51. The Reliability of Science and Statistics, the Dialectic of Reliability, Theoretical Reliability
51.1.
Political Decisions and Reliability in Scientific Policy
From an
anthropological perspective, human beings require the safeguarding of their
survival by minimizing, as much as possible, the moral margin of error in
political decisions. Inversely, this entails maximizing the ethical reliability
of such decisions. Scientific decisions, insofar as they are dependent upon
scientific policy—and by extension, upon the political ideology underpinning
such policy—are, in essence, political decisions. This means that the
acceptance of moral risk margins, expressed through the establishment of
thresholds of factual or rational error and reliability, whether applied to
empirical samples or to the rational critique of ideas, ultimately rests on political
choices framed by scientific policy.
The significance
of the reliability of a given model of scientific policy—irrespective of
whether it represents a dominant or an alternative paradigm—lies in the
necessity of trustworthy practices to achieve its guiding ideals. Chief among
these is the ideal of truth, upon which all other scientific ideals
morally depend. Importantly, the interpretation of truth is not absolute;
rather, it varies according to the prevailing model of scientific policy. This
dependence of truth on policy is extensively discussed in section 24 of Introduction
to Impossible Probability, where the relationship between ideology,
politics, and the acceptance of truth as a scientific criterion is elaborated.
51.2.
Reliability and Error as Dialectical Opposites
Reliability
may be defined as certainty. It exists in a relationship of inverse
proportionality with error: the greater the reliability, the smaller the
margin of error, and vice versa. Thus, reliability and error stand as opposites
in much the same way that certainty and uncertainty are opposed. However,
within the frameworks of materialist and idealist dialectics, such opposites
are not only contraries but also identical in their relation: each exists by
virtue of the other. The dialectical view therefore regards error and
reliability as two faces of the same phenomenon, whose tension defines the
limits of knowledge, truth, and scientific validity.
This
conceptualization situates reliability not as an absolute quality but as a
relational category that gains meaning only against its opposite. Insofar as
error must always be accepted to some degree, reliability is never perfect or
final but relative, historically situated, and conditioned by the
epistemological frameworks in use.
51.3. The
Subject–Object Dialectic in Impossible Probability
The development
of the statistical theory of probability—or what is here termed statistical
probability—within the framework of Impossible Probability is
grounded in a dialectical vision. At its core lies the dialectic of subject and
object, which finds mathematical representation in the relation between subject
and option. This foundational duality is introduced as early as section 1,
where differential analysis provides the groundwork for later distinctions
between empirical probability and theoretical probability.
According to the
dialectical principle, every thesis engenders its own antithesis. Applied to
the field of reliability, this means that every degree of reliability
necessarily implies a corresponding degree of error, just as every degree of
error simultaneously implies the presence of some measure of reliability. This
interplay is not merely a logical curiosity but a structural necessity of
statistical reasoning. It ensures that the science of probability is
perpetually self-critical, always oscillating between the poles of
certainty and uncertainty in its pursuit of truth.
51.4. Logic,
Ethics, and the Reliability of Science
The reliability
of science is nothing other than its degree of certainty. A science that proves
false is, by definition, unreliable. Consequently, within cycles of crisis and
scientific revolution, only the most reliable scientific models ought to prevail.
Nevertheless, history demonstrates that, for political and ideological reasons,
models devoid of logical coherence have often dominated intellectual landscapes
for extended periods.
A fundamental
characteristic of reliability is its dependence on logic. For something to be
reliable, it must first be logically consistent, and by extension, ethically
sound. A science that lacks logical structure and ethical grounding can
only be regarded as entirely false. Conversely, a science that is sufficiently
logical or sufficiently ethical may sustain an adequate scientific discourse,
even if it is not completely isomorphic with reality. Yet, because science
necessarily operates within the contradiction between reality-in-itself
and political reality-for-itself, crises in scientific development are
inevitable. Reliability, therefore, is always provisional, contingent
on both logical and ethical coherence, and permanently exposed to the
dialectical tension between truth and error.
51.5.
Reliability in Empirical and Technological Hypotheses
Reliability, in
its most fundamental sense, is equivalent to certainty. Within empirical
explanatory hypotheses, reliability refers to the certainty achieved in
establishing causal or correlational links between variables. For
example, an explanatory model in the social sciences is only reliable to the
extent that the causal attribution between two variables can withstand
empirical and rational scrutiny.
In the case of
technological hypotheses, reliability is understood as the certainty
that a given technology will produce results aligned with the ideals
of efficiency and efficacy required by scientific policy. Thus, the
reliability of technology is not only a matter of functional success but
also of political and ethical alignment, since technological outcomes
are expected to serve the broader goals set by the prevailing scientific
paradigm. In both contexts—explanatory and technological—reliability acts as
the measure of how far empirical evidence and practical applications can be
trusted to achieve outcomes that are scientifically valid and ethically
legitimate.
51.6.
Reliability de facto and Rational Reliability
Because
reliability is the dialectical opposite of error, the two must be understood as
identical in their relational structure: to accept a margin of
error is to accept, inversely, a margin of reliability; and to accept a margin
of reliability is to acknowledge, inversely, a margin of error. This
interdependence underscores the impossibility of absolute certainty in science.
Within Impossible
Probability, two distinct forms of theoretical error are identified—de
facto error and rational error. Correspondingly, there exist two types of
theoretical reliability:
- Reliability de facto, which is inversely
proportional to the margin of de facto error arising from empirical
limitations such as sample representativeness.
- Rational reliability, which is inversely
proportional to the rational error allowed by scientific policy in the
critical evaluation of ideas [the critical reason, the critical
probability].
These two modes
of reliability, one grounded in the empirical necessity of sampling
and the other in the rational acceptance of ideological or methodological
limits, together delineate the full spectrum of reliability in
scientific inquiry.
[In the case of
GAI, it could be suggested that GAI lacks ideology, but this is not true. As
long as it is a system of ideas—the categorical system, the conceptual scheme,
the conceptual map, the conceptual models—it is an ideal construction of
reality, essentially built upon a definition of efficacy and efficiency. The
simple act of defining conceptual decisions based on ideals of efficiency and
efficacy is an ideological act. While for the defenders of the free market—such
as the United States—efficiency and efficacy may be central, this definition
may not be the same for the defenders of socialism. At present, the most
important model of socialism is China {note that we do not refer to China as a
communist society, even if this is the ultimate goal of China; right now, China
is state capitalism, in other words, socialism}. What is important to highlight
about China is how it has been able to achieve a very significant level of AI
development, even further than other countries based on the free market, such as
Japan or the United Kingdom. If this book is no the place for an ideological
debate, it would be advisable to analyse which characteristics of the social
state of China have contributed to this advancement. In 1949, the United
Kingdom was still an empire, and China had just ended its civil war. In 2025,
the United Kingdom is in decline, and China is a superpower. The relationship
between China and the United Kingdom is, obviously, inversely proportional. But
we need to acknowledge that in future models of Global AI, the differences
between the Global Artificial Intelligence of America and the Chinese version
will not only be grounded in the types of algorithms used, but also in how each
team in the race will train their respective AI models according to different
concepts of efficacy and efficiency, based on their political agendas. In other
words, directly or indirectly, the Global Artificial Intelligence of America
will be trained under a very clear pro-capitalist ideology, while the Chinese
version will be trained under a very clear agenda of socialism with Chinese
characteristics. In short, all Global AI will be the replication of an
ideological program, and its purpose will be to apply a global ideological
agenda based on the ideology in which it has been programmed.
In other words,
those agendas seeking to promote global justice and equality must work on
developing their own Global AI models if they want to succeed in the
competition for global dominance in AI. Otherwise, it might only be achievable
through an international order, by establishing some form of international
agreement regulating the limits and legal frameworks of these supermachines in
order to ensure that they serve the common good.
The ideas of
Marx and Engels about the future leadership of the proletariat do not make
sense in a future dominated by machines. Our opinion is that the working class
will be banished. The dictatorship of the proletariat will never happen,
because there will no longer be a proletariat. Something different is the
building of the social utopia, which dates back to Thomas More, and even much
earlier. Anarchism and communal property were the very first forms of social
organisation among human tribes in the Palaeolithic, where what the men hunted
and the women gathered was shared by the whole tribe, without class
distinctions, and where hierarchy in the decision-making process was not about
creating an Orwellian global order of control or a new technological feudalism.
From our
perspective, at some point we need to reconsider the very nature of the concept
of work and the social system itself. With our current AI, work can be
automated, unemployment will be massive, and we will need to rethink social
values and modes of organisation without discarding any ideal. Anarchism and
socialism, like the model pursued in China, are still valid frameworks—provided
they can adapt to our Cyborg Revolution. At this point of cold war between the
US and China, it is important to remember Henry Kissinger as the man who made
peace between these two countries possible.]
51.7.
Anthropological Limitations and the Relativity of Reliability
The reason
reliability can never be absolute is rooted in the anthropological condition
of the human being. Humans are inherently limited, incomplete, and
inconsistent. As such, the mathematical reliability of any phenomenon can never
be total or perfect. Nothing is absolutely reliable; at best, it is partially
or incompletely reliable.
This means that
reliability is never impartial or neutral. It is always relative, partial, and
inevitably ideological, because it depends on the scientific policy and the
ideological commitments underpinning it. Thus, every assertion of reliability
reflects not only an epistemic state of knowledge but also the political and
moral framework within which that knowledge is evaluated.
[Even in this
paragraph we can grasp an idea of why Global AI cannot escape the reality of
ideology. As long as, even for GAI, de facto error and sampling are
necessary, it cannot know the entirety of the universe—it can only acquire
partial knowledge. And all knowledge, as long as it is partial, is not neutral;
it is, in essence, ideological. At some point, this is something that even the
supermachine is going to inherit from us.]
51.8. Human
Contradiction and the Necessity of Rational Critique
As developed in
section 2 and expanded in section 7 on the infinite, the anthropological and
philosophical need for reliability arises directly from the contradictory and
dialectical nature of the human being. From the rationalist perspective, the
human is a synthesis of res cogitans (thinking substance) and res
extensa (extended substance), a synthesis of objectivity and subjectivity,
reason and emotion.
This duality
ensures that the human being can never be absolutely objective or rational,
because part of their constitution is irreducibly subjective and emotional.
Human subjectivity and emotion derive from the material and physiological
nature of the species. A being that is necessarily empirical can never be fully
logical. This is the contradiction between matter and form, which is critically
resolved in the human entity through the exercise of rational critique.
The necessity of
rationally criticizing ideas of reality stems from this condition: the goal is
to reach the most objective possible approximation to reality, even if never
complete. At best, humans can achieve a certain degree of isomorphism between
idea and reality, but never perfect correspondence. This is why reliability is
always partial, contingent, and in need of constant rational evaluation.
51.9. The
Origin of Error and the Antinomy of Science
The empirical
limitations of the human being in the face of the infinite constitute the
origin of error. As explained in section 7, human self-awareness of its own
subjectivity and emotionality prevents the attainment of absolute certainty.
Consequently, absolute reliability remains a utopia, at least at the present
stage of scientific development.
This condition
makes the first Kantian categorical imperative—to transform actions into
universal maxims—an impossibility or utopia in the domain of science. Science
today can only ever be partially true, operating within margins of error or
reliability set by scientific policy. But if a science is only partially true,
it must also be partially false. This leads to a logical antinomy: science
is simultaneously true and false.
We recognize
that, within accepted margins of error, current science is true. Yet we also
acknowledge that its truth extends only until the point at which the inevitable
margin of error becomes manifest, at which moment the falsity of science
materializes. Science is thus a dynamic and antinomic enterprise, oscillating
between partial truth and inevitable error.
51.10. The
Relationship Between Reliability and Margins of Error in Science
Science is true
to the extent that it is reliable, and it is reliable in inverse proportion to
the margins of error accepted by scientific policy. These margins—whether
theoretical, de facto, or rational—constitute the critical boundaries of
reason.
In this sense,
scientific truth is not absolute but proportional. The more restrictive the
margins of error allowed by policy, the greater the reliability of scientific
outcomes; conversely, the broader the acceptance of error, the weaker the
reliability of scientific truth. This proportionality reveals the inherently
critical dimension of science, in which truth is not static but constantly
redefined through the dialectical interplay of error and reliability.
51.11.
Differentiation Between Theoretical Error and Empirical Error
Within the
framework of Impossible Probability, error is not a monolithic category
but must be differentiated into distinct forms. On the one hand, there are
theoretical errors, which include both de facto error (arising from the
necessity of sampling) and rational error (arising from the acceptance of
ideological or methodological limits imposed by scientific policy). On the
other hand, there exists empirical error, which is irreducible to theoretical
formulations.
This distinction
carries with it a corollary: just as there are theoretical forms of reliability
(corresponding to theoretical errors), there must also be empirical
reliability, which reflects the degree of certainty achieved in practice when
confronting data as they manifest in reality. The differentiation between
theoretical and empirical error—and correspondingly between theoretical and
empirical reliability—is essential for a comprehensive understanding of
scientific validity, because it acknowledges both the rational-logical and the
material-empirical dimensions of error.
51.12.
Empirical Error and the Dispersion of Data
Whereas
theoretical error is bounded by margins accepted either de facto
(sampling limitations) or rationally (policy-driven choices), empirical error
is bounded by the dispersion inherent in the data themselves. In other words,
empirical error is a function of the variability of occurrences within the
observed universe, and it depends directly on the object of study.
This form of
error is addressed from section 16 onwards, where different contexts are
distinguished—such as studies of equality of opportunity, positive bias, or
omega models. Each of these cases requires specific treatment, since the
dispersion and structure of empirical data vary according to the phenomenon
under investigation. In the case of omega models, where multiple ideal options
exist simultaneously within a given universe, empirical error takes on
additional complexity, a theme explored in section 20.
[As I have said
many times, I was born into a Marxist family. From the very beginning of Introduction
to Impossible Probability, it is very clear that the target is the analysis
of the relation between bias and equality. At that time, I was involved in the
emergence of a social revolution in Madrid, the 15M movement, and later I
became a member of the anarchist union CGT, and afterwards of Solidaridad
Obrera (Workers’ Solidarity). Even in London I maintained contact with
anarchists (Solidarity Federation) and Marxist organisations (Socialist Workers
Party, Newham branch).
We must not
forget that José Rodríguez Delgado was a disciple of Juan Negrín. This is the
very origin of Cyborg Robotics in Spain: Civil War, dictatorship, and the Cold
War between the US and Russia. In that context, I wrote the book and this blog.
At that time, my ideology was rooted in social equality. Understanding how Impossible
Probability was born makes it easy to see why dispersion was identified as
empirical error, because the theory itself was born under a very progressive
agenda pursuing social justice.
Throughout my
whole life I have been oscillating between different ideologies, even
oscillating between different genders. Oscillations between different
philosophies and sexual orientations have taught me to love and to learn who I
am, and to recognise the importance of the Transhuman Revolution in the future
adaptation of humans to our supermachine.
Something we
need to learn from Henry Kissinger is the importance of being open to the
future and to different ideologies. The point is not to destroy China or
Russia, but to find ways to transform societies while working together, as Karl
Pribram and Alexander Luria once did. This approach can also be applied to
future transitions in Spain, future transitions in Europe, future transitions
in Ukraine, and future transitions in the relations between the United Kingdom
and Northern Ireland. In his last years, Henry Kissinger was a clear advocate
for peace in Taiwan, peace in Ukraine, and peace in Europe.]
51.13.
Empirical Models of Error and Reliability
Section 16
further develops the empirical structure of chance (azar) and its
relationship to reliability, by examining concrete models of empirical error
and empirical reliability. These models are indispensable within what Impossible
Probability terms inter-measurement statistics—a statistical
approach that operates across multiple levels of interaction, whether
intra-individual (within a single subject across conditions) or
inter-individual (across multiple subjects) in different measurements.
The construction
of such models demonstrates that error and reliability must be understood not
only at the theoretical level but also as practical, empirical realities. The
articulation of empirical error models ensures that the statistical treatment
of variability remains faithful to the observed structure of data, rather than
being subsumed entirely under abstract theoretical assumptions.
51.14.
Synthesis of Theoretical Reliability
Given that much
of the present discussion has focused on theoretical error, it is necessary at
this point to synthesize the concept of theoretical reliability. While the
details are already extensively developed in earlier sections—specifically
section 3 (on the definition of reliability), section 5 (on the relation
between reliability and truth), and section 11 (on rational error)—this
synthesis serves to highlight the central principle: theoretical reliability is
the inverse of theoretical error.
In Impossible
Probability, theoretical reliability thus represents the degree of
certainty that can be rationally and logically ascribed to scientific
statements, contingent upon both empirical sampling and rational critique. Its
synthesis consolidates the dialectical view that reliability and error are
inseparable and that theoretical reliability is always relative to the margins
of error one is prepared to accept.
51.15. De
Facto Error and the Representativity of Samples
De facto
error refers to the unavoidable error inherent in any scientific study that
requires the acceptance of a sample. No matter how large or well-constructed
the sample, the probability of error in representativity is always equal to the
inverse of the sample size. Thus, to accept any sample is already to accept
error.
Even if the
sample size increases and the inverse approaches zero, the presence of error
cannot be entirely eliminated. Over sufficient time or within an infinite
horizon, every de facto error proves to be inevitable. This principle
underscores the necessity of humility in scientific claims: representativity
can be maximized but never rendered perfect. The reliance on samples is
indispensable to statistics, yet it always entails a concession to error, a
structural feature that no scientific method can overcome.
51.16. The
Sample as an Essential Aspect of Impossible Probability
The definition
of the sample emerges as a fundamental aspect of Impossible Probability,
since the type of sample directly determines the degree of representativity
error. In universes of infinite subjects or options—defined by the possibility
of infinite singular qualities—the probability of representativity error is
given by the inversion of N (the sample size). Consequently, Theoretical
Reliability is necessarily equal to the difference between unity and the
inversion of N:
This expression
formalizes the structural relationship between sampling and reliability in
infinite universes, showing that reliability can only be understood relative to
the inverse of sample size.
51.17. The
Tendency Toward Error in Infinite Universes
The meaning of de
facto Theoretical Reliability is that, as N tends toward infinity in
universes of infinite subjects or options, error tends toward zero and
reliability tends toward its maximum possible value. However, within the
framework of Impossible Probability, even if N were to reach
infinity and the probability of representativity error were to tend toward
zero, this does not imply the absolute elimination of error.
The reason is
that even a probability that tends toward zero—expressed as an infinite series
of decimal zeros—remains, in practice, an Impossible Probability:
Although
mathematically reducible to zero, the error remains structurally inevitable
when considered in the context of infinite time. Thus, even in universes of
infinite options, error cannot be annihilated but only minimized, confirming
the principle that in a sufficient or infinite timeframe, error is always bound
to emerge.
51.18.
Theoretical Reliability in Universes of Limited Options
In universes
where options are limited—whether by social or material constraints, as
explained in section 9—the sample is defined by direct scores or frequencies.
Even in such cases, it is possible to encounter infinite frequencies or
occurrences, meaning that while the number of options is materially or socially
finite, the frequencies associated with them may still be infinite.
This leads to a
phenomenon analogous to that in infinite universes: if the sample of
frequencies tends toward infinity, error, although tending toward zero, will
remain inevitable—provided that the timeframe is sufficient or infinite.
Thus, in
universes of limited options, the probability of representativity error is
inversely proportional to the sample of direct scores or frequencies.
Accordingly, Theoretical Reliability is expressed as:
This formulation
demonstrates that the structural link between reliability and error persists,
regardless of whether the universe of options is infinite or finite, though in
limited universes it applies specifically to frequencies rather than to options
themselves.
51.19.
Theoretical Reliability and Rational Error in the Critique of Ideas
From this
perspective, de facto Theoretical Reliability is inversely proportional
to de facto error, and can be mathematically expressed as the difference
between unity and the inversion of the sample. By contrast, rational
reliability is inversely proportional to rational error and depends on the type
of study being carried out within rational critique.
Whether a study
is classified as a model of error or of reliability will depend on how rational
error is conceptualized and on the criteria set by scientific policy. In this
sense, rational reliability is not determined by empirical representativity but
by the degree of error one is willing to accept when subjecting ideas to
critical rational evaluation.
51.20.
Studies of Error and Studies of Reliability
In Impossible
Probability, a study may be classified either as an “error study” or
a “reliability study” depending on whether the moral variable X is
calculated in terms of a percentage of error or of reliability. This classification
underscores the moral and political dimension inherent in scientific evaluation:
whether one frames the object of analysis in terms of accepted error or
accepted reliability is itself a decision shaped by scientific policy.
Thus, the
designation of a study as an error-based model or a reliability-based model
reveals more than methodological preference—it reflects the underlying
philosophical and ethical assumptions guiding the research process. Error
and reliability are not only technical categories but also moral and political
categories embedded within the dialectical structure of Impossible
Probability.
51.21. The Model of Equality Validity (Validez
de Igualdad)
An illustrative
case is the model of Equality Validity. In this model, critical
probability is defined as the product of the Maximum Possible Theoretical Bias
and a percentage X of error divided by one hundred. By definition, this
constitutes a study of error, since the calculation is grounded in the
acceptance of a percentage of error. Consequently, rational reliability is
expressed as the complement of this percentage: one hundred minus X, or the
percentage of reliability.
The formulation
can be expressed as:
Here, X
represents the percentage of error, while 100 – X represents the corresponding
percentage of reliability.
This formulation
underscores the principle that the acceptance of error is unavoidable in
critical rational analysis: equality can only be validated by recognizing, and
quantifying, the permissible error margin.
51.22. The
Model of Equality Significance (Significación de Igualdad)
In contrast, the
model of Equality Significance shifts the focus from error to
reliability. Here, the critical rational test is applied to the difference
between the Maximum Possible Theoretical Bias and the absolute value of the
Level of Bias. This difference is compared to a critical probability defined
not in terms of error but in terms of reliability, expressed as a percentage X
of reliability divided by one hundred.
The formulation
is expressed as:
Here, X represents
the percentage of reliability, while 
represents the percentage of
error.
In this model,
the moral variable X is interpreted directly as reliability rather than error.
This shift illustrates how the conceptual framing of a study—whether centered
on error or reliability—determines its methodological and moral orientation.
51.23.
Classification of Studies According to the Calculation of Critical Probability
From the
preceding models it follows that, in general terms, studies can be
classified as either “error studies” or “reliability studies,” depending on
whether the critical probability is calculated as a percentage X of error or of
reliability.
Thus:
- Every error study will have a margin of rational
reliability equal to one hundred minus the percentage of error accepted by
scientific policy.
- Conversely, every reliability study will have a
margin of rational error equal to one hundred minus the percentage of
reliability.
In both cases,
the dialectical reciprocity holds: every acceptance of error entails the
acceptance of reliability, and vice versa. Yet, crucially, the acceptance of
rational error implies the recognition that, however reliable a model may be,
error remains inevitable. Given sufficient or infinite time, everything
possible—including what is initially deemed impossible—becomes inevitable.
51.24. The
Dependence of Theoretical Reliability on Error
Theoretical
reliability is structurally dependent upon theoretical error. This error may be
of two types:
- De facto error, which arises from the
empirical necessity of working with a sample (since without a sample, no
statistical analysis is possible). Therefore, one hundred minus the inversion
of the sample equals de facto reliability.
- Rational error, which reflects the acceptance of
limits established by scientific policy in the rational critique of ideas.
Therefore, one hundred minus the percentage X of critical error equals the
percentage of reliability.
This dependence
highlights the inseparability of reliability and error: the former can only be
defined in relation to the latter.
51.25. The
Difference Between De Facto Reliability and Rational Reliability
The distinction
between the two forms of reliability can be formalized as follows:
- De facto Reliability is always equal to
unity minus the inversion of the sample, regardless of the type of
universe under study.
- Rational reliability, however, depends on the moral
variable X, which represents the percentage of error or reliability
accepted in the rational critique of ideas.
This dual
structure makes explicit the twofold grounding of reliability: one in empirical
necessity, the other in rational choice.
51.26.
Empirical Reliability as a Necessary Complement
In addition to these
models of reliability—whether de facto or rational—it is essential,
within Impossible Probability, to acknowledge empirical reliability.
Since every theoretical value is necessarily paired with an empirical value,
empirical reliability must be taken into account alongside empirical error.
This
consideration is indispensable for rational critique at the inter-measurement
level (that is, in contexts where statistical analysis addresses
interactions within or between subjects), as developed beginning in section 16.
51.27. The
Inevitability of De Facto Error
Even if, at the
theoretical level, one were to adopt a critical rational position accepting
only 100% reliability and 0% rational error, the persistence of de facto
error remains unavoidable. The reason is simple: the necessity of employing a
sample. [ And this is unavoidable even for GAI, unless our supermachine could
make infinite computations at the same time. As we have said many times,
nothing is impossible given the right conditions; the point here is what
conditions would be necessary to reach that level of intelligence. We, as
humans, are not able to reach that point. The question is whether a Real
Intelligence—not a limited human intelligence, but a true Real
Intelligence—could be able to do that.].
The acceptance
of a sample is simultaneously the acceptance of empirical reality, and with it,
the inevitability of error in representativity. Without samples, there is no
statistics; but every sample, by definition, carries error. Thus, reliability
can never be absolute.
This principle
also exposes the philosophical implication: accepting reality always entails
accepting some measure of contradiction with our ideals. Science cannot escape
the gap between what is empirically given and what is normatively desired. De
facto error is therefore not only a statistical necessity but also an
ontological condition of scientific knowledge.
This augmented translation is based
on the post
published in https://probabilidadimposible.blogspot.com/,
On 3 March 2013,
Rubén García Pedraza
imposiblenever@gmail.com
