Fuzzy Logic: quantifying truth


About the notion of quantifying truth, if useful to measure an intermediate truth “x/100%” (and something that can be true “2x/100%” and “2+1/100%”, and…”nx/100%”….).

The numerical truth-value in fuzzy logic (a many-valued logic) is the measure of a co-essence or of an undetermined mixture of a value (false, 0) with its opposite (true, 1). It is a complex score of a proposition.
This co-essence is named fuzziness, and it is measured as co-distance of a certain mixed-score, called FIT (the Fuzzy Information unit), from two opposite BIT (1 and 0). A FIT 0.3 is a truth value implying the co-essence of the score 0.3 of trueness with 0.7 of falsehood.
The fuzziness is a sort of numerical evaluation of BITS, namely of those couple (or n-ple) of basic numbers 1 and 0 of Boolean logic (where BITS imply the classical value “true” and “false” of ordinary classical logic).

Fuzziness is a vagueness or indetermination beetwen 1 and 0, which is measured.

Now, the fuzziness, as co-distance of a FIT from two opposite bits can be also displayed as the internal part of a “Boolean Hyper-cube”.
The Boolean hypercube is the three-dimensional version (improperly called “hypercube”, because it is expandable to a multidimensional one) of the normal Boolean square (which contains the table of Aristotelian truth-value, normally opposite each other, as the vertexes 01, 00, 11, 10). Imagine a square with 4 vertexes (01, 00, 11, 10), they are BITS and are all opposite.

Now imagine that a Boolean cube will have the triples 000, 001, 011, etc. as opposite vertexes (if you are familiar with the magic square of opposite and contrary predicates in Aristotle, you can have a picture of Boolean square).

You can now conjecture the Boolean Hypercube with vertexes 0000, 0001, 0011, 0111, ecc.

What does it mean to say that something is .5 true? This is a point not located on of the vertex of the hypercube, but at an internal point of the volume of the Hypercube, at a “certain distance” from more than one vertexes.
There is no statistical or predictive value of trueness, here, but the evaluation of trueness somehow “static” (there is no projection towards the future as in the case of probabilistic predictions.).

A truth-value of .3576 will be “statically”, but “vaguely” and “in a certain, undetermined measure”, lower than .9999.
Those values re-introduce through the expression “in a certain measure” semantics into formal logic. Just because FITS are, if you want, a Tarskian numerical evaluation of other numbers (the BITS).
Those measures are dimensions of meaning and context.

Finally, the same degree of fuzziness of a FIT can be measured (a sort of metalinguistic semantic of semantic), as the degree of vagueness of a set.
The points near to the vertexes or equal to them (.9999 or 1) are less fuzzy than those in the core of the Hypercube: for example .5666, which is fuzzy more than .9999.
The core of the hypercube (0.5) is completely fuzzy (vague, indetermined).

For an introduction to Boolean Hypercube see:



The metaphors are part of quotidian language and I don’t think that fuzzy logic can be a generalization of all MVL logics, maybe there is some paraconsistent language more general than a MVL logic (I suspect it would be something very similar to our quotidian language).

Anyway, the use of numerical values does not restrict the application of fuzzy logic to dimensions of semantics and context which can be straightforwardly quantified, such as temperature, distance, and height, – just because fuzzy logic was expressly introduced, since 1965, to re-connect words (and its metaphorical use) to numbers.
I attach here for you a precious source, the first article of Lofti Zadeh originating all the western math on this important philosophical tool, which all consequences in favor of induction, of solution of strange dichotomies (like i.e. mind/body) are not completely developed. See:https://core.ac.uk/download/pdf/82810078.pdf

We surely know the common sense about “out of sight, out of mind”. It recalls us the first movement of science, outside the limits of our closest experience (the experience of what we have under our noses, literally). It is the same appeal of rhetoric to a local audience to spread the wings of our fantasy toward a wider world, which will be described, rather than from cosmological maps (as in science), from metaphors (an in literature and in the tribunals).
What is a metaphor? We take the experience of single things in front of our nose and give it a new meaning, “allusive” and conjectural of things more distant from our normal experience (far away in space, in time or distant from our sensibility of Westerners, perhaps of men if we refer to sensibility of animals or extra-terrestrials). More banally, these distant things are often, simply a map of dispersed tokens, so that every general term (a universal term or a concept) is both a metaphor and a theory.

The internal dialectic of a single metaphor between examples and universals (or distant things) is analogy. The analogy is paraconsistent, because it relates, in a way possible or dispositional, what is present and true to what is universally possible and likely. And its aim is to persuade us (inside the field of rhetoric), about reality of what is distant, or make us learn a theory, about a distant universe (inside the field of science), in both cases through that conjecture that is the metaphor.

The relationship between the actual current of the example and the verisimilar of the universal (plus all the intermediate rhetorical figures between example and metaphor) is a dispositional and fuzzy relationship. Analogy is often (not always) fuzzy. Not always, because we have i.e. the proportion (a:b=b:c) as another form of analogy or the Tomistic analogy of Creatures to God (the transcendent term is infinitely not-quasi similar).

Here an explanation of fuzzy nature of analogy and of metaphors, especially inside literature, law, rhetoric and science:
– The use of numerical values does not restrict the application of fuzzy logic to dimensions of semantics and context which can be straightforwardly quantified, such as temperature, distance, and height., – just because fuzzy logic was expressly introduced, since 1965, to re-connect words (and its metaphorical use) to numbers.
– A set of numbers can be evaluated by FITS, but every single FIT is a word (a general term, a universal, a concept, a theory, etc.). For example, a set of different body statures can be evaluated by an Arbitrary Membership Curve (AMC) called “tall”: on the abscissa of a Cartesian graph we have the set of statures, on the ordinates in the same Cartesian plane we have the fuzzy evaluation of membership from 0 to 1.

Now, for example who is 1.54 meters tall is, according to such AMC, .2 tall and, at the same time, .8 short (there is a fuzzy borderline between the two neighboring words & AMC “tall” and “short”).
– The adverb “very” and “a few” can modify the inclination and the base (with respect to the abscissas of the Cartesian plane) of these two fuzzy-neighboring AMC-words “tall” and “short”. The AMC very “tall” will have a stricter base on abscissas and a strong inclination (who is 1.80 meters tall, will be .5 “very tall” and .5 “short”, while he could be .8 tall and .2 short).

Every adjective, verb, new connected proposition to those AMC-words will vary the sense, the meaning and the “proximity” of the description of such statures, enabling us to depict a real man, present in front of our eyes. The complex linguistic statements like “he is humorous man, very tall, coming from San Francisco and allergic to strawberries” is a combination of many vague FITS-word-metaphors-AMC, and the focus and the intersection of such various words and the related AMC will help us, applying all the correct properties (AMC), to visualize such man in front of our mental eyes.
– The different fuzzy FITS, related to the various AMCs which in complex way, describe such man “here and now” (absolutely not “out of sight, out of mind”) can be summed and crossed (as a well ordered group or system of fuzzy sets). So that you calculate, for instance, if the expression “he is humorous man, very tall, coming from San Francisco and allergic to strawberries” is true to a specifiable degree.

Surely we are merely scratching the surface of semantics, but if from such man, who is an organism, you want to infer something about “a community is like an organism”, which is a metaphor starting from this man “here and now”, – you can do it.
– The metaphor will be the procedure of taking the linguistic descriptions of many men (the systems of many fuzzy sets) on a hypothetical abscissa and evaluating it with the AMC “community”, stating which men more or less represent a community, then adding many other adjective, verb and new connected propositions, then conjecturing the analogy of such community with an organism.

The conjectured analogy will be a logic relation of fuzzy possibility, which has surely a certain fuzzy AMCP (Arbitrary Membership Curve of Possibility): for example, such metaphor will be vaguely .2 “possibly” true and .8 possibly false.
– “Possibly” is an adverb which modify the range (inclination and base) of the resultant general (alethic) curve of the entire metaphor.What I have outlined here is called in the scientific literature “computing with words” or “soft computing”.
See this original article:


Network Analysis of Economy


A simple example of network analysis of impact over economy structure of fiscal political provisions.

Many can agree that in the context of European fiscal crisis today’s rise in VAT may be a necessary evil. Moreover, we can disagree that indirect taxes such as VAT are less harmful.

According to S. Strogatz theory of social networks VAT should menace the weak ties (which are the cement of economical society) between economical operators/agents preventing mutually beneficial exchanges from taking place.

Also economical hubs could be menaced. For example, Italian government raised VAT to 21%. Here the problem: why not considering the theory of social network of Strogatz as mathematical reason against this provision?

The theory forecasts that an attack (fiscal in this case) against the hubs (enterprises and businessman) of a social network (economy network) can make the network collapse.

A second example of network analysis can come from FAO politics against poverty.

If we try to define type of wealth or poverty, the issue is: are they referred to material sources and goods or to intangible ones?

We agree only partially. Poverty regards entire person, so both consciousness, body, social condition, culture, food availability, safety, wellness, sanity.

Our conjecture is that a new perspective (network analysis) for FAO should be fighting against groups of political and economical concentration (hubs), into developing nations, which prevent population from epidemical diffusion of wealth, information, education and sanitary assistance.

These hubs are actual Governmental or local administrators into developing nations of Western society aids.

Network analysis could demonstrates that economical systems too much aristocratic (the corrupted central-African governments are such hubs collecting western aids) inevitably crash. Richs become richer, and poor poorer.

While a more chaotic (but not excessively chaotic) distribution of aids could bypass the hubs, and enrich populations.

This is an appropriate model of logic and math capable to enable a scientific conjecture abut deep structure of social sciences and of humanities.


Because humans and societies are, also, networks.

Social science and small worlds theory: a new math for humanities?

Graphs and networks, hubs and epidemical diffusion of poverty. Could FAO challenge poverty and unequal distribution of prosperity?

Think to what would happen if Bakunin and other socialists had guessed to possibility of math of social networks! See this quick introductions:




A proposal: Two political models of individual interaction inside economical networks

We heard that Warren Buffett recommended to “know when quitting an investment”, this seems humility applied to economic individual operators, a formula for poverty relief and a caution against speculation.

It seems opposite to S. Ambrose (c. 340 – 4 April 397, archbishop of Milan) rule of sacrifice in favour of the poor, which seems humility applied to economic “collective” operators. The saint wrote « The land was created as a good for all, for wealthy and poor: why, you rich, have exclusive pretension over the land? […] You [rich] does not give the yours to the poor [when you make charities], but you give back each to his own; namely, the property is common, and it was released in common use, while you only have the use of it» (Naboth, 1,2; 12, 53).

Calling B1 the first rule and A2, the second, let say that if we consider these rules as dramatically opposite, then the prevalence of B1 humility type would give raise to wild capitalism, the prevalence of A2 humility type to communism, – while the cooperation between the two rules would entail a sort of “strange” cooperation between capitalism and workforce (anything similar to “Rerum Novarum” Rights and Duties of Capital and Labor as sketched by encyclical issues of Pope Leo XIII on May 15, 1891).

Recently reading any essays of George Soros about the logic of Boom-bust of economic bubbles, we couldn’t avoid to recognise in this kind of Strange collaboration of capital and workforce the same “borderline area between order and disorder” of a economic bubble in the phase of his development, when it is far from the equilibrium, is growing incorporating false perceptions and influences over the fundaments of the market.

Two enemies (capital and labour) in a reciprocal attempt to be humble?

Whoever can imagine what could come from such socio-political strange cooperation?

A response to global crisis?

A coordination between order and disorder?

A disastrous bust of actual capitalistic views, which gave rise to global crisis?

An explanation about Self-sacrifice, as model of interaction inside economical networks

Sacrifice, as humility and generosity, implies a certain just degree of solitude and self-denigration or passivity. This is clearly a sufferance (which is a sort of evil), but deserves respect considering the greater outcome of, without immediately advancing this humble man’s fortune, advancing both the same humble and his society peace and goodness, which outcome will be coming from a reciprocal help (with reciprocal just disadvantages).

Hume’s rejection of humility as social factor was just an empirical impression (a sentiment or a Hume habitude), arbitrary and a mistake as whatever empiricism, which believes to habitudes.

Effectively, definition of humility seems reinforce the idea of paradox into it, when pointing out that realism of humble own self does not give raise to overestimation of the same self in interpersonal behaviour. This seems a strange kind of realistic sacrifice, very similar to George Soros minding structure of his realistic adaptation to crisis and disasters of Boom-bust of economic bubbles: the humble prevents a bust, and sacrifice himself best before the booming bubble of his ego explodes at the contact with reality.

Not only economic success, but also cultural, political and religious hope can be improved by this kind of humility.

In our opinion, the position of antireligious view, which sees religion (and his natural concept of humility) as a tool of power, which tries to incorporate religion into politics, is fruit of a clearly known north European tradition (initially Dutch, then British and finally American, via your WASP tradition).

It was the Peace of Westfalia in 1648 to stabilize this tradition, after Thirty Years of religious war, started because sovereigns wanted to decide religion views of their subjects.

The Westfalia treaty, paradoxically (this deserve a specific consideration) stated and consolidated the “same” confusing and apparently peaceful principle “cuius regio eius religio” (each single power of each crown can decide religion of their subjects), which principle was the same confusion which pumped up the booming bubble of the war…the same false perception for which in this chat it seems that nobody knows that humility is “religion”, over, before and after any kind of politics or economic success.