists are already corrupt and depend on other corrupt humans, then the probability becomes higher and higher that they say that, for example, „»X« has not been proven false“, although it has been proven false.


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x-coordinate <=> centuries (0 <=> the year 1800)
y-coordinate <=> degree (magnitude)
------------------------------------
y = (½)^x <=> philosophy
x = 2^x <=> nihilism

Currently (x = 2 ) the degree of nihilism (y = 4) is 16 times higher than the degree of philosophy (y = ¼); the current degree of philosophy (y = ¼) is 32 times lower than it was in the year 1500 (x = –3 and y = 8), the current degree of nihilism (y = 4) is 32 times higher than it was in the year 1500 (x = –3 and y = 0,125).

When mathematics and physics left philosophy they became scientific disciplines. Contemporarily the degree of nihlism was very low, almost imperceptible. Currently the degree of philosophy is as low as nihlism was at the time when mathematics and physics left philosophy and became scientific disciplines, whereas the degree of nihlism is as high as philosophy was at the time when mathematics and physics left philosophy and became scientific disciplines, - One can have the impression that nihilism is an awful revenge.

If we want to save the philosophy, then we have to fight against the nihilism. The nihilism is an enemy of both philosophy and science, but nevertheless the number of nihilistic „philosophers“ has been exponetially increasing, followed by the number of nihilistic „scientists“.

Who can stop the nihilism?


The statement that there is an „inifinite difference“ between two sequenced numbers is similar to the statement that a real physical contact between two bodies or particles is not possible because of the charges of their electrons on both outside lanes of both atoms: both charges are negative (each electron always has a negative charge).

But we know that 0 + 1 = 1, 1 + 1 = 2, and so on, and we know that we can have contact.


Maybe Galilei exaggerated when he said that mathematics is the language of the nature. Anyway. We - the humans - have no other choice than to use our language in order to explain the observed nature (universe), because this explanation can only be done by the use of the language we have (and we have no other), scientifically spoken: by the use of linguistics and mathematics - and the intersection of both is logic.


Your way of „linguistics > objects > consciousness“ (**) must be considered as one way containing two ways:

1,1) Linguistics => objects => consciousness,
1,2) Consciousness => objects => linguistics.

Both ways (1,1 and 1,2) of the one way (1) are necessary - for example: for language development and language acquisition, and also for consciousness development and consciousness acquisition.

By the „way“ (): One of these „objects“ are those of logic (including mathematics and philosophy [including ethics and laws]).


According to the number theory of mathematics „zero“ is „not positive“ (which means „apositive“, „the lack of positive“) and „not negative“ (which means „anegative“, „the lack of negative“). The right alternative word for „negative“ is „antipositvie“, and the right alternative word for „positive“ is „antinegatvie“. The word „apositive“ means just „not posiitive“, thus it can be „negative“ and/or „neutral“. But „antipositive“ means „the opposite of positive“, thus „negative“, and „antinegative“ means „the opposite of negative“, thus „positive“.


If one logic statement (for example: as a part of a syllogism) contradicts another, then one has to check it again and to eliminate the false one.


Who said that „humans of »X«“ are not humans? „Humans of »X«“ are humans - that is logical.

You (**) do not have any logical argument because of your false definitions, false premises, and thus false conclusions.

An example from the realm of physics and chemistry:

In the past scientists claasified all metals as being „heavier than water“. So this was the syllogism: Major premise: Gold, silver, ..., iron, ... and so on are heavier than water. | ! (LATER THIS BECAME FALSE) !
Minor premise: Metals are are gold, silver, ..., iron, ... and so on.
--------------------------------------------------------------------------------------------------------
Conclusion: Metals are heavier than water. | ! (LATER THIS BECAME FALSE) !

That syllogism had been true for a long time - until the potassium was discovered. Since this discovery of the potassium the following syllogism has been being true:

Major premise: Potassium is lighter than water, although all other metals are heavier than water.
Minor premise: Some metals are potassium.
-------------------------------------------------------------------------------------------------------------------------
Conclusion: Some metals are lighter than water, although all other metals are heavier than water.

You see: The first syllogism (see above) had to be corrected by the second syllogism (see above), because scientist discovered the potassium!

Here follows your false antitheistic example again: **.

Again: You do not have any logical argument because of their false definitions, false premises, and thus false conclusions.

In addition: You have committed a blatant straw man fallacy.


**

**

Please, count them twice! Are they twelve or thirteen?


Concepts do not change, if they are true - that means: logically true, correctly defined, logically correct. But if they are not true, then they change - mostly just after the changing of the power relations. Currently there are many untrue concepts.


Information storage.

There are many information memories.

Concerning (1) nature: in all things of the universe, thus in everything that exists, thus also in brains.

Concerning (2) human culture: (2,1) in brains again; (2,2) in libraries; (2,3) in machines, thus also in computers, robotors, and so on.


Mathematical formulae do not show and prove or disprove anything and everything. But mathematical formulae are very suited for economics, despite the fact that some of them are completely redundant.


The German philosopher, logician, mathematician Friedrich Ludwig Gottlob Frege (1848-1925) is the father of analytic philosophy, of mathematical logic (=> logistic, symbolic logic ...), thus also the philosophical father of Bertrand Russel (1872-1970) and all other analytic philosophers.

**

The German philosopher, logician, mathematician Friedrich Ludwig Gottlob Frege (1848-1925), the founder of the modern mathematical logic (=> logistic, symbolic logic ...), the father of analytic philosophy thus the philosophical father of Bertrand Russell (1872-1970) and all other analytic philosophers. Frege influenced everyone, also Edmund Husserl who followed Frege especially by adopting his distinction between logic and psychology (cp. Frege’s „Sinn und Bedeutung“) which led Husserl to his kind of phenomenology.


Again: Frege is the father of analytic philosophy, thus the philosophical father of Russell and all other analytic philosophers.

Frege was already famous before Bertrand Russel was born. Back then, everyone of those Europeans who were interested in mathematics, logic, philosophy read Frege; even certain Americans (especially those who had studied in Germany) read Frege.


The German Einstein had even two scientifical fathers who were also German: Georg Friedrich Bernhard Riemann (1826-1866) as the precursor of Einstein's relativity theory and David Hilbert (1862-1943) who submitted the theory of the general realativiy five days before Einstein did it.


The German philosopher, mathematician, inventor, engineer, technologist, historian, diplomat, and policy adviser Gottfried Wilhelm Leibniz (1646-1713) was probably the greatest universal genius of all times - besides Leonardo da Vinci. Leibniz invented the infinitesimal calculus in 1665 (published 1684 - 3 years before Newton published it, 1687); Leibniz also invented and engineered the first calculating machine in the world (the earliest form of a computer), in 1673 - 268 years before the German inventor and engineer Konrad Zuse invented and engineered the first real computer in the world. Leibniz invented and originated more tham the said things, and he also founded the academy of sciences in Berlin and became the first president of it.


Write numbers from 1 to 6 into the cells of the diagram of size 6 x 6, so that each number occurs exactly once in each row and in each column. A brick must contain an odd and an even number. Two half-bricks in a row at the left and right edge of the diagram form one whole brick.

Ziegelmauer

Good speed!


A weighing problem.

On an ordinary beam balance the following shapes are in equilibrium:

• Circle and triangle with the square;
• Circle with triangle and pentagon;
• Two squares with three pentagons:

How many triangles weighs a circle?

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The age of an uncle and his niece.

An uncle and his niece meet on a treat. The uncle says: „If one multiplies each age of three people, one obtains 2450. If one adds each age of the three people, one gets twice your age. „Well“, says the niece, „but that's not enough to elicit the age of three people“. The uncle agrees and says: „This year one of those three people celebrated a very special birthday. I celebrated this very special birthday five years ago.“

How old are uncle and niece?


Your watch has stopped. So it does not work anymore. The little hand of the watch indicates approximately ten o'clock, and the big hand of the watch indicates approximately two o'clock. Both hands of the watch form an identical angle. When did your watch stop precisely?

**


The reputable house.

A few families live in a house from which we know the following facts:

• More children than parents live in this house.
• More parents than boys live in this house.
• More boys than girls live in this house.
• More girls than families live in this house.

No family is childless, each has a different number of children. Every girl has at least one brother and at most one sister. One family has more children than all the other families combined.

How many families live in this house and how are they composed?


The dice game.

Each round of a dice game consists of two fair dice; the result of one throw is the product of the eye thrown numbers. A game consists of 5 rounds.

Bob throws in the second round by 5 more than in the first, in the third round by 6 less than in the second, in the fourth round by 11 more than in the third and in the fifth round by 8 less than in the fourth.

How many points did he score in each of the 5 rounds?


The Italian Book.

Last week I bought a book in Italy. The cashier got hundred Euros and gave me twice as much and five cents more back than my entitlement was. Obviously the cashier had confused the amount in euros with the amount in cents.

How expensive was the book?


A bridge between Germany and Switzerland has two parts: a German and a Swiss part - duh. There is a difference between them in height, namely: 54 cm. Why?

Hochrheinbrücke (Laufenburg)


Aristhomegel

There are three persons hidden.


In a cellar there are three light switches. One of them turns on the light of the first floor. You do not know which one it is. You may go but only once in the first floor to look up. How do you find out which one of the three light switches turns on the light of the first floor?


Two Liars.

Five persons A, B, C, D and E chat:

A: „B lies if and only if D is telling the truth.“
B: „If C is telling the truth, then either A or D is a liar.“
C: „E lies, and also A or B lies.“
D: „If B is telling the truth, then A or C too.“
E: „Among the persons A, C and D is at least one liar.“

Two persons are lying. Which?


100 Pessimists.

100 pessimists have written 100 senntences on a sheet of paper. Each pessimist has written 1 sentence. The 100 sentences are numbered from 1 to 100. The first pessimist has written: „Exactly one sentence on this sheet is wrong.“. The second pessimist has written: „Exactly two sentences on this sheet are wrong.“. .... And so on. Which sentences are wrong, which right?


Here you can see a large rectangle, consisting of 10 squares:

Recteck mit 10 Quadraten

How big are the sides of each square at least, if they are all different in size and integer (thus: in whole numbers)?


Does logic contain different types of implication?

Two examples:

1) There is one type (usually but also mistakably called material implication / conditional) that connects „p“ and „q“ to a new statement that is false if and only if the first part of the statement is true and the second part of the statement is false:

p q p --› q
T T T
T F F
F T T
F F T

The notation is „ ¬ p v q “.

So the statement „if the Earth is a planet, then 2+2=4“ is false according to this type of implication, whereas the statement „if 2+2=4, then the Earth is a planet“ is true according to this type of implication.

2) There is another type (usually but also mistakably called logical implication / entailment) that is like this:

Major premise: All M are P.
Minor premise: All S are M.
Conclusion: All S are P.

In this case „q“ (conclusion) follows logically from „p“ (major and minor premise) if each semantic interpretation of a language that makes „p“ true makes automatically (just due to the logical form of „p“ and „q“)„q“ true too.

The notation is „ p ||— q “.

The symbol „ ||— “ is also mentioned in the ASCII code, and could be interpreted as a mix of „ |— “ and „ |= “. The symbol „ ||— “ is more used in linguistics than in logic itself but it is a logical symbol as well.

The truth table associated with the material conditional p-›q is well-known.
„The material conditional (also known as »material implication«, »material consequence«, or simply »implication«, »implies« or »conditional«) is a logical connective (or a binary operator) that is often symbolized by a forward arrow »-›«. The material conditional is used to form statements of the form »p-›q« (termed a conditional statement) which is read as »if p then q« or »p only if q« and conventionally compared to the English construction »If...then...«. But unlike the English construction, the material conditional statement »p-›q« does not specify a causal relationship between p and q and is to be understood to mean »if p is true, then q is also true« such that the statement »p-›q« is false only when p is true and q is false. Intuitively, consider that a given p being true and q being false would prove an »if p is true, q is always also true« statement false, even when the »if p then q« does not represent a causal relationship between p and q. Instead, the statement describes p and q as each only being true when the other is true, and makes no claims that p causes q. However, note that such a general and informal way of thinking about the material conditional is not always acceptable, as will be discussed. As such, the material conditional is also to be distinguished from logical consequence .

Materiale Implikation als Mengendiagramm

Venn diagram of A -› B.
If a member of the set described by this diagram (the red areas) is a member of A, it is in the intersection of A and B, and it therefore is also in B.“ **


Three Ladies.

Three ladies gather for a meeting: Mrs. Red, Mrs. White, and Mrs. Green. One of the ladies says: „That's strange, one of us is wearing a red, another one a white, and the third one a green blouse“. „This is really amazing“, said the lady with the red blouse, „because no one of us is wearing the blouse which corresponds to her name“. „That's right“, Mrs. White adds.

Which lady is wearing which shirt?


„Fractal“ is a mathematical concept, thus very theoretical; so it is a very reckless idea to believe in it as if it were a physical fact.


Weekday.

Seven people, A, B, C, D, E, F, G discuss which weekday is today.

A: „The day after tomorrow is Wednesday.“
B: „No, today is Wednesday.“
C: „You both are wrong, Wednesday is tomorrow.“
D: „Today is not Monday, not Tuesday, and not Wednesday.“
E: „I am pretty sure that yesterday was Thursday.“
F: „No, yesterday was Tuesday.“
G: „All I know is, that yesterday was not Saturday.“

If only one statement is true, on which weekday was that conversation?


Two Children.

A boy and a girl are talking: „I am a boy“, says the blond child. „I'm a girl“,says the black-haired child. At least one of the children is lying.

What hair color does the girl have?


Greetings from ....

The following picture shows the island where I spend my holidays:

Menorca

Which island is it?


Perfect Logicians.

Players A and B have got the number 12 written on their foreheads. Everyone sees the number on the front of the other but does not know the own number. The game master tells them that the sum of their numbers is either 24 or 27 and that this numbers are positive integers (thus also no zero).

Then the game master asks repeatedly A and B alternately, if they can determine the number on the own forehead.

A: „No“.
B: „No“.
A: „No“.
B: „No“.
A: „No“.
....

After how many „no“s does the game end, if at all?


Six people in two groups.

There are six people A, B, C, D, E, F which are in each case either in group 1 or group 2. The following statements are given:

1. Both A and B are in 1.
2. F is in 2, and if E is in 2, then C is also in 2.
3. D is in 1, and if F is in 2, then A is also in 2.
4. A and E are both in 2.
5. D is in 2, and E is in 1, and if C is in 2, then B is in 1.
6. D and B are both in 2.
7. The statements 1-6 are wrong.

Who is in which group?


Many people fear mathematics, and many people are cynics. Now, combine this two facts, please!


Mathematics is an abstract discipline, y and it is - of course - logical. And logic is in your mind, your subjective mind.

If you say that something is objective, then you refer to the world, thus to something outside your subjective mind.


„Understanding“ and „thinking something is true“ are processes that belong to the same root(s). Animals with a primitive (not complex enough) brain do not distinguish between „understanding“ and „thinking something is true“. You need to have a well enough working complex brain in order to distinguish between „understanding“ and „thinking something is true“.

My argumentation is an evolutionary biological (especially neurological) one, and I compare the phylogenetic evolution with the ontogenetic development. You can be sure that animals with a primitive (not complex enough) brain are not capable of distinguishing between „understanding“ and „thinking something is true“. So you need to have a well enough working complex brain in order to distinguish between „understanding“ and „thinking something is true“. The said roots are evolutionary biological (especially neurological) roots, mainly the nervous system that leads to a primitive brain that leads to a more complex brain that leads to a still more complex brain ... and so on.

„Higher animals“ like great apes, dolphins, some bird species, for example, are capable of what a nearly two years old human child is capable of; I say that, for example, bonobos and chimpanzees are capable of corrupt behaving, although merely in a primitive way.


Just think about it:

Epistemology for Beginners


The core is what we can call „information“ - in order to be „in form“ (to survive) . This leads at last, namely when it comes to higher culture, to the question: „How can I be sure that the information is true?“ All understanding has to do with information, but not all information has to do with understanding. A stone that gives information to a geologist does not need to understand the information that it gives. And all knowledge is information, but not all information is knowledge. Belief is also based on information, but not all information leads to belief. Information is the superordination of belief and knowledge.

Epistemology for Beginners


Belief and knowledge are exactly the same, but they have the same evolutionary root.
Eliminating belief does not epistemologically help, because knowledge did not accure without help. If you believe that knowledge is absolutely independent, then you are more a believer than those who say the opposite.

All understanding has to do with information, but not all information has to do with understanding. A stone that gives information to a geologist does not need to understand the information that it gives.

Eliminating belief does not epistemologically help. Knowledge did not occur out of the nothingness and also not without help. If you believe that knowledge is absolutely independent, then you are more a believer than those who say that knowledge is not absolutely independent.

Information is in the outer circle - as the superset of belief and knowledge -, and it is also an intersection of belief and knowledge. Both belief and knowledge have their origin in information (their intersection) and lead to information (their superset). The intersection and the outer circle had been one circle (without belief and knowledge) before belief and knowledge were „born“. A stone (for example) does not have belief or knowledge but does nevertheless give information.

Information is the whole process, whereas understanding is merely a part of it. You do not need to know or to understand the informations you give. For example: I have got information about you, but you do not know this information. Another example: trees do not know and not understand the information they give and get. Many many other examples can be given. Most living beings are without understanding but with information. And these most living beings do what is true or false, although or, better, because they are not capable of understanding, knowing, thinking - but capable of giving and getting information. They do not need to know and to understand what true or false is - they just do it (and mostly with more success than those „higher“ living beings with knowing and understanding).

Plants, for example, seem to understand what the words „true“ and „false“ mean, but, of course, they do not, because they have no nervous system. They do not need to understand what „true“ and „false“ mean. But they act and react as if they understood the meaning of „true“ and „false“. And by the way: their actions and reactions are averagely more successful than those of the living beings with a nervous system.


First of all, one has to understand what others say and then, secondly, what they mean. If you read my words I am just writing, then you have to be capable of knowing the letters, the syllables, the words, the sentences, the whole text and, of course, the grammatical structure and the relations of all that, and after it you can begin with your interpretation of what the people mean, because the people and their world are part of the context but not the text itself.


Knowledge about mesophysical laws has a likelihood of about 98-99% truth. The primary task of our senses and brains is not to know complicated laws but to support our surviving.


Who is depicted here?

Hilliam Billary Clinton


Imagine you inhabit an epistemological house with two floors. The first floor as the lower floor is your belief and the second floor as the upper floor your knowledge. If you take away your first floor, you are not able anymore to inhabit your house; but if you take away your second floor, you can remain in your house and just inhabit the first floor.

Belief and knowledge have the same roots, but they are not equal, because belief is more relevant than knowledge when it comes to epistomological certainty. Knowledge can be easier destroyed than belief. If you are uncertain, then remember your epistemological beliefs, because your beliefs make you more certain again than knowledge. The conclusion that knowledge can give you more epistemological certainty than belief is a fallacy. If you want to maintain your knowledge, then support it with your belief - like the lower floor supports the upper floor. This does not men that knowledge is not relevant. No! Knowledge is jeweled, but it is more fragile than belief. That is the reason why knowledge needs more to be maintained or nursed than belief. But this maintaining or nursing is not possible without belief. That is the reason why belief is more relevant than knowledge. Your knowledge is of no benefit to you without belief. It is worthless without belief.

If someone wants to make out of knowledge belief or/and out of belief knowledge, then the most effective way is to change the semantics of both words, namely by exchanging both meanings. That is what the rulers and their functionaries have been doing for so long by their so called „political correctness“, which is just not more than rhetoric, propaganda, semantical supremacy. They are destroying knowledge, because they try to replace it by belief, which they call „knowledge“.


John and Gerry, who are walking along with a clearly visible number written on their foreheads, have to know a certain number range, thus the upper limit and the lower limit of the range of their numbers, and they have to know another aspect, for example: a possible sum, a possible difference, a possible product, a. possible quotient of their two numbers (for instance: Gerry only knows a sum of the two numbers of a certain number range, whereas John only knows a product of the two numbers of the same certain number range). So they know enough, even more than enough (!), in order to solve the riddle.


If ...:

Nature (including culture)

Then ...: how could we depict logic?


Two Numbers and Two Mathematicians.

Two natural numbers between 2 and 20 are selected. Mathematician S. knows the sum, mathematician P. the product. Both mathematicians know the lower limit of the two numbers, but not the upper limit.

S.: „I can not imagine that you can find out my sum.“
P.: „Now I know your sum.“
S: „Now I know your product.“

What is the sum?
What is the product?


Information is serving self-preservation. Without self-preservation or, more exactly, without any interest in self-preservation information would be useless.


„Logic is merely the proper use of language (»dialectics«).“ (**) Yea!


The word „belief“ is originally not meant „religiously“ or even „theologically“.

Now, the trick is to not use belief as a dogma but merely as an epistemological „crutch“. If there will be more certainty, then you will not use it anymore and put it in your „cellar“.

It is at least no advantage or satisfaction to you, if you must always say „I know nothing“ or „I know that I know nothing“. Philosophy and science do not have 100%-answers. So it is better to live with an epistemological „crutch“ than with stupidity or/and lies.

The epistemological „crutch“ helps you to find a solution or not, to come a to yes/no- or true/false-decision. It does not dogmatize you, or, in other words, it depends on your personality and character whether it dogmatizes you or not: if it does, then you are not a good philosopher or scientist; if it does not, then you are a good philosopher or scientist. Science would never have been successful without help like what we call „empirism“ („observation“, „experiment“, „extrapolation“, and so on and so forth), „deduction“, „induction“, and other „crutches“.

If this all turns out as a dogma, then it is not the „crutch“ that is to be blame but those humans who are corrupt or too dumb.

Science and philosophy have always used such „crutches“. Otherwise they would never have developed (historically evolved).

....

Belief is needed.


A society with an economy that is based upon information (including knowledge and belief) is much more environment-sparing than a society with a money economy that is based upon energetic resources. Information (but not energy and resources) can be reproduced arbitrarily. So information is the better money basis. I would suggest a money system of two monetary units: „I“ („Information“) and „E“ („Energy“), so that, for example, 100 cents would consist of 98 I-cent and 2 E-cent, and both could not really be separated from each other.

Epistemology for Beginners


It can never happen that 1.0 = 0.999 (**).

It has to do with the infinitesimal calculus (inveted by Gottfried Wilhelm Leibniz).

The equation of 1 = 0,999... does at last not absolutely work: although the difference of both numbers becomes smaller and smaller, they can't become equal, because there remains always a rest, an infinite small rest but a rest. So this equation works mathematically, of course, but that does not mean that it also works logically, thus philosophically. It is a solution for mathematicians but not for philosophers. One can always say that there is a rest that denies the equation.

This also indicates that mathematics and philosophy are two different disciplines, and history has shown that they have to be different disciplines.


There is logic, and there is mathematics. All mathematics must be logical, but not all logic must be mathematical.

Mathematics is a subset of logic.

**


Example: „Achilleus“ - Zenon's fallacy.

The error is the confusion and permutation of (a) the thought of the succession of time with (b) the thought of the succession of space. One could also say: It is a misjudgement of the fact that the merely mathematically infinite divisibility of a stretch or a time length says nothing aginst its real finiteness.

If reality was (it is not) merely mathematical, then Achilleus could not reach the turtle, thus the mathematical solution (see: a) would be right in any case (because: reality = ideality); but our reality is also resp. mainly physical (see: b), and we have senses and brains for experiencing (observating, perceiving) this reality, so that we can know that Achilleus can reach the turtle. All this (see: a and b) means that we can solve the „Achilleus“ problem exactly, thus mathematically.

The merely mathematically infinite divisibility of a stretch or a time length does not contradict its real finiteness.

We have to distinguish between (1.) the realm(s) of ratiocination / logic / mathematics and (2.) the realm(s) of physics / chemnistry / biology. So if one logical / mathematical task does not only contain a mathematical subtask but also a physical subtask (like the „Achilleus“ task does), then we have to consider that two subtasks.


Some rationalisations are not deceptive, other rationalisations are deceptive. It depends on how they are used.

Rationalisations are deceptive for those who are deceptive, especially self-deceptive. And people are not equal. So there are people who are more deceptive than others. And there are some people who use rationalisation for deception and others who do not or at least seldom. But the main point is that rationalisation has a positive character as well, and this positive character is in conflict with the negative one - there is and will never be a „winner“. The current zeitgeist has influenced certain people so much, that this people think rationalisation would only be deceptive, but that is not true.


Russell and Whitehead built upon Frege, yes. But Einstein did not built upon Newton, although both can cosmologically be regarded as relativists. Einstein was influenced by the physicist Planck and the mathematician Hilbert. (Hilbert submitted the same general relativity theorie [GRT] on the 20th of November 1915, five days before [!] Einstein), but Einstein published it before Hilbert).


There are three most important branches of philosophy: aesthetics, ethics, logic. As Goethe said: „dem Schönen, Guten, Wahren“ („to the beauty, good, true“). This was meant as unit, thus as the classical philosophy. So I think that there are some aspects or things that can also objectively be considered as beauty: symmetry, shapeliness (well-proportioned aspects or things), certain geometrical figures, beings consisting of structures that are based on certain mathematical numbers (e.g.: the Fibonacci sequence or the golden cut).

Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, ...):

  
 Wachstum der Sonnenblumenkerne

Golden cut (1,6180339887...):

Interestingly, the Fibonacci numbers show some noteworthly mathematical specific features:

Due to the relations to the previous and the following number growth in nature seems to follow an addition law. The Fibonacci numbers are directly associated with the golden cut. The further one progresses subsequently, the more the quotient of successive numbers approaches to the golden cut (1,6180339887...) - for example: 13:8=1.625; 21:13=1.6153846; 34:21=1.6190476; 55:34=1.6176471; 89:55=1.6181818; 144:89=1.617978; 233:144=1.6180556; ... and so on). This approach is alternating - the quotients are alternately smaller and bigger than the golden cut (golden number, golden ratio):

Fibonacci-Zahlen und Goldener Schnitt

The Fibonacci numbers are the sums of the „shallow“diagonals (shown in red) of Pascal's triangle:

Fibonacci-Zahlen im Pascalschen Dreieck

„Liber Abaci posed, and solved, a problem involving the growth of a population of rabbits based on idealized assumptions. The solution, generation by generation, was a sequence of numbers later known as Fibonacci numbers. Although Fibonacci's Liber Abaci contains the earliest known description of the sequence outside of India, the sequence had been noted by Indian mathematicians as early as the sixth century.[17][18][19][20]

In the Fibonacci sequence of numbers, each number is the sum of the previous two numbers. Fibonacci began the sequence not with 0, 1, 1, 2, as modern mathematicians do but with 1,1, 2, etc. He carried the calculation up to the thirteenth place (fourteenth in modern counting), that is 233, though another manuscript carries it to the next place: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377. Fibonacci did not speak about the golden ratio as the limit of the ratio of consecutive numbers in this sequence.“ **

Fibonaccis Kaninchen


Science has to do with two sides of its „coin“: theory (logic, language) and empirism (scientific practice, experience) - both connected with deduction and induction.


A = A is the principle of identity.

The full verb „is“ is not ambiguous .

The „is“ itself can never be wrong, because ist stands for the principle of identity. What can be wrong is the use of the “is“.

Several people use the language in several ways, so some people even use the verb „is“ in a false way.

Normally, poor or incorrect judgement is and should be corrected by teaching the correct judgement. But the next question follows immediately: „What is the correct judgement?“. The only possibility we have is to keep on referring to logic, because all other possibilities can and often do lead to the misuse.

What happens to a logic built on misused identifiers as well as poor judgement? It would be a logic that is very much reduced for most of the people. „Less is more“, „black is white“, „male is female“, „left is right“, „right is wrong“, „war is peace“ ... and all the other uncountable examples of the misuse of words would boom (like in Orwell's „1984“, for example). It would be like it almost already is.


All mathematics is logical, but not all logic is mathematical.

Mathematics as a subset of logic


Let us compare the set „linguistics“ and its subsets with the set „sun“ and its subsets.

1) Set: Linguistics 2) Set: Sun
1,1) Subset: Logic 2,1) Subset: Hydrogen
1,1,1) Subsubset: Mathematics 2,2) Subsubset: Helium
1,1,2) Subsubset: Others 2,3) Subsubset: Others

Question: What happens if you take the hydrogen away from the sun?
Answer: The sun becomes bigger because of the helium burning.

If there were no mathematics, then logic would use linguistics instead of mathematics (like the logic of children, especially of little children, does).

Observe your little children when they try to calculate in a really mathematical way for the first time. You should find out that they use language and a bit later also their fingers in order to come closer and closer to the real mathematics.


A lioness (for example), although not capable of counting, ascertains the absence of one of the cubs.


Interestingly, the most exact branch of science is not a branch of natural science but a branch of spiritual science: mathematics. Mathematics is not a branch of natural science but a spiritual science the most exact branch of science.

Mathematics is a spiritual science, thus: a science. In German, there is the distinction between Naturwissenschaft (natural science) and Geisteswissenschaft (spiritual science), and Sozialwissenschaft (social science) is „something“ between them.

Mathematics is the most exact science, and - interestingly - it is not a natural but a spiritual science.


Do you belive that scientists have „even declared (for sociopolitical reasons) that science has proven that logic doesn't work. “ (**)? If that is true, then they did something like a declaration of bankruptcy. A „science“ that has „proven that logic does not work“ is no science. In other words: The current „scientists“ are no scientists.

I think that this sociopolitical development with such a „declaration“ (see above) is a very ugly one. At last there will be no practical science anymore (at least no one which is practiced by real humans), and "no practical science" means "no science in use, only false definitions of it".

Mathematics should remain what it has always been: an „unphysical“ („non-physical“), thus an „unnatural“ („non-natural“) branch of science which is the most exact one, thus also the best one when it comes to help all other branches of science.

If someone is badly talking about mathematics, then you can be sure that this someone is not a scientist.


Mathematics is not a branch of natural science, as we know, but it is a branch of science. So it must be a branch of another kind of science, and I call this another kind of science „spiritual science“ (following the German „Geisteswissenschaft“ - „Geist“ means „ghost“, „spirit“ -, although „Geisteswissenschaft“ is often translated by „humanities“, but I do not think that that translation is the right one). The translation is a bit difficult, but we know that mathematics as such has nothing to do with physics, with chemistry, with biology, ... and other branches of natural science. Mathematics is a „subset“ of the „set“ logic.


My thoughs are not English. So I have to translate each thinking element into the English language. In other words: I am aware of the fact that „Geist“ and „spirit“ are not the same. The words „Geist“ and „Ghost“ have the same root. They had the same meaning before this meaning split. So maybe it is not possible anymore to properly trannslate „Geist“ into English, which means that it is also not possible to properly trannslate e.g. „Geisteswissenschaft“ into English.


On the internet, 20% of all nodes attract 80% of all links. All this seems to obey the 80/20 rule (**).


Philosophy is primarily about logic. In other words: „Philosophy without logic“ is no philosophy. Even if you put other philosophical fields first: you have to always answer the question whether your thinking about them is logically right or false (wrong). If ontology, epistemology, phenomenology, ethics are not logically right, then they are almost nonsensical, without any philosophic and scientific basis; and ontology, epistemology, phenomenology even contain the word „logic“, so any comment is superfluous in those cases.

Logic comes before all other branches of philosophy. Just as „mathematics without logic“ is no mathematics at all, „philosophy without logic“ is no philosophy at all.

A child in a womb can already behave according to logic - but not according to ethics. Every child’s development shows clearly that logic comes before ethics. Also is behaving according to ethics earlier than knowing about ethics.

Living comes before thinking. That is absolutely right. But that does not mean that ethics comes before logic.

It goes like a circle. When living without ethics has reached thinking, then it has reached logic and starts going backwards: from logic to living, which is now a living with ethics.

Even the most primitive laws are based on ethics based on logic. So they are primarily based on logic. The reason of any taboo and any totem may be ethics, but reason is not cause. They are caused by logic (based on logic), because only logic can lead to ethics. Ethics without logic is not possible. Logic without ethics is possible. Even an anarchist has to argue logically when it comes to the elimination of laws.

Do bacteria have ethics? No, but they are behaving according to logic. Logic does not require ethics, but ethics requires logic (otherwise such „ethics“ would not really be ethics).

So if we are arguing according to development in general or evolution and history in particular, we have to put logic first. Logic was before ethics.

A child in a womb can already behave according to logic - but not according to ethics. Every child’s development shows clearly that logic comes before ethics. Also is behaving according to ethics earlier than knowing about ethics.

So again: It is absolutely right that living comes before thinking, but one should not confuse ethics with living, because ethics does not mean „living“ (but the philosophical [!] answer to the also philosophical [!] question: „what should we do?“). Living can but does not have to lead to thinking, and logic can but does not have to lead to ethics.

It is just the development that shows why logic is the first field of philosophy.

I know that in modern times ethics is the one that philosophically attracks more than the other philosophical fields. But that does not mean that ethics must or should be put first.

In order to have ethics logic is needed. The „herd morality“ and „ethics“ are concepts, created by language, by human language. Concepts must be defined, must be logical. So logic comes before ethics. Ethics depends on logic. There is no „herd morality“ without logic, regardless how romantic (beautiful) the counter „arguments“ are.

Language and logic preceded the concept „herd morality“.

It is our - the human - language that also preceded e.g. the logical concept „herd morality“ and not the other way around. The concept „herd morality“ is based on an interpretation, on language, on thinking, on logic. Wether there was a „herd morality“ before it was invented logically by using language logically (philosophically) or not is a matter of the interpretation and changes during the time; but I have good reasons for saying that language preceded e.g. the logical concept „herd morality“, and I have given evidence for that. Try to teach a child of a certain developmental age what ethics is by using logic, and you will be successful; but try to teach a child of a certain developmental age what logic is by using ethics, and you will be unsuccessful.

The modernity of philosophy is a philosophy of ethics. Okay. But this does not prove that ethics comes before logic - the reverse is true, because it gives evidence for the developmental fact that logic comes before ethics.

The historical development of the philosophical question of our current subject - „logic comes before ethics“ - can be called „modern war of philosophy“ and has a parallel in science: „modern war of science“. On the one „war front“ („left“) are fighting ethical philosophers and social scientists, and on the other „war front“ („right“) are fighting logical philosophers and natural scientists and spiritual (especially logical, mathematical) scientists. (Note: there are also „spies“, „renegates“, „defectors“, „deserters“ in that said „war“). - If the ethical-social side will „win“ that „war“, then the science as we have known it and will have known it till then will be finally „dead

Rules are spiritual. The spiritual side of language (not the physical side of language: sounds, phonemes etc.) contains the consistency of language, thus logic, the father of mathematics. Yes. Also, logic is the father of ethics. Logic comes before ethics. It is possible to understand logic without ethics, but it is not possible to understand ethics without logic.


Numbers are constructs of thoughts, logic, reasoning.

And the term „natural numbers“ doesn't mean that they „are“ natural, but that they „refer to nature“.


There is always someone who can use information or misinformation, for whatever reason.


Semantics is a subdiscipline of the disciplines (1) semiotics, (2) linguistics, (3) logic, (4) mathematics. It can only deal with meanings and definitions. Each linguistic lexem (word) that can be find in a encyclopedia, a dictionary, a lexicon can only be described by its meaning and defintion, perhaps supported by other language forms (see: (1), (2), (3), (4) and the chart below), but not by more.

So if you want to know what, for example, a „circle“ is, then you have to refer to (a) the meaning and definition of the word „circle“ and to (b) the history of its meaning and definition, which means that they can change over time. But the result of this change (caused e.g. by an experiment) is always either a new or a renewed kind of meaning and definition.

And mathematics is a subset of logic, logic is a subset of linguistics, linguistics is a subset of semiotics, and they all are language.

Language

The smaller a subset is or the more properly, coherently, consistently the subsets and sets are connected, the more exact is the information.


Four steps:

1) Perception - based on the sense organs (subjective) and signs (objective). Pre-Knowledge (semiotic language).
2) Knowledge through linguistic skills - based on perception and semiotic language (=> 1) and on linguistic language.
3) Knowledge through the pure logic of language - based on perception and semiotic language (=> 1), on linguistic language (=> 2) and on pure logical language.
4) Knowledge through mathematical language - based on perception and semiotic language (=> 1), on linguistic language (=> 2), on pure logical language (=> 3) and on mathematical language.

Now an example: We want to know what a circle philosophically means.

If we know how and wherefore mathematicians use certain definitions, then this does not necessarily mean that they use it in order to get the truth. They are just searching for consistent statements (in their mathematical language).

The „higher“ Occidental mathematics has much more to do with functions than with numbers. Its geometry has mainly become a functional theory too. But what does that tell you about the circle when it comes to the first three steps I mentioned above? No mathematician denies the meaning or/and definition of a circle giving in a currently valid dictionary. We already had a similar discussion about „1 = 0.999...~?“ (**). 1 and 0.999...~ are never identical, but according to the Occidental mathematics functions have become more important than numbers, because functions do work (just: function) much better than pure numbers.

And what about the physicists? Do they say that sunrise and sunset do not exist according to your perception? Do they deny that the Sun is going up and down according to an observer? Do they insist that you have to always say that sunrise and sunset are caused by the Earth rotation? No.

In other words: Does the answer to the question whether a circle is just circular (without sides) or has sides just in order to calculate in a better, the Occidental way of mathematics not also depend on perspectives?

I mean: Would you say that sunrise and sunset do not exist, namely in the world of your perception? Certainly not.

So do we at last not have the same discussion here as almost always: subjectivity versus objectivity (**).


We should have more than one currency, and the first one should be a currency of knowledge, wisdom, information.

And we must take another direction and slow down .

If we do not get that first currency of knowledge, wisdom, information and do not take another direction and slow down, then we will get the huge catastrophe. It is possible to avoid this. But it requires responsible rulers instead of the current ones who are godwannabes, too greedy, too corrupt and going to bring the huge catastrophe to the humans.


Schools, universities and mass media are intended to damage the intelligence of people.

Two points are important here:

(1) Cooptation of schools, universities and mass media as institutions working for the globalists who want the monopoly and monarchy..
(2) If the economic and - in particular (!) - the demographic situation is like the one we have in our western countries, then the average intelligence decreases, and teachers, professors, journalists which do not go along with the mainstream have to damage the intelligence, otherwise the colleagues will punish them by mobbing and firing.

Someone asked me recently whether one needs education. The answer depends on whether one means (A) the education as such or (B) the school education which is basically a state education.

(A) If the education as such is meant, then: yes, one needs education.
(B) If the school education which is basically a state education is meant, then: yes (Ba) and no (Bb).

(Ba) Yes because of those who are genetically less intelligent and can use the school education as a chance to become more intelligent.
(Bb) No because of a situation like the described one (=> 2).


If, for example, A equals B, then there is no quantitative difference between them, so: A = B then. I believe that in real life equality has the tendency to make also a qualitative difference indifferent, thus equal, so that there is at last a qualitative indifference. In other words: if you have no quantitative difference, then you have to expect that you will - sooner or later - have no qualitative difference either.


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