The limits of science

Author: Spiros Kakos

Man has to awaken to wonder — and so perhaps do peoples.
Science is a way of sending him to sleep again.

Ludwig Wittgenstein, Tractatus Logico-Philosophicus

I. Introduction – About Science

Exact Science has been for a long time now the tool used by most humans in order to understand the physical world. The great successes of sciences like physics or astronomyin predicting things and helping the everyday life of people has established “exact” science as the ultimate tool to discover the truth. This has unfortunately led to a decline of the importance other scientific fields of human thinking have – sectors as important as philosophy, history, religion, linguistics. We tend to forget that law or history can be as scientific as quantum physics. We tend to forget that science is seeking the truthwith a systematic way and that fields of science like physics or chemistry are only a small portion of it. Science is not only physics. It is also the exploration of human affairs, the attempt to explain why humans fight each other, the struggle to understand what “bad and good” is. Anthropology, sociology and law are fields of science in the same way cosmology is. Science is not only about evidence. Many people confuse science with “empiricism”, that is the philosophical dogma that all valid knowledge can be based on human experience only. These people tend to forget that even cosmologists and physicists dream about parallel worlds or alternate universes, hypotheses that can never be proved or disproved by evidence.

Before someone starts dealing with science, he must pay a visit to a good philosophical dictionary so as to make sure that he understands all words with their correct meaning. I strongly recommend the Dictionary of Philosophy, Dagobert D. Runes, 1942, New York as a basis for your knowledge/ word seeking.

René Descartes. Portrait after Frans Hals, 1648. A (great?) philosopher of science

It is unfortunate that the above-mentioned misconceptions have led humans away from thinking about humans. Fortunately many thinking people of our time have pinpointed the problem and insist on thinking “scientifically”, rather than thinking “scientifically as physicists”…Science is not only “thinking numbers based on physical evidence” – it can also be “thinking logically” or “thinking systematically”.

And even more important is the fact that really great science is about thinking “out of the box”, it is about thinking in a way that one would consider “illogical”… The greatest scientific theories were the result of irrational thinking of great minds, who went outside the “logic” of their time…

Everywhere science is enriched by
unscientific methods and unscientific results,
[…] the separation of science and non-science is not only artificial
but also detrimental to the advancement of knowledge.
If we want to understand nature,
if we want to master our physical surroundings,
then we must use all ideas, all methods,
and not just a small selection of them.

Paul K. Feyerabend,
Against Method: Outline of an Anarchistic Theory of Knowledge (1975)

II. About exact science: A definition

Exact science is based on observation and induction. You observe one phenomenon, then you observe a similar one, then another one and so on, until you reach to a conclusion about how such phenomena work. Then you formulate a theoriticalmodel that predicts similar phenomena in the future. If your model works, then your theory is accepted by other scientists (the infamous “peer-review” model, which can lead to weird applications of auto-cencorship for not widely accepted ideas [1] – but this is only out of the scope of this article). Until a phenomenon not following your set of rules is observed…

Other fields of science

Besides the “exact” sciences, there are many other fields which exist. These other scientific fields are based on the “logical and structured way of analyzing a specific subject” and include sectors like anthropology, linguistics, law, psychology etc.

One of the most negative impact of the “exact” sciences’ domination in modern times is the demise of these other equally “scientific” fields. It is a good sign that people are beginning to realize the mistake in that and a regeneration of interest in these “human” sciences is observed. People realizing that there are more things than having GPS devices or new high-technology clothing which play MP3 while you wear them. Understanding our past (via History), other people (via Anthropology) or our own selfs might be far more important…

Definition of Science

Science is the systematic search for truth.And in that context physics and chemistry are not the only fields of science that exist. Many people confuse science with “empiricism”(i.e. all knowledge is based on human experience only). Empiricism is a philosophical dogma and a very outdated one, I might say. [2] And it is of great importance to understand that many scientific breakthroughs have been conducted via totally illogical and “unscientific” (at least according to the common definition of “scientific”) bursts of genius inspiration. Outbursts which many times have nothing to do with anything that can be sensed or be part of human experience; for example, any research on the notion of ‘infinite’ or research related to the existence of ‘multiple universes’ or dimensions which we cannot feel.

Given any rule, however ‘fundamental’ or ‘necessary’ for science,
there are always circumstances when it is advisable not only to ignore the rule,
but to adopt its opposite. For example, there are circumstances when
it is advisable to introduce, elaborate and defend ad hoc hypotheses,
or hypotheses which contradict well-established and generally accepted
experimental results, or hypotheses whose content is smaller
than the content of the existing and empirically adequate alternative,
or self-inconsistent hypotheses, and soon. […]
It is clear, then, that the idea of a fixed method, or of a fixed theory of rationality,
rests on too naive a view of man and his social surroundings.
To those who look at the rich material provided by history,
and who are not intent on impoverishing it in order to please
their lower instincts, their craving for intellectual security
in the form of clarity, precision, ‘objectivity’, ‘truth’, it will become clear that
there is only one principle that can be defended under all circumstances
and in all stages of human development. It is the principle: anything goes.

Paul K. Feyerabend, Against Method: Outline of an Anarchistic Theory of Knowledge (1975)

III. Limitations of exact science

Exact sciences like physics have many limitations, often disregarded by their “followers” (i.e. people who think that measuring, evidence-based exact science is all that there is in the scetor of human knowledge-seeking). I will discuss the main of these limitations here.

A. Axioms of Exact Science turn into Dogmas

The main limitations of science are a result of the things science takes from granted – i.e. of the axioms it uses as the basis for any further research. When you use an axiom, then you start building castles on sand. You cannot prove axioms and if you base everything on them, then you guarantee that your whole theory cannot be ultimately proved. (something proved by Gödel at the end – see his Incompleteness Theorem) Needless to say that science cannot exist without axioms. This is an inherent limitation of science which is not bad per se; the problems start when we forget that we use those axioms and start thinking of them as “self-evident truths” instead of arbitrarily chosen starting points.

Some of the main (potentially wrong, according to my opinion, but this is not what is important here) axioms of exact sciences are listed below.

1. Sciences like physics have excluded anything spiritual from the “equations” of the universe. Physics axiomatically says that the cosmos consists of nothing more than electrones, protons and other particles that obey some physical laws – while at the same time denying anything of ‘spiritual’ nature. In that context, no wander scientists cannot find ‘evidence’ for God or clues for the existence of any kind of ‘Purpose’ in our existence. After you have axiomatically accepted that a system consists of A, B and C only, how do you expect to find D anywhere? [2] The science of biology also makes the same mistake: it uses an axiom as dogma without ever questioning whether it is right or wrong. Modern biology takes for granted that humans are animals and that evolution rules apply to everything, without prooving it. Modern science is based on the doctrine of materialism[3] , also known as “physicalism” [4]. However we must remember that materialism is a dogma and not a proven case.[5]

2. All natural laws are universal and apply to everything and everyone. This has never been proven yet. It is just a thing scientists believe that is true. [6] This axiom is also what causes problems in the explanation of the basis of our human nature: “free will”. If we are to accept the existence of universal physical laws then no free will can exist. But most of us think otherwise. Most of use feel that we “decide” what to do.Science simply cannot explain that and to take it for granted would mean that we will need to discard a big part of our very nature.

3. All things are measurable. This is based on a highly materialistic view of the world and has nothing to do with reality (whatever that word means…).Things like moral, emotions, aestheticsand love cannot be measured, even though they are very important for human life. Science fields like physics, mathematicsand chemistrysimply cannot deal with these things.

4. We can know everything. Many scientists wrongly believe that humans will someday come to know everything, that there is no such thing as “un-knowable” area. However Godel has proved them wrong: he proved that there are truths that cannot be proved anytime by anyone.

5. Our Logic works correctly. This may sound odd, but it was one of the main axioms used to form the foundations of science. Out logic “must” work properly if we are to trust it. [6]

We also tend to forget the main issue: Logic is based on axioms! This is what makes illogical not something “wrong” but just a different option of axioms contrary to the ones we have used so far!

An indicative list of the axioms used in the infamous “objective” Mathematical Logic (source):

Zermelo–Fraenkel axioms
These are the de facto standard axioms for contemporary mathematics or set theory. They can be easily adapted to analogous theories, such as mereology.

  • Axiom of extensionality
  • Axiom of empty set
  • Axiom of pairing
  • Axiom of union
  • Axiom of infinity
  • Axiom schema of replacement
  • Axiom of power set
  • Axiom of regularity
  • Axiom schema of specification
  • Axiom of choice

Other axioms of mathematical logic

  • Von Neumann-Bernays-Gödel axioms
  • Continuum hypothesis and its generalization
  • Freiling’s axiom of symmetry
  • Axiom of determinacy
  • Axiom of projective determinacy
  • Martin’s axiom
  • Axiom of constructibility
  • Rank-into-rank
  • Kripke-Platek axioms

ILLOGICAL is then by definition something which does not follow these axioms.
And things would be fine if we stayed there. However things become increasingly dogmatic when we start forgetting that we even use axioms!~

6. Everything can be replicated in an experiment. Because science needs experiments to prove or disprove theories, it cannot deal with one-off events (that happen only once and cannot be reproduced). This is a simple but rather important axiom: we believe that all phenomena can be studied by experiment or observation. What happens with things that happen only once in the Universe’s history? A very good example is the creation of the Universe. If it did happen only once, how can we replicate?

And here we should note that the biggest scientific discoveries were made by great thinkers despite of contrary hard experimental data of their time! De Broigle created the theory for the double nature of particles despite that no experimental proof existed then with regard to this. Everett has created his theory of multiple worlds and he has convinced with this most scientists today, despite that this theory can never be confirmed with experimental data! Einstein thought of the theory of relativity based on mind experiments and not on physical experiments! When D.C. Miller published his experimental criticism of the theory of relativity [13] Einsteinsaid that “I did not take them [the experimental results of Miller] seriously not for a moment”. [11] When he wasasked where he drew his conviction from,he said “fromthe intuition andthe general sense of the situation” (die Vernunft der Sache). [12][14] It must also be noted here that even Descartes (to whom we owe the dogma that everything in the world can me mechanically replicated) in his great work Dioptrique found the law of refraction with the use of mathematics only and NOT with experiments!!!! [1]

7. Mediocrity and Copernican principle (principle = not proven declaration): In cosmology, the Copernican principle, named after Nicolaus Copernicus, states the Earth is not in a central, specially favoured position. More recently, the principle is generalised to the simple statement that humans are not privileged observers. In this sense, it is equivalent to the mediocrity principle, with significant implications in the philosophy of science. The mediocrity principle is the notion in philosophy of science that there is nothing special about humans or the Earth. These two principles combined form the basis of our current cosmology. [7][8] Even though the Theory of Relativity states that we can choose ANY point of reference for basis of calculations in the universe (which means that we can easily put Earth in the center of everything and form the physical laws with that as a reference point), even though the universe seems the same in any direction we may look and all galaxies seem to drive away from us (as if…we were in the center of the universe as Hubble himself admitted, but then denied simply because that would be opposing these two “principles”! [9][10] ) some people still maintain their “belief” (dogma?) that humans are just grains of dust in the cosmos. I do not say that I know for sure that we are or weare not.But I cannot agree with someone that takes that for granted. I cannot argue with dogmatic people…[read the related article Earth is at the Center of the Universe?for more on that]

8. Dialethism is false.All science is based on the axiom that a proposition can be either true or false (i.e. that dialethism is false; this is also an axiom of mathematical logic by the way). However there are substantial evidence towards a different “reality”. Consider for example the logical proposition “this proposition is false”. Is it false? If yes, then it is true. Is it true? If yes, then it is false. Graham Priest has argued that the only way out of this infamous paradox is to accept a different axiom: that a logical proposition can be true and false at the same time! [2] Other great philosophers have also argued towards the point that the distinction between “right” and “wrong” could be something imposed by the limited abilities of the human mind (see Feyerabend – Harmonia Philosophica).

9. Time exists. People in the past may have felt that time, as Newton described it and used it, was indeed something that “exists”. We think time passes. But there are more and more scientific views (see Godel and Rovelli, to start with) are in favour of the theory that time is just an illusion. If this is correct, the implications to philosophy could be icredible. And the implications to science also would be tremendous: all our ideas about motion and events is based on this elusive concept of time! [3][4][5][6][7]

10. The notion of “change” exists: At the time before Socrates in Greece, the idea that things “change” was a topic of discussion between philosophers and not a matter solved. How can a thing be changed without losing its identity? Perhaps things do not change eventually, said Parmenides. The cells which constitute our body as humans are changed several times during our lives. How do we know that we are who we think we are? Is there a “reality” beyond what we see? Finally the theory of Democritus and Leukippos (according to which things are changing) prevailed over the theory of Parmenides, and that has defined profoundly our scientific thinking ever since. Is that what is actually happening though? [22]

READ ALSO:  Why does life exist? A very scientific (and theological) response…

11. The whole can be analyzed if we examine its parts. This is not certain by any means. If we examine hydrogen and oxygen, we will never find out any information about the wetness of water. If the universe is holographic, as many modern physicists postulate, then by examining the parts we achieve nothing. [See the Harmonia Philosophica knol for the implications the non-existence of “time” and “change” could have to the main issue that troubles people from the very start of their existence: Death]

More dogmas

The dogmas of science are practically endless. Rupert Sheldrake pinpointed a few more in his lecture “The Science Delusion” (see here). An indicative list of dogmas I have collected over the years follows:

  • Everything is matter
  • Matter is unconscious
  • Laws of nature stay the same. For now and for ever, this is what we have. Except of course from the moment of the Big Bang when all those laws were created. It is like the joke which states “Give us one free miracle and we’ll explain the rest”. The miracle in this case is the sudden creation of all matter, energy and fixed laws of the Universe in an instant. 🙂
  • The sum of matter and energy stays the same. (that is, except from when a huge mass and energy was created out of nowhere in the Big Bang)
  • Nature’s purposelessness
  • What humans inherit from their parents are material (everything is in the genes)
  • Your mind is inside your head. Memories are in the brain (even though no one knows how it works) [and despite the evidence we have against this idea, I would add – see “memory” and “mind” in Harmonia Philosophica] [17]
  • Psychic phenomena (like telepathy) are not possible, despite the evidence against that view
  • Mechanistic medicine is the only medicine that works. No alternative theories exist.
  • Occam’s razor: Why should the most simple solution be the correct one? If the real solution is complicated, we will never find it… (see here)
  • Balance is inherently natural. But why even think about that? Keeping balance requires much effort. (see here)
  • Viruses come from the “outside”. But how many know that there are theories which postulate that viruses could come from within? (read here)
  • It is impossible to achieve >100% efficiency in thermal machines. Really? (read discussion here)
  • The observed exists. But how many of us have considered that thinking about the observed precedes the observation? (see here)

The above-mentioned axioms are the basis for the limitations of science. However one might say that this is not a problem – that every theory must start from somewhere. I cannot agree more. My objection is not in the use of axioms per se, but in our completely forgetting that we use those axioms. When we believe that our science is based on “true” arguments, then we forget the basis of our science. True science can draw strength from the continuous questioning of the underlying axioms/ principles we use; this is something we should not be avoiding but something we should actively seek!  When we forget that we use axioms (and that if we use other axioms we will reach completely different conclusions) then those axioms turn into dogmas. And dogmatism, in any form, is not a good thing…

The true mystery of the world is the visible, not the invisible. Oscar Wilde

B. Exact sciences cannot measure

It sounds strange to say “exact science cannot be exact”, but it is absolutely true!

Ask a physicist to measure the length of a table in your house. He will take the necessary tool to measure length and will measure, let’s say, 80 cm length. But is this true?

Just imagine another physicist comes to your house and measures the same table with a different – but more accurate – tool. He will measure the length equal to 80.095 cm. Is this correct? Another ones comes to your house and with a tool of greater accuracy measures the length equal to 80.0949988988171716 cm. Could this be our final measurement? I am afraid not. Every time you use greater accuracy, you end up with a different number!

OK, one might say. I will use a SEM and measure the length at the atomic level. Try it. You attempt to do just that only to realize that at an atomic level you stumble on the uncertainty principle of Heisenberg: you cannot know where the electrons are exactly!

How do we “know” π if we do not know its digits?

What does this mean? Does it mean the table has no length? It must have a length, since we see it in front of our eyes. The point here is that the table has a length, but our science cannot measure it. That is not a limitation of our science today. We know that we will never be able to measure the exact length of the table due to quantum mechanic phenomena occuring.

Final outcome: you do not know and will never know the exact length of your kitchen table! Weird conclusion for what we call the “exact sciences”…

C. Main limitations of scientific tools

Other limitations of science come from the tools it uses. Some of them are discussed below.

1. The tool of ‘induction’ is by itself a problem for science. Lets say you observe a frog and see its green. Then another frog and you see that it is green also. Then another, and another – until you are convinced that all frogs are green. Then you write a theory about frogs. Everythings seems quite good up to this point, quite ‘real’, quite ‘scientific’. Until you observe a black frog… [3]

2. Science is based on our senses. The limitations of them may pose significant limitations to how we understand the world, that we may never be aware of [1]. Since we do not know if our senses work “correctly” (mainly because we do not have a benchmark as to what is the “correct” way for senses to be receiving signals from the world), we will never know how “close” we are to “Reality”.

3. One of the main problems of science is that we do not have a single clue about what the ‘real’ reality looks like, so that we can understand how close we are to the ultimate truth with our scientific theories. Withour being able to know what the goal is, it is very hard to know if you are going the correct way [1].

4. Science uses Logic as a tool to reach to conclusions. However even Aristotle, the founder of Logic, did not know how logic could be useful: as a tool to reach the truth or as merely a tool to analyze language and its structure? Many modern philosophers, like Wittgenstein, think that human language has many limitations and that due to these limitations, one must be careful as to talk only for things he/she can talk.

The faith in the whole structure of science is based on the faith that logic works. If the latter collapses, then science is without any justification at all.One of the greatest mathematitians of all times, Russel, actually proved that logic has great limitations. The greatest logician after Aristotle, Godel, proved that science cannot prove it can prove things! Even logic requires faith to rely on after all…

D. Mathematics cannot spell numbers

From the beginning of human science, mathematics is considered to be the most crystal clear, provable, safe, well documented and better founded field of knowledge. Due to its nature, mathematics were the first field were an attempt to set the foundations of a fully justifiable / provable theory was conducted – and failed (see Hilbert program, Russel and Godel incompleteness theorem).

However mathematics have problems even in more fundamendal things. Try to ask a mathematician to write down the π number. He will start writting the first digits 3.14159… and then stop. You will ask him “why did you stop?” and he will answer “I stopped because π has infinite digits and we do not know all of them. We have also proved that its infinite number of digits does not follow any repetition pattern. So we cannot write all of them”. But you are not satisfied…You want to know what π is.

The impressive thing about the above story, is that you will never get an answer and that mathematicians feel comfortable with that! Mathematics have named some numbers as “irrational” (“άρρητοι” in Greek), meaning that they cannot be expressed in writting since they have infinite digits that will never follow a pattern. One of these numbers is π. The square root of 2 is another example of irrational number.

Does that explanation is enough for the thinking human? No. When mathematics claim to be the most exact and well-founded scientific field, it sounds rather “basic stuff” to ask for a mathematitian to just write a number down on paper. But this is exactly what he/she cannot do! They say that we should be happy with the 1 billion digits we have calculated for π, but can we be happy when the “measurer” cannot measure?!?

This is more than just a good “trick” to play with. This shows an innate inability of mathematics to use its own language so as to just speak! And if we start with that, who knows what other inabilities we have overlooked?

E. Exact science does not understand reality

Exact sciences are a tool to formulate theories so as to explain what we see with our senses. Those scientific fields tell us nothing about what we call “reality”. Reality is what “exists”. We filter that reality via our eyes and ears and we then attempt to understand what that “world of our senses” is. Science provides models to describe physical phenomena – nothing more; nothing less. To engage into talking about reality based on science is simply a categorical mistake. (on the other hand religion accepts the reality of what we experience raw without any need to put it into the little boxes scientists build while formulating theories; that is why for example religion easily accepts the notion of free will while at the same time science has a really hard time even thinking about it in a universe full of equations regarding lifeless particles as part of the Standard Model)

SCIENCE                            RELIGION

Theory  <——–>  World of senses  <——–>  Reality

For example, things fall on the Earth. That is the reality. We sense that reality with our eyes and “see” apples fall onto the soil. We then try to explain what we see by formulating the theory of gravity. Many people think that since apples fall due to the theory of gravity and that since we see the apples, then the theory of gravity “exists”. That is not correct: when the theory of gravity is proven wrong and replaced by another theory (that is happening all the time with all scientific theories), apples will continue to fall! Our theory, our interpretation of what we sense, will have changed, but that would have no effect whatsoever to the thing we call “reality”. Another example is the invention of the transistor. The transistor works as the modern theories of physics say. However when all these theories are replaced by totally new ones, the transistor will continue to work…

The fact that reality continues to “work” has absolutely nothing to do with the fact that our models work or not. The former does not grant “validity” to the latter. At the point where science attempts to move from observation to general theoritical models, it enters the realm of uncertainty…

IV. Failures of Exact Science

Science like physics andchemistryhave failed to give explanations for many things we see in our everyday lives. Some of them include:

1. No scientific theory exists that requires ‘causality’ (i.e. that everything happening has a prior cause). As far as scientists are concerned, there could be things happening and their cause happening before them.

2. No scientific theory exists that requires ‘time flowing forward’ as we feel it happening. As far as scientists are concerned, the ‘arrow of time’ may as well be heading backwards. Some scientists today have attempted to explain that some scientific theories (like thermodynamics) really demand the arrow of time to go forward, but not with great success.

3. No scientific theory explains human goodness, human altruism. The theory of evolution – no matter how good it explains many things about species evolution – cannot explain why you may endanger your own life to rescue a complete stranger [see Evolution and Intelligent Design – The way to an agreement ].

These are just indicative examples and it must be noted that we do not examine here if science is correct or not in saying specific things. For example and as far as the point no.2 above is concerned, time could be one of our greatest illusions and science could be right in not finding evidence to support the “passing of time” (see Godel’s circular and timeless universe on that). However this does not matter to my argument.What is important here is the innate inability of science to give a definite “yer”-or-“no” answer to questions, an inability too evident to be ignored.

Last but not least, it is of paramount importance to note that the fields of exact science are indeed the best tools we have to understand the physical world. Scientists today have created really good models of nature that make predictions and can help us live better lives, work more productively, understand universe in much more detail than ever before. We must just be careful not to consider these tools perfect, while having an open mind to examine also other ways of searching for the truth. Sometimes living a better life stems out of things as simple (and thus difficult) as love and compassion, not out of having better Internet or faster cars.


V. Conclusions – Going Forward

We must use exact science carefully and always have in mind its limitations. Humans are more than electons and protons and this calls for the simultaneous use of other ways of thinkings – not only observation and induction. There are other ways that also help in searching for the truth. Believing in one thing only can be really dangerous. Believing that only the ‘scientific’ way os thinking exists can eliminate humanism, morality, altruism from the world. Many human values are not understandable by science. More philosphy and less ‘scientistism’ in todays society of gadgets will prove more than useful…

VI. Other interesting books

1. “The meaning and limits of exact science” (Sinn und Grenzen der exakten Wissenschaft), Max Planck.

2. “Nature and the Greeks”, Erwin Schroedinger.

3. “Philosophy – A graphic guide to the history of thinking”, Dave Robinson and Judy Groves.

4. ‘Tractatus Logico-Philosophicus’, Lugwig Wittgenstein.


  2. ‘Dissent Over Descent’, Steve Fuller.
  3. Dictionary of Philosophy, Dagobert D. Runes, 1942, New York.
  4. Eliminative Materialism, Stanford Encyclopedia of Philosophy
  5. Physicalism, Stanford Encyclopedia of Philosophy
  6. Materialism’s Slipping Hold on Science and Culture, Bruce Chapman, Seattle P-I, 1997
  7. Does Science Need Religion?, prof. Roger Trigg, Warwick University
  8. Mediocrity Principle [Wikipedia]
  9. Copernican Principle [Wikipedia]
  10. Hubble, The Observational Approach to Cosmology
  11. Quotes of dogma from “The Observational Approach to Cosmology”: (1), (2), (3)
    The Observational Approach to Cosmology, Edwin Hubble, 1937, p. 50, 51 & 58.
  12. Science or God?, John Polkinghorne, Editions Travlos, Athens, 1996, p. 138.
  13. Farewell to Reason, Paul K. Feyerabend, Editions Ekkremes, Athens, 2002, p. 261.
  15. Letter to Besso, cited by Carl Seelig, Albert Einstein, Zurich, 1954, p. 195.
  16. Great Feuds in Mathematics: Ten of the Liveliest Disputes Ever, Hal Hellman, Alexandreia publications, Athens, 2010.
  17. Consciousness and the End of Materialism: Seeking identity and harmony in a dark era, Spyridon Kakos, IFIASA, 2018

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  11. Jonatan Hägglund

    π… — I have a hard time differentiating the exact definition of digits with that of irrational numbers such as e, π, etc. They have an exact definition, expressed as a RELATION. The very nature of any model trying to describe reality is an approximation dealing with ideal values to some extent but, unlike mathematics, they are not a matter of mind games disconnected from the physical reality. Thus: dealing with ideal values has not the same impact on mathematics as with , e.g., physics, since the mathematical realm is an ideal one…

    1. Spiros Kakos

      Untitled — The notion of “infinite” is a basic notion for mathematics and the most problematic one…Infinite digits, infinite limits, infinite series, infinite sets all appear and are used in mathematics but their relation to “reality” (if such a thing actually exists) is something not very well formulated. Even though mathematitians have invented symbols to express it, that does not mean they have solved the question of “what it is”.One question that can be asked is: how can we even say that a number with infinite number of digits “exists” (even though we do not know what “exists” means, but that is another subject…), when the total number of particles in the Universe is about 10^70? How can we have a number of infinite number of digits when the whole universe does not have enough computational “capacity” to hold more than a certain number of digits if we used every particle as a bit of information?

  12. Brian Fraley

    Untitled — You bring an interesting perspective to the issue of science. I think it’s important for people to not be too arrogant or sure of what they believe. Scientific thinking can certainly lead to strong feelings about how things are. On the whole I think scientific thought has been successful. But also, I think a good scientist is an open minded one.

    1. Spiros Kakos

      Untitled — Thanks for the comments. I aggree with you that the true scientist is an open minded one and that it is of great importance to recognize the limits of our knowledge and capabilities.

  13. Andrew Marsh

    Irrational numbers — I have to say that I don’t understand your point about our inability to write irrationals as a terminating sequence of decimal digits. Pi can be defined perfectly in many different elegant ways. Geometrically, analytically etc. One can perform arithmetic operations on the number without any need to write it as a decimal. What is so special about decimal expansions?

    1. Spiros Kakos

      Untitled — Actually I do not know whether I have made my argument clear. What I intend to show with the article is that science (and a part of science is mathematics) is not the key to ultimate “knowledge” as some people believe. I do not claim to know anything more than anyone else, I just want to point out the main limitations of science and the underlying axioms it uses. So I agree that we should not be more confident for number 2 than number Pi, since they are both constructs. The construction of Pi is not something to argue with. I could also define a number called “Kakos” and noone would argue with me, since I am the one who defined it…However Pi and all irrational numbers (like the square root of 2) have an interesting property: even though it is well defined in many different ways, it cannot be calculated as a value. It is not the definition I am arguing about, it is the calculation of Pi that I find as an indication of our inherent inability to grasp reality with the tool called “mathematics”. You may define an infinite series of numbers and still be able to know that its sum is 5. You may define many mathematical constructs and then calculate them. But what if you define a construct and then you are not able to calculate it? What would that mean about our ability to understand reality? It is not a number that was imposed on us by some aliens, it is a number that as you said was constructed by us. And still, we can’t tell where it stands on the line of numbers.As far as infinity is concerned, it is true that using the notion of infinity you can reach conclusions that seem correct. And indeed Newton and Leibnitz used infinity (note: with the term “infinity” I refer to the infinately small terms ‘dt’ or ‘dx’ used in the Infinitesimal calculus). However even they were not so enthusiastic of that notion…To start from the beginning, Democritus in ancient Greece talked about atoms and infinitely small “things” in space, time and geometry. However the paradoxes of Zenon made the use of infinity problematic and not all Greek mathematicians accepted that term. Euclid defined a point as “something with a position but with no size” in an attempt to exclude the notion of infinity from his works (infinity is not mentioned in his Elements). Aristotle excluded the term of “infinately small or big” from all geometry. Archimedes used the notion of “infinity” for his theorems in his work “The Quadrature of the Parabola”, but then – since he did not accept the existence of such a term – he presented his results/proofs by using the method of exchaustion (that is, with the notion of “limit” and not the notion of “infinity”). That method is similar to the method of (ε, δ).The one who insisted on using the term of “infinity” in mathematics was cardinal Nicolas de Cusa, because he thought that infinity was “the source, the medium and the ultimate purpose of every knowledge”.Leibnitz did not claim that infinity “existed” (as you say, it is a construct of human), only that it can lead us to correct results as if it existed…Neweton, even though he used infinity to reach his results, he then presented them in a completely Eucledian and finite way…Bishop Berkeley (it is astounding how many people of the church use to do mathematics, despite many people believing that there is a “war” between science and religion) in his work “The Analyst” made an excellent criticism on the notion of “infinity” that was never refuted by mathematicians of his time. Moreover and in the 19th century, Weierstrass also proved that we can use the notion of limit without having to use “infinity” at all (something like the method of exchaustion of Archimedes).Now, we ofcourse use both. Like Pi, infinity is still in the game but noone has ever concluded to whether that “thing” is related to something in what we call “reality” (see the Platonic Ideas World) or not. My point is just that we should not trust blindly science to lead us towards “reality”, since not even mathematicians (the most clear-cut and theoritic scientists of all) have a clue on what the tools they use for thousands of years really “are”…

    2. Andrew Marsh

      Untitled — I’m afraid that I still don’t understand your arguement. Why should we be any more confident about the existence of the number 2 than the number pi? Or the square root of two? They are both mathematical constructs that are extremely useful in modelling reality. Is there something in the construction of pi that you object to? “What is more interesting is that everything that can be done in mathematics with the use of the notion of infinity can be done without it also!” This is a very bold statement that I find extremely hard to believe. Would you like to expand on this?”In the same way, number Pi (π) is consisted of an infinite number of digits.” Only if the expandsion of a number as a convergent series of powers of 10 is for some reason a definition of that number. Pi can be defined as the ratio between the circumference and the diameter of a circle. We can use this definition in many useful ways without ever needing to use decimal expansions.

    3. Spiros Kakos

      Untitled — The science of mathematics is the science of expressing numbers and finding relations between them. In that context, everything that is connected with the notion of infinity is problematic (e.g. π has an infinite number of digits). Infinity is the limit of our knowledge – not the knowledge of today but of the knowledge we will have at any point in time ever. You may say that (lim(x) with x increasing is infinity), but that would mean that you have actually named that limit “infinity” (the same way you could name it “Maria”) and called it quits, without actually KNOWING anything about that “limit”. Naming the things you don’t know “infinity” does not mean that you actually “know” them…What is more interesting is that everything that can be done in mathematics with the use of the notion of infinity can be done without it also! “Infinity” is a man-made theoritical structure. And it actually contradicts reality in many ways.Take for example the notion of a “straight line”. Some mathematicians (not all) postulate that a line like that is constructed by an infinite number of points. But if we start to “cut” the line into an infinite number of small pieces, then we will end up with pieces that have zero length (that is the “limit” in our case). So is a line consisted of a sum of “nothings”?In the same way, number Pi (π) is consisted of an infinite number of digits. However we don’t have even a clue about where the “limit” of that infinite line of digits will be. We cannot say π is between 3.14 and 3.15, since that would mean that we simply ignore the fact that the next decimal digit signals us to search the limit between 3.140 and 3.142 and so on. If you want to fool yourself you can do that pretty easily. But if you are a real mathematician, you will try to find the place where that number will “settle in”. And you will never can.In that way, we may use number Pi as a monkey uses a computer to press a button and get a banana for reward. The monkey does not know anything about how the computer works. Neither do we know anything about Pi…PS. You can easily construct a triangle with a hypotenuse equal to the square root of 2. However that number is irrational. In that way we are confronted with one of the major problems in philosophy: irrational numbers can and do exist in reality (e.g. on the piece of paper were we have drawn the triangle) but not in theory! Rather metaphysical I would say…PS2. Expressing something you cannot understand in many different ways does not mean that you understand it. Expressing π as an infinite series of numbers for example, simply transposes the problem you have from “define Pi” to “tell me the limit of that series of numbers”. Two ways to say the same thing: I cannot spell Pi.

  14. Burçin Danacı

    Untitled — I agree with some of the things you wrote. There might be more than one explanation for an observed phenomena, but when one of them is accepted by the majority, nobody doubts it again. Scientists should be sceptic. But I don’t think religous beliefs can help us with that. You can take the existence of God for granted, you don’t have to question it. But this doesn’t apply to sciences like physics and biology. A scientific explanation should be questionable, otherwise it will turn into another dogma, like the ones you have rightfully criticized.

    1. Spiros Kakos

      Untitled — Thanks for the comment. I mostly agree with you. I did not actually intented to place religion beliefs into play as a solution/answer to the limitations of science. Religion beliefs are a very big issue indeed and I try to analyze them in my “Religional Science” knol. Thanks again!

  15. Claes Johnson

    Untitled — Dear Spiros:I agree: A coordinated choir is propagating the message that reductionist physics/mathematics is a model for all of science. But this song does not contain complexity and thus misses the essenceof scientific modeling of reality. It is not enough to stare at an elementary particle to understand the world. My main goal is to open to a synthesis of physics and soft science based on computation simulating the complex interaction of many agents.Current physics seems to be a catastrophy from scientific point of view, completely removed from any rationale and reality. Maybe this is the prize for putting religion in the wardrobe?Best regards,Claes

    1. Spiros Kakos

      Untitled — Hello and thanks for the comment! I have read some of your work and it seems really interesting and of high-quality. The limitations of science exist, but I do not actually relate them to religion. I believe that science and religion touch two very different fields of knowledge (see my “Religional Science” knol for more on that). Indeed modern science has been encapsulated and trapped into specific models of the cosmos and into specific ways of thinking. The bad news is that there seems no possible way out – at least at this point.

  16. Mee Mee

    Thoughts / Reflections — “Things like moral, emotions, aesthetics and love cannot be measured, even though they are very important for human life. Science fields like physics, mathematics and chemistry simply cannot deal with these things.”I believe that morality, emotions and aesthetics can be measured, but not in a general way (i.e., all humans have the exact same experience of morality, emotions, etc.). For example, if chemistry does not provide us with a means for understanding emotions or moods, how can antidepressants possibly work? Is this a hoax? If so, then the pharmaceutical industry is bound to eventually colapse, right?I think the only failure of science has to do with constraints or costs. Some things are too costly for people to measure exactly. It’s to expensive to develop technology to measure things like tables exactly. However, when you look at the sciences in which people have a need for things to measured exactly (there is some economical benefit) usually humans progress towards better and better means for measurement until the return for such development tapers off (think of a growth function).When you consider the economics of science, you then come to find that perhaps there are definite answers to questions, it just becomes a matter of whether humans will ever need these answers in order to continue to exist in our ever changing environment.

    1. Spiros Kakos

      Untitled — The prediction that he will “want” to dring watter means exactly that: that he WILL WANT to dring water. If what you say happens, then no determinism applies to that mans decisions.

    2. Mee Mee

      Untitled — Free will is agency. Determinism is simply the idea that things can be determined; we can predict certain things to a degree of accuracy. I believe that these two ideas, determinism and agency, are not mutually exclusive. For example, perhaps we determine that a man will become thirsty and want to drink water after he has exercised and not drunk any water for some time. The man might hear us discuss this, and perhaps he is rebelious and decides that he does not want to drink the water and thus not provide us evidence that will help us test our drinking water model. In this situation, both a determinism and agency exist. So my response to the statement: “‘If you have everything represented with specific mathematical functions for example, then there is no room for what we call “Free Will”.’ is that it is not correct because based on the definition of determinism and agency (or free will) the two are not required to be mutually exclusive (and they are not required to be mutally inclusive).

    3. Spiros Kakos

      Untitled — I find it a good exercise to try to find which philosophical dogmas lie behind every opinion I express. I have some philosophical views in which I believe and so do you. The representation of everything related to human mind with mathematics is based on the philosophical assumption that the human mind is something that deterministically obeys physical laws. If you have everything represented with specific mathematical functions for example (is that what you mean by the way?), then there is no room for what we call “Free Will”. Everything is pre-determined by these “mathematical representations” and we can make any predictions we like for the future emotions of every human. Is my thinking correct or not?

    4. Mee Mee

      Untitled — Well, I think you brought up a very good point when you said we have to agree about certain terms we use in our discussion to help us understand each other better. I think maybe instead of taking a stance as to whether there are inherent limitations to science or not, it will be much easier and more interesting (pleasing) for us to approach this discussion by looking at specific arguments you have made in your post and then discussing what appears to be true and what might be questionable or a point of disagreement.OK, so one thing I notice you say is this:”3. No scientific theory explains human goodnes, human altruism. The theory of evolution – no matter how good it explains many things about species evolution – cannot explain why you may endanger your own life to resque a complete stranger”Well, I think that it is very hard for humans to intuitively come up with a reasonable theory because humans have many characteristics unlike other species. Humans are very successful in a range of environments and so to make a statement about humans in general is very difficult. We are diverse. However, I did find an interesting study done on a specific species of wasps: think the problem is that this question is very hard (expensive, technically complex) to test for humans, even if such studies were made longitudinal. There have been some theories and attempts at empirical testing: Hamilton’s Rule has been tested (I think it was a Hamilton and Axelrod paper) and Game Theory presents the idea “Tit for tat.” Maybe the explanation is that confidence in oneself serves specific function and that this confidence just happens to result in risking one’s life for others. Afterall, isn’t a man in a uniform attractive? Even if he risks his life for his nation… I will read your other post on Creationism in a bit.Ok, I will also discuss human thought and consiousness a little bit. I think that it is possible for people to have very, very similar experiences and to be able to measure the similarity. This can be done by understanding much of the physical components to an emotional state. I read a bit on wikipedia about the physiology of anger: think that two people with very similar physiological states would both be feeling similar feelings. (I would not call these feelings identical, just similar enough that “anger” or “sadness” was a word that was general enough to represent both people’s feelings.) This is a hypothesis I would make based on the few studies I have read. I would need to have knowledge of how to use technology and knowledge of how to interpret the data derived from this technology in order to test this hypothesis with specific studies. However, I think studies of this nature can be done.Hm, when I say: “I would not call these feelings identical, just similar enough that “anger” or “sadness” was a word that was general enough to represent both people’s feelings.” what I am talking about is the level of generality. (This appears to be a very important concept, though I have only heard of it once in a discussion group that I irregularly attended, so I cannot speak expertly, though I think I have a good intuition about it.) Using one expression of an addition alone is a very rough way to describe an idea. Using “1+1=2” is very, very general. It easily speaks to a large number of people. However, perhaps there is an expression in complex analysis that is, well, complex. This type of expression may speak to a large number of people AND it seems highly likely that this number is quite a bit smaller than the number of people who comprehend “1+1=2.”I think the same level of generality applies to conciousness. I am having a really hard time explaining my idea, so I will give you an example of how simple mathematics are useful in expressing complex emotion. The emotion I choose in this example is “wonder.”When I listen to Mozart ( ; Requiem) I feel a very large amount of wonder and passion. There are 46,378 views for this Youtube post. Only 7 hours earlier, user ‘number999999999’ responded to Requiem, calling it “wonderful…”Mozart expressed this emotion called “wonderful…” in a cryptic language known to the layperson as “sheet music.” ^_^. In addition, there are codes and precise measurements that were used to support the operation of my computer, the internet, Youtube, etc. Many simple mathematical representations were used in the construction of all these man-made artifacts; and when combined in a very specific manner, result in an expression which inspires the feeling of wonder to millions.So, the ways with which we describe human emotions can, in some sense, be described mathematically. There are differences in the how this emotion will be expressed. Some people will listen to it loudly,…

    5. Mee Mee

      Untitled — others quietly. The invariant aspects of this expression, though, are what copyright lawyers are interested in. And this is what I am interested in too.Exactly how much can we reproduce? If we want, how similar can we make one experience as good as another? And will this reproduction be economically feasible? Will it be cost-effective? Because if it is, then it is just a matter of time before we can make better and better copies of things we want copied. And, if my theory that “people with very similar physiological states would both be feeling similar feelings” is accurate AND we humans are able to reproduce physical things with greater and greater accuracy, then it is likely that people will be capable of having increasingly similar experiences.

    6. Spiros Kakos

      Untitled — Hi Maria. Thanks for the reply once again! Your comments are valuable and help me clarify some things. One point I must clarify is that I refer to the “Exact Sciences” in general and not to some specific scientific community and not to other scientific fields (e.g. law, sociology etc). In order to find our way out, we should agree on which are the characteristics of EXACT sciences in general, without being limited by any specific scientific community or sector of exact science.For me, I have pinpointed some major / essential characteristics of exact sciences to be:1. Measurement.2. Experiment.3. Induction logic.These are the things I refer to in the Knol and analyze their limitations.Now I cannot tell whether you disagree with these specific limitations I mention, or if you think that there is no such distinction between “Exact sciences” and “Other sciences” (e.g. that psychology will some day manage to measure everything as physics does). Is that the case?If yes, I must say that you will have a point when practice proves me wrong. Because until now no scientist in human sciences (“non-exact sciences”) has managed to create resonable models that incorporate measurements as in physics or astronomy. Until now we have no idea how to mark an emotion as +2 or as -1,92. If we do, it will be because we ourselfs created a model that includes such numbers. But every model which refers to human thinking and/or emotions is bound to intefrere with the very essense of our existence: you cannot measure anger as a number because you cannot tell what is happening inside the human brain. You may now say that we may know in the future, but that is hardly an argument in favour of you: when we do know we can have another discussion. But now the fact is that these things cannot be measured.Human thought and consiousness are things that seem to be subjective and very personal to each and every one of us. Modeling thought with mathematical models implies that if someone else reads these models will understand the thought of another person, as someone understands the “1+1 = 2”. But this cannot be true. Even if I tell you “My anger is now +2”, you will not have understood what I think and how angry I am. You will not have access to how my consiousness conceives that anger, how I REALLY feel inside. Again you may say that “someday we will have the tools to know”. Then I would ask what data do you have so that you are so sure that it is a matter of current limitations of science and not of inherent limitations of science? And I would also assure you that when that day comes I will gladly change my view and admit that I was wrong. But right now the facts tell me otherwise.I do not know if what I said was useful. Waiting for your feedback…

    7. Mee Mee

      Untitled — Ok, you may think that the construct of electric voltage is different from the construct of an emotion (such as anger), however I cannot tell exactly how this affects your argument.Your conclusion doesn’t seem to be stated accurately. I would say that the correct conclusion from my comment would be “the scientific community may feel more confident in their measurement of some constructs than others.” I think that further conclusions require the expertise of a researcher in the social sciences or some type of psychiatric studies. There are models for how people think that make use of some precise tools of measurement. Based on my experience I would say that the accuracy and scope of these tools has less to do with inherent measureability of the question, but the development of the constructs and technology used to measure them.I think your conclusion: “our science – as it now exists – has limitations still applies.” Is still too vague. If you differentiate between science (the theory and methods used) and the knowledge of the scientific community you will have an accurate conclusion. It is just linguistics.For example, I may decide that perfection in running means a living creature can run 75 miles per hour. I live in the U.S. and I may never see this occur. It is possible for me to become frustrated and state that there are limitations to running in general because I have not seen anything living run 75 miles per hour. However, cheetas are reported to run 75 miles per hour in Africa. In this example, the physical construction of the cheeta meets conditions which allow it to run according to my ideals for perfect running. The living things in the U.S. have not. Just because some living creatures meet conditions which allow it to perform to my ideals and others do not does not mean that there are limitations to running in general. It simply means that there are principles which determine the performance of running.Similarly, there may be principles which determine the performance of any scientific community. Some scientists may perform more according to ideals, some may not. This does not necessarily make any statement about the process of SCIENCE, rather it makes a statement about the conditions which affect performance in SCIENTIFIC ENDEAVORS.I have worked hard to make my ideas clear in this post, I hope they are intriguing and clear.

    8. Spiros Kakos

      Untitled — If we follow what you say, then even things science measures are constructs created by the human mind and we cannot even be sure about them. Why is the voltage 0,2V and not 0,21V? Because we have constructed a theory of electricity and we have defined 1V as something very specific based on other specific definitions and assumptions. So the “applied” part could be an idea in our minds.However there is a basic difference between the “vaguety” of electricity voltage definition and that of anger or emotions. The difference is that our measurements of electricity can be applied and be used in everyday life, but no theory which entails measurement of emotions can be used in any specifically useful way in our lifes (to make predictions for example).So finally you could say that there things “more measurable” than other”, or that “some things are measurable as part of a prediction model, while others are not”. Either way, the conslusion that our science – as it now exists – has limitations still applies.

    9. Mee Mee

      Untitled — Measuring anger is just a question of construct. You can measure things associated with the construct of anger. But the problem is that people mentally associate anger with many things which others do not agree with. For example, one person may think that shouting is a sign of anger, while another person believes that shouting in a certain tone IS by definition anger. Somethings we “cannot” measure are simply unmeasurable because the construction of them is vague. This has less to do with science limits and more to do with human limits concerning linguistics. Science in itself is theoretical, measuring is applied science and it is not a sure thing whether limits in applications of science are due to failures of science itself or mistakes people may make simply because they are human.

    10. Spiros Kakos

      Untitled — I do not agree with your reasoning. Cost is not the limit of science. Science has its own inherent limits and it cannot possibly deal with non-measurable things. You cannot say that “anger in this person is 5.2” like you measure a circle’s diameter. I cannot understand what you mean by that “general way” you mention. Maybe you can elaborate.The understanding of chemistry reactions in the brain do provide information about exactly that: the chemistry of the brain. We cannot claim that we understand anything more than that. And I really cannot tell you what this chemistry means since we are not even close in understanding the real mechanisms of the brain. Perhaps that chemistry only deals with the results of our emotions or thoughts – so dealing with it is just dealing with the effects and not the real cause.

  17. James S. Kim

    It is obvious that orientalism expnands a cope of science — Although original science has been developed in Europe, oriental-ism including the China culture is now expanding and applying to the development of advanced science. Note that the China culture has been revealed to be conceptually similar with the ancient Greek culture, where religion and scientia (originality of science) are integrated. Oriental culture is more adaptive to participate in religious science research than western culture, which relatively more relies on newtonian science. For example, as indicated in this article western modern science is mostly based on dualism initiated by Descartes while oriental philosophy such as ‘Tao’ is more natural oriented. One of examples for oriental culture based science research is new age science, which has been emerged from the late of 1960. What do you think?

    1. Spiros Kakos

      Untitled — Every thinker that thinks outside of the as-is frame of thinking adds something to the scope of science. In that way I agree that countries which have different way of thinking than the old-good- “Western” way of thinking indeed add something. Oriental countries for a long time held different school of thought, although I admit I am not very aware of all the details. Do you have any good related links? I would like very much to add some of these ideas to my knowledge.

    2. James S. Kim

      Untitled — Originally, I meant China but any oriental countries such as Japan and Korea can be an example. Moreover, ancient Greek can be an example as we know from famous Greek and Roman myths. What do you think?

    3. Spiros Kakos

      Untitled — So you mean that oriental-based science is increasing the scope of science? By “oriental” you refer to which countries exactly? Maybe Islam?

    4. James S. Kim

      Untitled — ‘cope’ is my typo and it should be ‘scope’. However, scope of science is still not very good terms to represent the correct meaning in my thought so I changed my original text a little for reader’s clarification. Thank you. -James

    5. Spiros Kakos

      Untitled — I am sorry but I cannot clearly understand what you say. What do you mean by “cope of science”? Maybe it is my English, sorry about that. :(Do you mean that East-based science is beginning to play a major role?

  18. James S. Kim

    Does ‘exact’ science represent either ‘deterministic’ or ‘newtonian’ science? — It seems that exact science represents perfect science, which is interested in only single perfect result. Although the meaning of ‘exact’ is similar to ‘deterministic’, I recommend to consider the use of ‘deterministic’ because ‘exact’ requires too tightness and can make readers confusion. One of references in this area is famous book ‘the tao of physics’ which is written by famous physicist ‘Fritjof Capra’. -James

    1. Spiros Kakos

      Untitled — Thanks for the info James! Indeed a lot of confusion can be created by using the right words.And indeed modern science is based on determinism. I used the term “exact science” as I found it used by Max Planck in his work “Meaning and Limits of Exact Science” (Sinn und Grenzen der exakten Wissenschaft). I will try to find that book you mention and get back to you with more on that.

  19. James S. Kim

    What is ‘Religious Science’? — Religious science can have two different meanings. One is an imagination and traditionally empirical based research without every proofs and another is related to the fact that the amount of fundamental science knowledge is too huge to be treated by individual human brains (or minds). Creativity is the most important for the former definition while reliability is the most important for the later definition. What do you think?-James

    1. Spiros Kakos

      Untitled — It all depends to what characteristics you think religious thinking has. For me, belief in some metaphysical ideas religion postulates can and is based on logic and evidence. Take for example the anthropic principle argument, which is based on so many data of the universe being well fine-tuned for life.

  20. Nadia Amin

    Untitled — I recently came across your Knol and have been reading along. I thought I would leave my first comment. I don’t know what to say except that I have enjoyed reading. Nice Knol. I will keep visiting this Knol very often.

    1. Spiros Kakos

      Untitled — Thanks Nadia. Much appreciate your comment. You can visit my other knols as well if you wish. Any new comments or suggestions are always welcomed.

  21. Kenneth Chua

    Religious bias — I can’t help but think you have a religious bias in your knols. “Believing that only the ‘scientific’ way os thinking exists can eliminate humanism, morality, altruism from the world.” – a common religious argument against atheism that is completely false. We don’t need a God to tell us how to behave. There are secular moral systems, you know? []Also, you made a diagram putting religion between the “world of the senses” and “reality”. And you never explain what religion has to do with any of it. If anything, religion likely takes you further from reality since it is based in faith instead of reason.Mathematics: it was long ago accepted that mathematics has to be based on unprovable axioms. This is nothing special and has no bearing on science.Materialism as dogma: yes, it is a dogma, just like everything else if you use the word “dogma” like that. Nothing can be known for certain, therefore every idea is a dogma. The statement that materialism is a dogma only serves to discredit it, and doesn’t say anything of actual substance. Also, how can you criticize dogmas when in the next breath you promote religion?

    1. Kenneth Chua

      Untitled — I don’t think Logic is based on religion, so that one’s okay.I would say evolution is what created morality in babies, not God.

    2. Spiros Kakos

      Untitled — If the theories of Aristotle are flawed to your eyes, maybe stop using Logic…Concerning ethics: Who gave those babies the sense of moral? 🙂 They came by “chance” to their brain?

    3. Kenneth Chua

      Untitled — Aristotle: Yes, many of the ancient philosophers were religious and based their philosophies on religion, which is why their philosophies are flawed to atheists.Secular ethics: I suppose you’d rather I believe in your moral system because it came from an ancient book claiming to be the word of God? Sorry, I’m not convinced by that. Secular ethics are based on reason and moral intuition. Did you know babies have moral instincts? – they don’t need to know God’s word to understand morality. []Faith: Maybe I will look over your other knols and leave comments there as well.

    4. Spiros Kakos

      Untitled — The religious bias you think I have also applies to Aristotle who founded Logic? Because he also had formulated some arguments in favour of a First Cause in the world… Does it apply to Godel as well? Please refer to my arguments. You say there are secular moral systems. Very nice. What do these systems say? You “have” to do that because what? Where are they based? Can you convince me with a secular (a word which is really weird, are the 70% of Europeans who believe in a God “not secular”?) moral system? If yes, how can you do that? Please give me the relevant equation…Concerning dogmatism, you feel so cool in accepting that mathematics “have” to use unproved axioms (you mean *have* because a secular system of thought says so?)… That’s very good for you. Maybe I can use you as a reference for proof of what I write…Concerning religion and faith, I have written many things in the “Religion and Science unification” knol. Eagerly waiting for your comments there. In summary, faith is not the same as being a fool. Someone can believe that something happens based on evidence as well. And there are many good arguments in favour of the existence of a God, the best ones provided my mathematics…

  22. Robert Steadman

    Science is only one side of the coin: — You claim in the header that “Science is only one side of the coin”So what would the other side of the coin be? I am not trying to be deliberatley annoying or petty by asking this, but I would really like to know if you have something as concrete as science on the other side of the coin.

    1. Robert Steadman

      Untitled — Well, the truth is, IF there is another side of the coin, we don’t know what it is, therefore we can’t say with any certainty that there is NO science in it. As Einstein said: “The miracle in the universe is that there are no miracles.” Of course there are things that we don’t understand… but to assume they are beyond comprehension or measurement seems premature. Until we KNOW what it is we are dealing with, we can’t call it GOD, we can’t call it scienceless, we can’t call it more essential, we can’t call it more powerful. I think we should reserve judgement until we have exhausted all scientific avenues. In the past there have been several things that we thought would be impossible to understand; yet, with time and persistance we have conquered these things with an entirely scientific understanding.Science never employs the fallacy of: “If it isn’t A, then it is most certainly B.” Tests are done until it is discovered to be B. Over and over again. Now, I know you are of the opinion that there are some things that Science CAN NOT explain. So I guess the biggest difference between you can I are that I say, there are things that science can NOT explain YET.

    2. Spiros Kakos

      Untitled — Thanks for the comment. The point is that science is indeed a very good tool. I have pinpointed that in my articles in Google Knol. However science cannot deal with everything: morality, love, emotions, trust, human relations and other similar things are beyond its scope (surely I hope you do not wait for an experiment to see if you should love your wife). So I understand that THERE IS another side of the coin with NO SCIENCE in it. There I “see” human ways of thinking that are related to intuition, fantasy, creativity, love etc. Things that are not as “concrete” as science, but more essential and powerful than science. What do you think?

  23. Kalle Schwarz

    science and life — if you can feel (yourself) you have a soul . if you can think symbolic, you have a spirit .scientists could not tell you, what feeling and thinking is . they masure only the shadows of the reality, because their instruments can not feel and think .you surely know plato’s cave parable . science only see the shadows . a dog, though it is not human, lives more in reality than a scientist .

    1. Kalle Schwarz

      Untitled — do you mean your comment on Harmonia Philosophica ?for me time is the first dimension of the world (whereas “world” is a construction of the mind) in the sense that dimension means direction .so, if time is the first direction, it cannot have a second direction . it’s one-directional or one-dimensional .science cannot mesure real time . real time is now . science can mesure an abstraction of time (the shadow of time) . it can mesure duration or length . but length is a dimension of the room .so you have the explanation, why physicists are speaking about a 4-dimensional universe where you can go back and forth in time . you can’t .

    2. Spiros Kakos

      Untitled — I agree. And would very much like your opinion on the “time” issue I just added. It is a “dogma” which I feel that affects our lifes fundamendaly.

  24. George Shollenberger

    Atheism Is Not a Science — As the author of “The First Scientific Proog of God”, I connected God to our finite world with authentic and rational thinking. So atheism is bad for all nations. In my October 2010 bloggings, I explain the eternity of God. I also show the Godhead unfolds those attributes of God that define the Intelligent Design of ourlower finite world. Thus, a completed science is not possible. See my work at George Shollenberger

    1. George Shollenberger

      Untitled — Hi Spiros.The blog that you saw began as a teaching website of my self-publiched book by AuthorHouse. Over four years have passed and I am still going forward ay age 81. My work is connected to Plato, Plato’s Parmenides, Anaxagoras, and your country. I am interested in your country because I concluded that, when Jesus Christ sought to learn as a young person, he went to Greece. In the Bible, the minds of St. John and St. Paul are Greek thoughts. Although many atheists, the good math/bad math website, and bloggers of the scienceblogs website challenged me for the first two years. They did not win anything. But they haven’s been around for two years. George

    2. Spiros Kakos

      Untitled — Thanks George. This is a quite interesting blog you have there!

  25. George Shollenberger

    Science and Theology Are Being Unified — In 500 B.C., the ancient Greek, Anaxagoras, said, ‘EACH THING IS IN EACH THING.’ In the 15th century, in the book ‘On Learned Ignorncee,’ Nicholas of Cusa repeated this statement in Bk, II, Ch. 5. On 9/4/10, I explain this statement on a blog at This statement is saying that a single world exists. This world has a higher world, where God is, and a lower world, where created things are. On 10/4/10, I present a related blog that shows how the higher and lower worlds can be unified. Since these higher and lower worlds are unified with coexisting opposites, this single world can never be known completely. So, the exact science of this single world will never be found.George Shollenberger

    1. George Shollenberger

      Untitled — Yes, there are many inconsistences among scientists on the same theory. I have opened a new knol on ‘theological science.’ at . The unity of theology and science will turn God and the Universe into ‘One World.’

    2. Spiros Kakos

      Untitled — Interesting theory. I also state something similar in my Harmonia Philosophica blog at Indeed the world seems to be “ONE”. Our many interpretations are merely the product of our different point of views on the same thing.

  26. George Shollenberger

    Connecting Our Work — Recently, I finally connected our work through Google. I connected your work to my knol work at and connected your knol worko also to my blogspot wotk at http://georgeshollenberger.blogspot/com/ . I have lots of respet for all of your knol wor. George

    1. Spiros Kakos

      Untitled — Thanks for the comment. I find your Blog rather interesting I might say! You can also check my blog at (it is bi-lingual, so just skip the Greek posts). I post there Philosophy Wires, commenting world news through philosophy. Let me know if you find them interesting.

  27. George Shollenberger

    Your World News on Blogspot — Your world news is very interesting.Deegeneration of DNA might be real. I say this because Nicholas of Cusa, a German of the 15th century, found that God is absolute maximum and absolute minimum. So, if one is working on the path of the infinitely large, one is on the way to God. And, if one is working on the path of the infinitely small, one is also on the way to God. Thus, the apples might have been the best earlier. I do believe in reincarnation. There, one might be refreshed with better apple. George

    1. George Shollenberger

      Untitled — On indivisible things, I am using the work of Nicholas of Cusa, who discovered that God is absolute maximum and absolute minimum. Galileo recognized these indivisibles when he was studying the extension of bodies, which always form wholes and have an infinite number of parts. Thus, each body in the universe (human, orange, apple, etc.) has an indivisible thing called a soul, or fundamental principle. In Ch . 6 of Matthew, Jesus Christ teaches us to talk and ask questions to God in order to receive help if the whole of a body is sick. The talk and questions to God might help sick nations such as Egypt, or help sick oranges or apples in some nations. George

    2. George Shollenberger

      Untitled — Anselm can be credired with identifying God as the greatest thing. He thus brought God into the region of ‘absolute” concepts. But when Nicholas studied Anselm, he found that the grearest thing cannot be less. So Cusa separated all absolutes from those things thar exist in a different region of things thar are ‘more or less.’ These things are calledl variables. In Cusa’s work, the world of absolutes are precisely separated from the world of variables. So, Heraclitus was right about the universe but was wrong about God and the region of unchanging absolutes. In God, I say that these absolures are attributes of God and connect God to the universe logically.The untimate minimum, which I call indivisibles, were developed by Cusa, Galileo, and Gottfried Leibniz. Leibnic called them monads in his book on Monadology. Leibniz thought that his monads were used by Greeks, who spoke of them enteles. I use indivisibles and call them ‘spiritual atoms.’ .

    3. Spiros Kakos

      Untitled — Thanks George. What you say is interesting, I never thought God as the ultimate minimum. But it is true that God is actually the idea behind all infinites (minimum included). If something is an apple and then turns into an organge, then maybe it was never an apple and it was never an orange – the most probable is that it is something else which can simply turn into an apple or an orange…

  28. Anonymous

    before science there was science — I read a good article–which I forget where I filed it–which explains how science didn’t begin with Galileo, but indigenous people were also scientific also.I am not a ‘scientist’ yet I employ some of the methods said to be of ‘science’. It is a natural human inclination.Now what I find sadly amusing is that scientists will NOT apply science as Spiros means here to the study of the religion from whence, what is known as modern science, emerged from! May be they are too busy with their specialization of the electron, or whatever I dont know, but surely you have to look at the bigger picture. And at the ROOTS.If they did look around they would see patterns–correlatations. For example, the ‘God’ of the Bible is a brutal war god. He is a ‘jealous god’ and would not tolerate the more ancient worship of the Goddess (yip. I said GODDESS!), and that this is evidenced both in the text of the biblical script and archaeological evidence. Why is this important?Well the whole story of the Goddess is immensely different from the patriarchal propaganda which was used to denigrate her. For with the ‘God’ story ‘he’ ,’spirit’, separates himself from nature, and in the ‘creation story’ blames Eve for the ‘fall’ of nature. Whereas the story of the Goddess was here spiritual immanence in matter. NOT as ‘spirit’ superior TO ‘matter’, but that matter being her body was spiritual and matter at the same time. (it is Plato that tried to argue the superiority of ‘spirit’ in ‘lowly matter’)Also they would find that in this myth is a very powerful taboo–and that is even the knowledge of entheogenic inspiration is forbidden which is what the Garden of Eden tale is all about! What can entheogenic inspiration encourage? Seeing and feeling and experiencing reality fundamentally differently! So what does that old myth and this current one share?Propaganda which denigrates nature, war mongering, and the war on entheogens!!Now WHY wouldn’t scientists think that this exploring of this old myth important? But you see many who dont are blind themselves to being devotees to the myth of scientism! YET if you could just convince them that if they took time to explore the old myth the present one they are cultists in will becomes more understandable. But doing so would just get abuse. Believe me I have plenty experience of this. You are held in contempt for speaking these things. Yet some of them will argue for ever the tired cliched ‘atheist’ verses ‘theist’ trip—but safely within the box of that inquiry! To explore reality you have to explore reality…

    1. Anonymous

      Untitled — Thankyou Spiros, I will think about it. Please let me link you to my recent blog post The Myth of Mental Illness and The War on Entheogens

    2. Spiros Kakos

      Untitled — You are very correct when saying that we have to go back to the roots. I understand you have comprehensive knowledge of some science history matters. Why don’t you write a Knol on the matter?

  29. P V Ariel

    Very informative piece — This knol is a very informative one. I posted one knol under the title “Do Plants too have sensitivity?” I invite you to co-author on this subject to the following link: Do Plants Have Sensitivity? A Pumpkin Mourned a Death and Similar Other Incidents Says YES:(An Open Knol to Share Your Views and Suggestions) [Internet]. Version 2. Knol. 2009 Oct 18. Available from: Do believe that a science writer like you can show some light on these incidents. hope you do something about it. Thanks

    1. P V Ariel

      Untitled — George, The link is not connecting the page instead its taking to blogsot pl. checkthanks for your response.Phil

    2. George Shollenberger

      Untitled — You need ‘Leibniz’:Philosophical Writing’s’ by G.H.R. Parkinson.It is available from chapter in phlosophy is called ”Monadology ‘(dated ,1714 ) His monads can be connected to the indivisibles of Nicholas of Cusa.Galileo’s work on the extension of bodies led him to say that all bodies are wholes and are formed by an infinite numnbr of indivisible parts. Leibniz’s true atoms are indivisibles. Nothing enters or leaves them. This is why they must perveive. These indicisibles form all the divisibles of the universe. Every indivisible is ‘in’ every other indivisible. So all indicisibles are functionally related.George Shollenberger is at at

    3. Spiros Kakos

      Untitled — Have not heard of that before. Sound interesting. How does he defend the case that “atoms perceive”?

    4. George Shollenberger

      Untitled — If you look at Leibniz’s Monadology, you will find the true atoms of the universe. These atoms are also spoken of as indivisibles, which form all divisibles. When doing studies on bodies, Galileo found that all bodies have an infinite number of indivisible parts. Now, Leibniz says that all true atoms can perceive. But he also says that the perception of some true atoms, like steel, are confused. If the confused ones form all nonliving things, then the unconfused things must be living things. Sinc plants are living things, Leibniz would say that plants have sensitivity because their perceptions are not confused.George Shollenberger at

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