Fuzzy Theory of Truth

 

What is a problem for me, maybe for all of us, is how propositions of science become scientific and accepted, given that data and facts are so different, as a genre, from a scientific proposition, so that is such a kind of problem how any facts become relevant for science and how pre-scientific theories become science.

So I propose that a variant-theory of truth, a fuzzy version, could be a possible reply to such problem. Please, read the following short outline.

Suppose a variant to Tarski semantic where a Tarski meta-language shows syntactically “equal to truth” the formal (syntactical) correspondence between an object-language “of facts” and a theoretical language “on facts”. This logical scheme for every empirical control (useful both for dialectic-argumentative refutation and for physical refutation), transforms a semantic correspondence (or the “spiritual” concept of truth) into an unsuspected syntactical comparison of symbols, which could be applied also to scientific theories and to their competition testing.

The correspondence will be, in the variant, a different syntax, that of a vague similarity (fuzzy similarity or fuzzy entropy) between (i) syntagms of variables and terms (symbols of propositions) of facts and (ii) syntagms of variables/terms/proposition of theories incorporated in two compared languages: this is a variant of Popper construction of Tarski semantic theory of truth, because Popper (and Tarski) comparison was a syntax of discrete and percentile comparison, something like a compared measure of percentage of empirical content of object-language and logical content of theory-language (in example: (a) “the snow is white” is partially true if, after an appropriate measure of “percentage of empirical content”, happens of necessity that (b) “the snow is white, but full of stings of grey humus”), while the comparison, in the fuzzy scheme, could be a measure of vague similarity between symbolized facts and theories.

In a simplified scheme, Tarski original scheme is

[50 % T] →L(a) = E (b)

which means: The logical content of (a) is correspondent at 50% (percentage) to empirical content of (b), which is to say that (a) is True at 50%. This syntax implies, directly, the reciprocal refutation [- 50% T] → L(a) = E (b) … Namely, (a) is absolutely false in 50% measure (a non vague measure)!

In the variant scheme the refutation is a little bit complex, but explains better some very common situations of everyday life, like political competitions, religious fights and sport match, and is, maybe, more adequate (even if is not more precise) to empirical contents:

[60% T] (G 20% AND W100 %) → L (a) ≈ E (b).

It means: The fact that the snow is white and full of grey stings is “vaguely” correspondent (similar or “vaguely similar”, see the symbol “ ≈ ”) to a theoretical proposition where the snow is vaguely and truly grey at 20% (if the grey is 20% sufficiently similar to white) and “absolutely” (digitally) white at 100% (independently if the snow is effectively a fact of snow covered by several stings of grey humus, given that we simply suppose the schematic theory that “the snow is white”), so that the proposition (a) is globally and “vaguely” correspondent ( “ ≈ ”) at 60% to empirical content of (b), which is to say that (a) is “vaguely” or “analogically” true at 60%, given that a rough calculation of “vague” similarity grade within grey and white colours could be [ G 20% + W 100% / 2 = 60% ]. NOTE: don’t worry for my arbitrary way of calculating pondered similarity vague grade: is arbitrary this choice to calculate fuzzy entropy and can be improved by mathematicians more expert than me.

Guess following examples of two opposite parties and imagine to shall measure the grade of their opposition.

Let’s say that atheist and theists are opposite in grade of 100% (like for example the concept of existent and inexistent).

Then consider the case of two football teams of the same city (like MILAN and INTER in Italy): they will be opposite in a lower measure: let’s say in a grade comprised between 80% and 60% each other.

Take, then, the example of two different partisan group of same Italian Communist party: they should be contrary (in a political sense) in a grade comprised between 20% and 30%.

Imagine, finally, Mr. Popper, the well-known philosopher, as doubting of his epistemology: Will differ from him in a lower measure?

These examples show, in my opinion, the simpler theory about fuzzy entropy, which concept replies to the dilemmatic philosophical query (dramatically producing great confusion since the times of Hegel): how much two opposite things are similar? Can opposites be similar?

Fuzzy entropy illustrates very clearly a logical theory answering to the problematic inquiry about the evanescent reality of similarity, best called as analogy, within different or opposite objects (no matter if they are tokens, arguments, minds).

Further, the original Tarski-Popper scheme is a logical theory of truth, which does not explain how both logical propositions and empirical propositions of facts penetrate into the meta-language of Tarski semantic.

This is the problem of the sources of knowledge, which Popper solved denying validity to induction and to privileged sources (as induction, verification, evidence, math, religion and other “authorities”), focusing his epistemology on the main relevance of empirical and logical control of theories. Popper would say that fact and theories are simply conjectures to be tested.

The fuzzy scheme of logical theory of truth has these extra benefits (further to the main result of more adequate schematization of empirical control of truth as correspondence):

1. It rehabilitates “induction”, given that a great collection of tokens can, in fuzzy logic, justify, in a logical sense, the abstraction of an inductive general law, which becomes the set of “propositions on fact” of a pre-scientific theory or the group of the analytical enunciations of particular facts (both incorporated into the “semantic” of empirical controls of variant-Tarski-meta-language). Here the explanation: there is a fuzzy theorem, about “vague similarity” (a general fuzzy entropy scheme of opposition grade) between the PART and the WHOLE, which says that “the PART vaguely contains the WHOLE, in certain measure (the measure of the part)” [P.V.C.W.]. This theorem applied to a great collection of tokens justifies the induction of pre-scientific general propositions (i.e. physical laws to be tested) and the analytical induction of general data from huge collections of particular data;

2. The fuzzy scheme of logical theory of truth and the theorem P.V.C.W. also explains how facts and proposition are creatively found and included into Tarski-Popper empirical controls (into their meta-linguistic semantics): similarity between facts and theories (between math and brute facts) allows the theoretician to discover new propositions (it is the art of scientific discovery, construed as such a kind of art of Topics), discovering and correcting propositions in the light of facts, and viceversa, in a continue internal feedback (dialectic, rhetoric and not simply based on laboratories testing).

2. The theorem P.V.C.W. and the concept of fuzzy entropy rehabilitate topics, dialectics and rhetorics as instruments of invention and comparison of facts and theories. Popper himself said that also non-empirical (or even metaphysical) arguments can control internal consistency of theories and eventual contradictions, which arguments should be the aware or not aware background of non empirical theories. Here the explanation: the mentioned theorem, about “vague similarity” between the PART and the WHOLE, suggests that science is a “PARTial” linguistic praxis of the WHOLE of entire human linguistic praxis, which includes also Religion, History, Economy, Art, and so on…Overall, finding new propositions on facts and new general analysis of particular data is not simply based on induction or on fallible Popper conjectures (of theories and facts based on previous innate knowledge), but also on an argumentative feedback, which is based on primary analogy between facts and theories.

3. Finally, the fuzzy scheme of logical theory of truth offers a wider range of empirical controls of truth of theories, given that this scheme of semantic allows type of “empirical refutation” different from “absolute contradiction” of Aristotelian Principle of non Contradiction (P.N.C.). While P.N.C. (with its companions: Principle of Identity and Principle of Tertium Non Datur) allows to make a choice between two incompatible theories, when one of these presents an internal or external inconsistency (contradiction with its premises or with is empirical conclusions)…what about when the theories are similar at any percentage? And when the internal or external contradiction is not 100%? When opposition to facts or to premises is not 100%?…Well, the refutation should be at any percentage!

4. The fuzzy scheme of logical theory of truth explains how people can understand each other, using a natural language (maybe also an artificial one like math or formalized logic), because if the propositions of a talker were not “partially similar” to counter-arguments of interlocutor (and partially different) there would be not that certain halo of ambiguity, where lies the basic possibility and basic originality of discussions. While using terms and propositions completely incompatibles would not prevent us from the deadlock of an absolute refutation (when any terms are 100% opposite). This happens, I think, also in definitions of symbols of new fields of math (I am not referring to very standardized matters like the derivatives calculus), where many mathematicians use variants symbolization and, anyway, they can talk reciprocally, each other.

I would call number 4) benefit as the language vagueness which appears to be the fundamental source of Philosophy as infinite theorization of new logical/empirical controls.

Annunci

Holistic Theorems

A short introduction: the problem of contingency and the Platonic conjecture of goodness as intelligible immortality

People may believe in contingency and set their moral compasses according to what they presume to be or be not God’s standards, and statistical research may suggests that inferences about beliefs in God or in contingency may instead point people further in whatever direction they are already facing. Ok, why not? I cannot persuade anybody to be faithful or not in God nor that objectivity of morality is in the goodness of being. Neither I can say that things are good (they just are) nor I can give evidences about the eventual real link between things, good and ethics objectives or compasses….The world doesn’t give explanation or moral explanation about itself. This implies no universal meaning against despair and emptiness. I cannot do anything: this is right. Let the things be…they will reveal that all is historical or contingent (things, compasses, inferences about God’s standard, morality, any link between things and good, etc.)…the main frame of space-time (the background of such contingency) will appear contingent as like as energy and matter or the fields of four fundamental forces. So what? How much is big and long lasting the entire universe of space-time, the total mass of matter, the entire wind of mortal spirits, all the moral acts, all of all? To what we will compare such big whole?…As Plato in the Dialogue titled “Parmenides” said: To nothing else than the same whole! This paradox OPENS the being to goodness…Please, consider the great number of paradoxes linked to “a whole universe to be compared to itself”. It will be young as it is young, big as it is big…and, thus, without any clear dimension, quantity, quality, etc. Plato concluded that the being cannot be sensible, but good and intelligible as so called “First Idea of Good” (Plato), and Parmenides that the being is unique, indivisible and without real contingent mortal human beings around…!, which opinions are false and apparent. Jaspers followed the same suggestion…

The problem of goodness as a relative concept: a different conjecture about “openness to goodness”

I disagree with the difference between “in the goodness of being” and “being for others’ goodness”. This is not a difference in that particular “being” which is the “love” of mankind, the “faith” and the “hope”, where it is particularly evident that “being good for others” is the same “heart of goodness of being”. This love of heart is what sustains, as the intelligible ideas of Plato (justly, he said that the main idea of “hyperuranium” is the idea of “Good”), the “whole universe compared to itself”, as described in the Plato’s Dialogue titled “Parmenides”. Namely, if the entire universe of subjects, of intentions, of 3rd Popper world, of matter, of space-time, and of energy should be compared to itself (precisely, to nothing else that the same whole!), then this self-referential whole would be without any clear dimension, quantity, quality, etc. This paradox requests that “it” shall be “open” to “who”, subtracting “it” to ambiguity of being both near “nothing” and near to “infinite something”. The whole “it” shall be completed by “who” is “good” for giving “permanence” and some “stable existence” to such ambiguous “it”. Plato concluded that the “natural” being cannot be neither “completely” real or existent nor sensible, but there should be some hyperuranium which is good and intelligible like the so called “First Idea of Good” (Plato), Parmenides said that the being is unique, indivisible and without real contingent mortal human beings around…!, which opinions are false and apparent (Jaspers followed the same suggestion)…In my opinion, science of natural facts (including psychology, neurosciences, etc.) is good, even studying “it” and discovering beauty of natural order inside the heart of “it”, but empirical or fallible Popper’s science should also consider self-referential whole as suggesting the incompleteness of reality and its openness to the invisible strength of “heart”, which is a “who” enlightening “it”.

A consequence: goodness as ethical criterion

I saw an interesting defence of violence in favour of democracy in K.R. Popper, which could be generalized to any violent defence of any moral value. The theory implies necessity as in the case of immediate facing with a choice to save or not your child from a killer, or democracy from violent tyrannies. The necessity cuts off any difference between ethics and meta-ethics! Simply, you have no time to decide or discuss.

Maybe, there is no universal law during such events. No choice during such state of necessity.

But, if the humans were contingent subjects as they appears, the entire human history would be only an event, including a certain amounts of irrelevant moments where the violence is not a choice simply because this would be just a rare moments of peace, when alive humans are capable (during the peace) to make decisions and discuss on and of levels and meta-levels of ethics.

Well, history in a philosophical sense, is a rare event, singular and due to humans and to existence of the Earth! But, out of philosophy, history could be the absolute memory of historical events when absolute moral beliefs of absolute hearts of men decided to defend a child from death and a people from tyranny, which fact is not holding a belief really strongly, it is just a really, really, strongly act of Love, which is an alive and kicking justice. The statistical absence of good conducts is not a proof in favour of mortal hyper-free human subjects.

Another consequence of holistic theorems: independence of good as the miracle of being

Mr. Dawkins said that if no sort of order which could be defined a miracle, due to its independence from the environment, can be there, then evolution is a real proof against possibility of project and instruction of a God’s project on nature. Why don’t figure the independence of the whole unity of every possible universe as the miracle, which could reasonably be the miracle? (G. Leibniz).

Morality and holism

The problematic essence of Holism as openness of a self-referential world to goodness introduces the discussion about morality. I agree that morality is inter-subjective, as the very origins of the words reveal it: morality > morals > mores > mos (Latin for ‘custom’, as for the Greek word ethics: > ethos).

Morality is a praxis of deeper and deeper pacific interaction between humans or other social subjects, where the moral value or the ethics principle is the whole good relation. The holism shall be taken as the thesis that the whole is more than the sum of its parts. Here is a correspondingly vague initial statement of non-separation of morality as a super-system, partially and paradoxically independent from the parts (psychology, language, nation, history, evolution, physiology, etc). If the state of the whole is not constituted by states of its parts, then holism is a methodological thesis, by means of which we could discuss morality of alien networks….namely of networks of aliens (every social subject different from humans).

A logical sketch of holistic theorems

We should try to use in next conjectures also (but verbal arguments are welcomed) Zermelo symbols and syntax in order to discuss consequences, on validity of “induction” (or invalidity), of different logical sets theories on analogy/similarity of sets.

The theme is just what I am trying to focus: something like a set which is, “and not is”, a subset of itself; this is the paradox of Russell (solved by him with theory of hierarchical types and metatypes of sets). Well, I think that this self-reference is not solved by Russell (and others), and the “barber’s paradox” involves some similarity, with itself, of this self-referencing set. This self-similarity is an holistic openness of the set.

This is my topic: similarity (even self-similarity) and its consequences on induction (procedure which takes a certain or high number of “similar” cases and develops universal or generic descriptions). This is an important field for common sense and science (and math), because Russell’s Paradox is both a linguistic and math problem (foundation of math: sets are the logical/linguistic foundation of numbers)…and Russell proposal of types is a “multiplication of categories”, which does not seem to be different from a “regressus ad infinitum”.

A theological consequence: infinity and God

This logical sketch of the infinitum is maybe a personal footnote to lesson of the Fathers of Catholic Church: We have no common definition of God, probably because God thinks of our minds in a plural way (and inside his wisdom, which is Love, our minds exist), and they are plural, so that our minds, being a plural reflex or image of God, obviously have a plural point of view (of faith and of love) about unique mystery of creator’s Love, who creates us from nothing (in nothing else than his wisdom and Love). At the same time, we think of a God, whose Love’s measure, number and weight is infinite (see S. Augustin, De Natura Boni Contra Manichaeos, Chapter 22 and ss), so that our finite view of a infinite nature of God’s Love shall be a disperse observation of single (among infinite) properties. If and when I could completely accept the good and even the sufferance (coming from plurality of all things) as a benevolent and mysterious gift of Providence, peace will reign in me, in my friends, my brothers and finally, in the universe.

Worship, pray, faith and mercy are unity of spirits. These qualities are, at the same time, properties, which refers to the same love of God and of humans, where any kind of love is infinity, gratuity, eternity, and purity. A common quality of these properties seems to be a vague unity of a plurality, and, at the same time, out of space-time boundaries, meanwhile completing our fragmentary existences inside space-time.

The same Christian fathers found interesting the concept of Plato about nature non sensible of the being called “First Idea of Good” (Plato), and I personally felt very instructive Parmenides and, particularly, Melissus of Samos about Incorporeal nature of Being.

In my opinion, a valid argument in favour of the holistic concept of being as incorporeal: It comes from Melissus of Samos (five centuries BC, fragment 5 of the presocratic) and from an eventual suggestion coming modern physics.

If entire conceivable nature is an unlimited but finite whole (it is suggested also by hyperbolic geometry of relativity general, which encourages such point of view), Melissus argued that this unlimited One has following remarks:

1.The One has no parts, thus no thickness.

2.Therefore, the One is incorporeal.

This argument is even consistent with a previous (not discussed there) Melissus’ claim that the One is extended and full, because a body extended as you want, but also with no limits, – is not a body.

Namely, thickness is simply the measure of the distance between a body’s limits. Since the One is unlimited, it cannot have thickness, then…

This argument could be still valid for the hyperspace of four-dimension universe of relativity. Ergo: the being is not simply corporeal, notwithstanding that on smaller scale (where we live), we relate one single limited body to other limited bodies, so that we have local dimensions, numbers, measure and weight.

Being could be spiritual?

The absolute reveal its paradox (corporeal and incorporeal), its absolute incompleteness. God shall reveal himself, the whole needs help.

I reply as follows: semantic of an absolute whole regards, directly, its ontology (semantic is usually a comparison of facts and propositions). In my suggestion a particular propositional view of Melissus was compared to facts of Physics, namely to hyperspace of general relativity.

Anyway, I agree that there is a logical jump in deducting from contradictory nature of absolute whole, at the same time corporeal and incorporeal, and from its incompleteness the demonstration of God existence. My suggestion is that nature does not reveal any “god” existence, it is even demonstrated and demonstrable that nature is not a god. This the point: God is not a priori solution, He has nothing in common with nature, neither you can make an abduction about God a priori and to valid demonstrable arguments about it nor you can say anything about spiritual nature of a incorporeal whole.

We can, anyway, feel that such contingent and inconsistent quality of nature is under suspicion, without any non-natural (spiritual) help, which could make more stable its equivocal ontologic inconsistency and, particularly, its absurd birth from nothing. Also admitting eventual Meinong’s ontology of nothing, such concept forbids to allow a creation from nothing “of the same quantistic jumps laws”.

My faith, due to a different kind of reasons (especially acceptation of witnesses of faith), is that our peace comes from serene acceptation that incarnation of God is such help that blessed and gave the gift of salvation to such inconsistent Whole, which, only because of and after such act of faith, reveals its nature of creature.

Any critical observations

I shall consider any clear observations.

Especially,

1) that an equivocal and inconsistent nature of universe proofs that there is no spirit in action and

2) that nothing is ever created from nothing, so that thermodynamics admits that the universe can well be eternal and eternally expanding and contracting, causing itself, needing no cause.

I also appreciated the conclusion that an eternal universe, existing from forever, might not have a cause; and if it has, possibly such cause should not be necessarily spiritual.

3) Finally, there is no empirical evidence nor logical proof for God causation, which you should admit only if this (such evidence or proof) would exist.

Here my reply: 1, 2 are consistent with Hawking theory of an eternal universe placed into imaginary time (for which the big bang is a normal event of an universe existing forever in the imaginary time…the time which flows in every direction of Kasper Wessel plane of complex numbers).

But I made appeal to Melissus, because they (1 and 2, together with conjecture of imaginary time) are subject to refutation by Melissus “demonstratio per absurdum” that an eternal and auto-consistent whole is both locally corporeal and globally incorporeal.

This is the entire logic and experience which, with a matemathical passage to limit, is demonstrated as absurd.

Of course, this is not the necessary logical proof or the empirical argument for God’s existence, it is simply the auto-exhibition by the reason that it has any limitations. This is simply a “preambulum fidei”.

We surely need and have right to a logical proof and empirical evidence for God’s existence. This can be deducted only from incarnation and from the fact that Jesus appeared to some of our fathers. Of course, we have to believe or to Jesus directly or to fathers or to his Church or his witnesses…I am a lawyer: we could start a legal process where possible…I cannot exclude (I am not completely kidding) that some historical evidence, plus other declarations like the synoptics…could be sufficient for a court as proof.

Some abductions, which testify in my opinion ancillary role of reason toward faith.

These suggestions regard invisible things (to which refers S. Paulus). One of invisible gifts of the Wisdom and the Word gave us is our friendship for life (ours and of others, which is Love), our reason (which is the undetectable love of invisible truth and its semantic), our logic (which treat with honour immaterial and imperceptibles entities like sets, predicates, logical ties, syllogisms, propositions, enthymemes and dialectic). How anyone can treat with contempt such gifts for his life (Love, reason/logic, will)? How our freedom can be reduced to anything of material, given that our whole flesh and blood desires to be recognized as a free spirit (at first from our self)?

I was very intrigued with the argument about negative existential propositions (i.e. “God does not exist”). They are impossible over an infinite domain (the absurd emerges as natural consequences of a dicotomic logic based on trinomial of three principles of non contradiction, excluded middle and identity), they could be not even empirically and logically scientific (according to method of fallibilism and to math which is based on said trinomial).

The absurd will be logical and empirical, due to method of controls, even if logically we have the abstract possibility that the Spirit could exist in a infinite domain and “I” as a single self could exist (with a passage to the limit) as non material (invisible) unity beyond every possible element.

We have to agree that the negative existential propositions about God and spirits (and about realities on the same latter level: conscience, reason, logic, truth, self, love and mind) are metaphors of a future inaccessible science. The status of such propositions is logically and empirically metaphysic: namely, they have the status of “possible existence”, subject to future, eventual empirical control and logically based on a quasi-consistent (fuzzy or vague) logic/math: the math of fuzzy frequency or vague probability. Will you agree that existential “possibility” is not black or white, true or false (Kosko, Zadeh, Lukasiewicz, Max Black, and others)?

Well, since ancient Hellenistic Greek philosophy such existential propositions (metaphors or possibilities of absolute entities) were expressly theorized (see theory of Plotin in Enneades about One and Augustin neoplatonic theory about God as unity in De Natura Boni).

So that I conclude that God (spirit, reason, self, mind, love) are somehow subject to definition (in a science of metaphors) as vague logical entities, which truth value cannot fall under the rules of non contradiction and, if they are a possible reality, cannot fall under the laws of a fallibilist control, while they could into a frame of vague logical/mathematical probability referred to those fuzzy sets which are the “whole speech” about absolute as witnessed by the “life” of witnesses of Christ.

The holistic experiment is dialectic (this is in my opinion the empirical control about such realities, very similar to the job of lawyers), and regards the logical contents of others theories.

The experiment is the holistic prolonged observation (intrinsically vague because referred to language speech acts) of others topics (linguistic theorizations), of others argumentation, of others logic of arguments, which ancients (Aristotelian) just defined as parts of “invention”, of dialectic, of topic, of rethoric, etc.

A consequence of holistic theorems at the regard of natural evolution

The intelligent design of Paley, opposed to stochastic evolution of Darwin, seems to be the opposition between what Popper imagined to be the “instruction” against the “trial and error” procedure of evolution.

Hawking seems to use the same argument: “Science predicts that many different kinds of universe will be spontaneously created out of nothing. It is a matter of chance which we are in.” He seems to make reference to chance and to “trial and error”.

Here, in my opinion, a valid counter-argument in favour of the holistic concept of being as incorporeal. This incorporeal nature of being could act as the original “instruction” from the top, which explains unity & order of a universe “a là Paley”.

The counter-argument to Hawking comes from Melissus of Samos (five centuries BC, fragment 5 of the presocratic) and from other suggestions coming modern physics.

If entire conceivable nature is an unlimited but finite whole (it is suggested also by hyperbolic geometry of relativity general, which encourages such point of view), Melissus argued that this unlimited One would have following remarks:

1.The One has no parts, thus no thickness.

2.Therefore, the One is incorporeal.

This argument is even consistent with a previous (not discussed there) Melissus’ claim that the One is extended and full, because a body extended as you want, but also with no limits, – is not a body.

Namely, thickness is simply the measure of the distance between a body’s limits. Since the One is unlimited, it cannot have thickness, then…

This argument could be still valid for the hyperspace of four-dimension universe of relativity. Ergo: the being is not simply corporeal, notwithstanding that on smaller scale (where we live), we relate one single limited body to other limited bodies, so that we have local dimensions, numbers, measure and weight.

Being could be spiritual? I simply understand that Melissus thought that an “absolute” cosmos (universe) reveals its paradox (corporeal and incorporeal), its absolute incompleteness.

So, maybe, God shall reveal himself, because the whole needs help.

We can, therefore, feel that such contingent and inconsistent quality of nature is under suspicion, without any non-natural (spiritual) “instruction”, which could make more stable its equivocal ontologic inconsistency and, particularly, its absurd birth from nothing. Also admitting eventual Meinong’s ontology of nothing, such concept forbids to allow a creation from nothing “of the same quantistic jumps laws”.

The “instruction” of this universe could be the solution to its strange mathematical “inconsistency” (under suspicion, due to Melissus argument). So, we could experiment the serene acceptation that a revelation of God is “such help” that blesses and give salvation to such inconsistent Whole, which, only because-of and after-such act of “instruction” a là Paley, reveals its nature of creature.

In Melissus argument the entire logic and experience, with a mathematical passage to limit, is demonstrated as absurd.

Of course, this is not the necessary logical proof or the empirical argument for God’s existence, it is simply the auto-exhibition by the reason that it has any limitations. This is simply a “preambulum fidei”.