Logical Positivism and the IPCC: 'The Best-Laid Schemes...'

There has never been a scientific scam in the history of mankind as big as the science swindle of "climate change." Nothing comes close. Modern scientific hustles like mesmerism, phrenology, eugenics, the Piltdown man, and even Lysenkoism, pale in comparison to the flimflam of anthropomorphic global warming (AGW).

There was, however, one astonishing episode in the early part of the 20th century in mathematics and logic which conceptually roughly parallels the current crisis of science behind AGW. It was the destruction of the dream of the Vienna Circle of the completion of logic. Kurt Gödel, the German mathematician and philosopher, put the philosophical fantasy of "the elimination of metaphysics through the logical analysis of language" to rest[i].

Gödel's two "Incompleteness Theorems" exposed fundamental flaws in the foundations of a school of philosophy known as Logical Positivism. In a somewhat similar vein, the release of the e-mails for the University of East Anglia precipitated the collapse of the house of cards of the Intergovernmental Panel on Climate Change (IPCC) and the "science" behind AGW.

The history behind the development of Logical Positivism is quite complex. Here is the abbreviated version:

The German logician Gottlob Frege was the first person to put all of logic within a formal and axiomatic system. He did this in his Begriffsschrift of 1879. Frege was (at least in some respects) a Platonist. He contended that logic was a science, the truth of which was independent of subjective input. He also argued that the truths of logic were fundamentally intuitive (rather than empirical) in nature.

In short, for Frege, we know the truths of logic because they are "eternal" and exist "outside" of human minds. (We don't just make up logic. It is an objective science[ii].)

But philosophers were moving more and more towards relativism. They viewed logic as a human artifact. More important, they believed that logic could be captured and fully delineated. (Compare this position with the IPCC's contention that human beings can influence and control the weather.)

Bertrand Russell and Alfred North Whitehead took the first major step in capturing logic with the publication (1910-1913) of three volumes titled Principia Mathematica[iii]. Ludwig Wittgenstein's Tractatus Logico-Philosophicus soon followed Principia Mathematica. Wittgenstein made the preposterous claim in the preface to his work that he "... believed myself to have discovered, on all critical matters, the final solutions to the problems." [Final paragraph of the preface. My translation.]

Wittgenstein's "final solutions" (a chilling phrase, since the first edition of the book was published in German, under another title, in 1921) was that mathematics and logic were no sciences at all, but merely collections of conventional (man-made) rules that could be applied to the real physical sciences. (Logic and math were tools designed by human beings to describe the empirical and scientific world in much the same way that language describes the everyday world. Math and logic contained no truth in and of themselves.)

Wittgenstein's Tractatus quickly become the Bible for the logical positivists, especially for a group of Austrian philosophers dubbed the Vienna Circle. Rudolf Carnap, for example, published Der logische Aufbau der Welt in 1928. He contended there (and in his Pseudoproblems in Philosophy) that many historical conundrums in traditional philosophy (like metaphysics, the existence of God, and objective moral values) are non-existent dilemmas that result from centuries of "misuse" of ordinary language.

Carnap, and other logical positivists, insisted that all of these "problems" could be solved (following David Hilbert) with a system of logic, which could be used to analyze and then purge "irrational" statements from ordinary language. The Vienna Circle was founded in part to try to finalize the logical system that would have the ability to sanitize philosophy of notions like God, metaphysics, and objective moral values.

Carnap and his fellow members of the Vienna Circle (most of whom were professors or graduate students of philosophy, logic, and mathematics) held meetings in coffee houses in Vienna[iv]. The two basic premises of this tight-knit group of thinkers are outlined in their manifesto of Logical Positivism: Wissenschaftliche Weltauffassung. Der Wiener Kreis (The World Conception of Science. The Vienna Circle).

The two main theses of the manifesto are:

1) Statements about the empirical world can be reduced to simple logical constructs and are true (or false).

2) Statements that are not about the empirical world cannot be reduced to logical constructs and are necessarily nonsense[v].

The manifesto states: "Certain difficulties, however, remained in this attempt at overcoming the foundation crisis of arithmetic (and set theory) and have so far not found a definitively satisfactory solution"[vi].

The task of the Vienna Circle was to provide a "satisfactory solution" to the crisis of mathematics and logic. They hoped to accomplish this by completing David Hilbert's attempt to provide a formally complete and internally consistent basis for logic.

Thus, the members of the Vienna Circle thought they were on the verge of "proving" that metaphysics and talk of "God" or "intuition" were just silly linguistic mistakes that could be purged from language once they finalized their holy grail of logic. In a similar manner, the IPCC has been busily collecting data with the specific intent of "proving" that man makes the climate exponentially hotter by releasing (of all things) CO2.

Sitting in the back of the meetings of the Vienna Circle was a quiet young mathematician named Kurt Gödel. He rarely spoke, but he listened. Gödel was a small, frail man. He would turn out to be the greatest logician since Aristotle. And like the person who leaked the CRU e-mails that derailed the faulty science of the IPCC, Kurt Gödel would smash the delusions of the logical positivists.

At first, Gödel set out to meet the challenge of David Hilbert:

[Hilbert] asked whether a ... symbolical logical system ... given its axioms and proof procedures, was both internally consistent (the axioms and proof procedures could not be used to prove two statements that contradicted each other) and complete (the proof procedures sufficed to prove every statement true in the system)[vii]. [Emphasis added.]

This was the complete and consistent logic the Vienna Circle was desperately hoping to produce. Gödel (and many of his colleagues) thought that he was intellectually up to the task of finishing what was known as "Hilbert's program." But instead of finishing Hilbert's program, Kurt Gödel, much to his and his colleagues' surprise, demolished it.

Gödel's Incompleteness Theorems are complex, and I will not discuss them in detail. They are also, however, beautiful and almost revelatory. I still remember the feeling that I had when I mastered Gödel's numbering (the method Gödel used to construct his two theorems) and was finally able to grasp the truth of them. It was like meeting the Truth face-to-face[viii].

Stated as simply as possible, Gödel's 1st Theorem proves that any system of axioms is necessarily incomplete. The truth of mathematics cannot be reduced to a formal proof.

Ironically, a computer can be programmed to verify Gödel's 1st Theorem. Load a computer with the 1st theorem. The computer spits out a routine that states that it cannot -- and never will be able to -- produce a formal proof of the completeness of mathematics. Contrast this point with the CRU's use of "fudge factors" in their computer models to "prove" global warming.

Even more bizarre, Gödel's 2nd Theorem demonstrates that any consistent system of axioms could not prove its consistency from within its (or any other existing and consistent) set of axioms.

This 2nd Theorem can also be loaded into a computer. And the computer dutifully reports that it cannot be consistent unless it is inconsistent. Computers are not gods. They cannot give us the truth. They can only regurgitate the information we feed them. And the IPCC has been feeding computers numbers that have been predetermined to give the IPCC exactly the results that it wants -- that AGW is real.

The battle of the logical positivists to establish a complete and consistent logic was defeated on both fronts by Kurt Gödel's Incompleteness Theorems. Logic is not mechanical.  It does rely on human intuition. And logical truths probably are natural, objective, and not man-made -- much like the weather.

Kurt Gödel was given scant recognition for the most important advances in logic since Aristotle. Gödel, after all, believed in God[ix]. He believed that truth is eternal and not an invention of human beings. In fact, Gödel stated:

[Apriorism] belongs in principle on the right, and empiricism on the left side. ... [One] sees also that optimism belongs in principle toward the right and pessimism toward the left. ... Another example of a theory evidently on the right is that of an objective justice and objective aesthetic values, whereas the interpretation of ethics and aesthetics on the basis of custom, upbringing, etc., belongs toward the left. ... [The] development of philosophy since the Renaissance has by and large gone from right to left[x].

Little wonder that Gödel was not popular with his fellow academicians -- even though, intellectually speaking, he stood head and shoulders above all of them.

Kurt Gödel singlehandedly crashed the house of cards of modern empiricist, positivist, and atheistic philosophy...sort of like whoever released those CRU e-mails has started to expose the scam that is the science behind man-made global warming.

As Robert Burns put it in his poem "To a Mouse":

But, Mousie, thou art no thy lane


In proving foresight may be vain:


The best laid schemes o' mice an' men


Gang aft a-gley,


An' lea'e us nought but grief an' pain,


For promised joy.

Larrey Anderson is a writer, a philosopher, and submissions editor for American Thinker. He is the author of The Order of the Beloved, and the memoir Underground: Life and Survival in the Russian Black Market.

[i] The phrase in quotes is taken from the title of an essay by Rudolf Carnap. Carnap was a prominent member of the Vienna Circle (der Wiener Kreis -- founded by Morris Schlick in 1922). Carnap was a staunch proponent of Logical Positivism.

[ii] Frege's position on the objective truth of logic is never clearly and plainly expressed in his writings -- but most scholars see his position as Platonic. For details on this topic, and as background for this entire article, I highly recommend my mentor Stanley Rosen's outstanding book, The Limits of Analysis.

[iii] At about the same time as the publication of Principia Mathematica, another German logician, David Hilbert, was developing the notion of logic as a "metalanguage" -- also called "metamathematics."

[iv] Formal meetings were held in a classroom in the Boltzmanngasse at the University of Vienna.

[v] Here is the apropos passage from the manifesto in English translation:
"It is the method of logical analysis that essentially distinguishes recent empiricism and positivism from the earlier version that was more biological-psychological in its orientation. If someone asserts, "there is a God", "the primary basis of the world is the unconscious", "there is an entelechy which is the leading principle in the living organism," we do not say to him: "what you say is false"; but we ask him: "what do you mean by these statements?" Then it appears that there is a sharp boundary between two kinds of statements. To one belong statements as they are made by empirical science; their meaning can be determined by logical analysis or, more precisely, through reduction to the simplest statements about the empirically given. The other statements, to which belong those cited above, reveal themselves as empty of meaning if one takes them in the way that metaphysicians intend. One can, of course, often re-interpret them as empirical statements; but then they lose the content of feeling which is usually essential to the metaphysician. The metaphysician and the theologian believe, thereby misunderstanding themselves, that their statements say something, or that they denote a state of affairs. Analysis, however, shows that these statements say nothing but merely express a certain mood and spirit."

[vi] The main "difficulty" with logic at the time was Russell's Paradox. I describe the paradox in endnote #5 here.

[vii] A World without Time, Palle Yourgrau, Basic Books, 2005, p. 24.

[viii] You can try it for yourself. There is an English translation of the 1st Incompleteness Theorem here.

[ix] Gödel even authored an ontological proof of the existence of God. (Never published.)

[x] Gödel, "The Modern development of the foundations of mathematics in the light of philosophy," 1961.
There has never been a scientific scam in the history of mankind as big as the science swindle of "climate change." Nothing comes close. Modern scientific hustles like mesmerism, phrenology, eugenics, the Piltdown man, and even Lysenkoism, pale in comparison to the flimflam of anthropomorphic global warming (AGW).

There was, however, one astonishing episode in the early part of the 20th century in mathematics and logic which conceptually roughly parallels the current crisis of science behind AGW. It was the destruction of the dream of the Vienna Circle of the completion of logic. Kurt Gödel, the German mathematician and philosopher, put the philosophical fantasy of "the elimination of metaphysics through the logical analysis of language" to rest[i].

Gödel's two "Incompleteness Theorems" exposed fundamental flaws in the foundations of a school of philosophy known as Logical Positivism. In a somewhat similar vein, the release of the e-mails for the University of East Anglia precipitated the collapse of the house of cards of the Intergovernmental Panel on Climate Change (IPCC) and the "science" behind AGW.

The history behind the development of Logical Positivism is quite complex. Here is the abbreviated version:

The German logician Gottlob Frege was the first person to put all of logic within a formal and axiomatic system. He did this in his Begriffsschrift of 1879. Frege was (at least in some respects) a Platonist. He contended that logic was a science, the truth of which was independent of subjective input. He also argued that the truths of logic were fundamentally intuitive (rather than empirical) in nature.

In short, for Frege, we know the truths of logic because they are "eternal" and exist "outside" of human minds. (We don't just make up logic. It is an objective science[ii].)

But philosophers were moving more and more towards relativism. They viewed logic as a human artifact. More important, they believed that logic could be captured and fully delineated. (Compare this position with the IPCC's contention that human beings can influence and control the weather.)

Bertrand Russell and Alfred North Whitehead took the first major step in capturing logic with the publication (1910-1913) of three volumes titled Principia Mathematica[iii]. Ludwig Wittgenstein's Tractatus Logico-Philosophicus soon followed Principia Mathematica. Wittgenstein made the preposterous claim in the preface to his work that he "... believed myself to have discovered, on all critical matters, the final solutions to the problems." [Final paragraph of the preface. My translation.]

Wittgenstein's "final solutions" (a chilling phrase, since the first edition of the book was published in German, under another title, in 1921) was that mathematics and logic were no sciences at all, but merely collections of conventional (man-made) rules that could be applied to the real physical sciences. (Logic and math were tools designed by human beings to describe the empirical and scientific world in much the same way that language describes the everyday world. Math and logic contained no truth in and of themselves.)

Wittgenstein's Tractatus quickly become the Bible for the logical positivists, especially for a group of Austrian philosophers dubbed the Vienna Circle. Rudolf Carnap, for example, published Der logische Aufbau der Welt in 1928. He contended there (and in his Pseudoproblems in Philosophy) that many historical conundrums in traditional philosophy (like metaphysics, the existence of God, and objective moral values) are non-existent dilemmas that result from centuries of "misuse" of ordinary language.

Carnap, and other logical positivists, insisted that all of these "problems" could be solved (following David Hilbert) with a system of logic, which could be used to analyze and then purge "irrational" statements from ordinary language. The Vienna Circle was founded in part to try to finalize the logical system that would have the ability to sanitize philosophy of notions like God, metaphysics, and objective moral values.

Carnap and his fellow members of the Vienna Circle (most of whom were professors or graduate students of philosophy, logic, and mathematics) held meetings in coffee houses in Vienna[iv]. The two basic premises of this tight-knit group of thinkers are outlined in their manifesto of Logical Positivism: Wissenschaftliche Weltauffassung. Der Wiener Kreis (The World Conception of Science. The Vienna Circle).

The two main theses of the manifesto are:

1) Statements about the empirical world can be reduced to simple logical constructs and are true (or false).

2) Statements that are not about the empirical world cannot be reduced to logical constructs and are necessarily nonsense[v].

The manifesto states: "Certain difficulties, however, remained in this attempt at overcoming the foundation crisis of arithmetic (and set theory) and have so far not found a definitively satisfactory solution"[vi].

The task of the Vienna Circle was to provide a "satisfactory solution" to the crisis of mathematics and logic. They hoped to accomplish this by completing David Hilbert's attempt to provide a formally complete and internally consistent basis for logic.

Thus, the members of the Vienna Circle thought they were on the verge of "proving" that metaphysics and talk of "God" or "intuition" were just silly linguistic mistakes that could be purged from language once they finalized their holy grail of logic. In a similar manner, the IPCC has been busily collecting data with the specific intent of "proving" that man makes the climate exponentially hotter by releasing (of all things) CO2.

Sitting in the back of the meetings of the Vienna Circle was a quiet young mathematician named Kurt Gödel. He rarely spoke, but he listened. Gödel was a small, frail man. He would turn out to be the greatest logician since Aristotle. And like the person who leaked the CRU e-mails that derailed the faulty science of the IPCC, Kurt Gödel would smash the delusions of the logical positivists.

At first, Gödel set out to meet the challenge of David Hilbert:

[Hilbert] asked whether a ... symbolical logical system ... given its axioms and proof procedures, was both internally consistent (the axioms and proof procedures could not be used to prove two statements that contradicted each other) and complete (the proof procedures sufficed to prove every statement true in the system)[vii]. [Emphasis added.]

This was the complete and consistent logic the Vienna Circle was desperately hoping to produce. Gödel (and many of his colleagues) thought that he was intellectually up to the task of finishing what was known as "Hilbert's program." But instead of finishing Hilbert's program, Kurt Gödel, much to his and his colleagues' surprise, demolished it.

Gödel's Incompleteness Theorems are complex, and I will not discuss them in detail. They are also, however, beautiful and almost revelatory. I still remember the feeling that I had when I mastered Gödel's numbering (the method Gödel used to construct his two theorems) and was finally able to grasp the truth of them. It was like meeting the Truth face-to-face[viii].

Stated as simply as possible, Gödel's 1st Theorem proves that any system of axioms is necessarily incomplete. The truth of mathematics cannot be reduced to a formal proof.

Ironically, a computer can be programmed to verify Gödel's 1st Theorem. Load a computer with the 1st theorem. The computer spits out a routine that states that it cannot -- and never will be able to -- produce a formal proof of the completeness of mathematics. Contrast this point with the CRU's use of "fudge factors" in their computer models to "prove" global warming.

Even more bizarre, Gödel's 2nd Theorem demonstrates that any consistent system of axioms could not prove its consistency from within its (or any other existing and consistent) set of axioms.

This 2nd Theorem can also be loaded into a computer. And the computer dutifully reports that it cannot be consistent unless it is inconsistent. Computers are not gods. They cannot give us the truth. They can only regurgitate the information we feed them. And the IPCC has been feeding computers numbers that have been predetermined to give the IPCC exactly the results that it wants -- that AGW is real.

The battle of the logical positivists to establish a complete and consistent logic was defeated on both fronts by Kurt Gödel's Incompleteness Theorems. Logic is not mechanical.  It does rely on human intuition. And logical truths probably are natural, objective, and not man-made -- much like the weather.

Kurt Gödel was given scant recognition for the most important advances in logic since Aristotle. Gödel, after all, believed in God[ix]. He believed that truth is eternal and not an invention of human beings. In fact, Gödel stated:

[Apriorism] belongs in principle on the right, and empiricism on the left side. ... [One] sees also that optimism belongs in principle toward the right and pessimism toward the left. ... Another example of a theory evidently on the right is that of an objective justice and objective aesthetic values, whereas the interpretation of ethics and aesthetics on the basis of custom, upbringing, etc., belongs toward the left. ... [The] development of philosophy since the Renaissance has by and large gone from right to left[x].

Little wonder that Gödel was not popular with his fellow academicians -- even though, intellectually speaking, he stood head and shoulders above all of them.

Kurt Gödel singlehandedly crashed the house of cards of modern empiricist, positivist, and atheistic philosophy...sort of like whoever released those CRU e-mails has started to expose the scam that is the science behind man-made global warming.

As Robert Burns put it in his poem "To a Mouse":

But, Mousie, thou art no thy lane


In proving foresight may be vain:


The best laid schemes o' mice an' men


Gang aft a-gley,


An' lea'e us nought but grief an' pain,


For promised joy.

Larrey Anderson is a writer, a philosopher, and submissions editor for American Thinker. He is the author of The Order of the Beloved, and the memoir Underground: Life and Survival in the Russian Black Market.

[i] The phrase in quotes is taken from the title of an essay by Rudolf Carnap. Carnap was a prominent member of the Vienna Circle (der Wiener Kreis -- founded by Morris Schlick in 1922). Carnap was a staunch proponent of Logical Positivism.

[ii] Frege's position on the objective truth of logic is never clearly and plainly expressed in his writings -- but most scholars see his position as Platonic. For details on this topic, and as background for this entire article, I highly recommend my mentor Stanley Rosen's outstanding book, The Limits of Analysis.

[iii] At about the same time as the publication of Principia Mathematica, another German logician, David Hilbert, was developing the notion of logic as a "metalanguage" -- also called "metamathematics."

[iv] Formal meetings were held in a classroom in the Boltzmanngasse at the University of Vienna.

[v] Here is the apropos passage from the manifesto in English translation:
"It is the method of logical analysis that essentially distinguishes recent empiricism and positivism from the earlier version that was more biological-psychological in its orientation. If someone asserts, "there is a God", "the primary basis of the world is the unconscious", "there is an entelechy which is the leading principle in the living organism," we do not say to him: "what you say is false"; but we ask him: "what do you mean by these statements?" Then it appears that there is a sharp boundary between two kinds of statements. To one belong statements as they are made by empirical science; their meaning can be determined by logical analysis or, more precisely, through reduction to the simplest statements about the empirically given. The other statements, to which belong those cited above, reveal themselves as empty of meaning if one takes them in the way that metaphysicians intend. One can, of course, often re-interpret them as empirical statements; but then they lose the content of feeling which is usually essential to the metaphysician. The metaphysician and the theologian believe, thereby misunderstanding themselves, that their statements say something, or that they denote a state of affairs. Analysis, however, shows that these statements say nothing but merely express a certain mood and spirit."

[vi] The main "difficulty" with logic at the time was Russell's Paradox. I describe the paradox in endnote #5 here.

[vii] A World without Time, Palle Yourgrau, Basic Books, 2005, p. 24.

[viii] You can try it for yourself. There is an English translation of the 1st Incompleteness Theorem here.

[ix] Gödel even authored an ontological proof of the existence of God. (Never published.)

[x] Gödel, "The Modern development of the foundations of mathematics in the light of philosophy," 1961.