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?
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.
xcoordinate <=> centuries (0 <=> the
year 1800)
ycoordinate <=> 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.
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 (18481925) is the father of analytic philosophy,
of mathematical logic (=> logistic, symbolic logic ...),
thus also the philosophical father of Bertrand Russel (18721970)
and all other analytic philosophers.
The German philosopher, logician, mathematician Friedrich Ludwig
Gottlob Frege (18481925), the founder of the modern mathematical
logic (=> logistic, symbolic logic ...), the father of analytic
philosophy thus the philosophical father of Bertrand Russell (18721970)
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 (18261866) as the
precursor of Einstein's relativity theory and David Hilbert (18621943)
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
(16461713) 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
halfbricks in a row at the left and right edge of the diagram form
one whole brick.
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?
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?
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:
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 wellknown.
„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 .
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 blackhaired 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:
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 16 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:
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.
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 9899%
truth. The primary task of our senses and brains is not to know
complicated laws but to support our surviving.
Who is depicted here?
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 ...:
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 selfpreservation. Without selfpreservation
or, more exactly, without any interest in selfpreservation 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/falsedecision. 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 environmentsparing 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 Icent and 2 Ecent, and both could not really
be separated from each other.
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
selfdeceptive. 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 (wellproportioned 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, ...):
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):
The Fibonacci numbers are the sums of the „shallow“diagonals
(shown in red) of Pascal's triangle:
„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.“
**
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.
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“
(„nonphysical“), thus an „unnatural“ („nonnatural“)
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 ethicalsocial 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.
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). PreKnowledge (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.
