arXiv subjects

Itala M. L. D'Ottaviano

Publications and source records attributed to Itala M. L. D'Ottaviano.

3 recordsLinked to original sources

arXiv2024

Pragmatic Nonsense

Inspired by the early Wittgenstein's concept of nonsense (meaning that which lies beyond the limits of language), we investigate two different types of nonsense: formal nonsense and pragmatic nonsense. The simpler notion of formal nonsense is defined in accordance with Tarski's semantic theory of truth; the notion of pragmatic nonsense is in turn formulated within the context of the theory of pragmatic truth, also known as quasi-truth, as formalized by da Costa and his collaborators. Pragmatic nonsense extends formal nonsense, the same way da Costa's pragmatic truth is an extension of Tarski's definition of truth. An expression is thus considered formally nonsensical in case the formal criteria required for the assignment of any truth-value (whether true, false, pragmatically true, or pragmatically false) are not met; and an expression, or even a well-formed formula, is considered pragmatically nonsensical if either the formal or the pragmatic criteria of relevance (inscribed within the context of scientific practice) required for the assignment of any pragmatic truth-value (pragmatically true or pragmatically false) are not met. We also introduce the concept of strictly pragmatic truth, which excludes pragmatic nonsense and necessarily depends on certain criteria of relevance, unlike the original definition of pragmatic truth/quasi-truth.

math.LO↗

arXiv2024

A simplicity bubble problem and zemblanity in digitally intermediated societies

In this article, we discuss the ubiquity of Big Data and machine learning in society and propose that it evinces the need of further investigation of their fundamental limitations. We extend the ``too much information tends to behave like very little information'' phenomenon to formal knowledge about lawlike universes and arbitrary collections of computably generated datasets. This gives rise to the simplicity bubble problem, which refers to a learning algorithm equipped with a formal theory that can be deceived by a dataset to find a locally optimal model which it deems to be the global one. In the context of lawlike (computable) universes and formal learning systems, we show that there is a ceiling above which formal knowledge cannot further decrease the probability of zemblanitous findings, should the randomly generated data made available to the formal learning system be sufficiently large in comparison to their joint complexity. Zemblanity, the opposite of serendipity, is defined by an undesirable but expected finding that reveals an underlying problem or negative consequence in a given model or theory, which is in principle predictable in case the formal theory contains sufficient information. We also argue that this is an epistemological limitation that may generate unpredictable problems in digitally intermediated societies.

cs.IT↗

arXiv2023

A Simplicity Bubble Problem in Formal-Theoretic Learning Systems

When mining large datasets in order to predict new data, limitations of the principles behind statistical machine learning pose a serious challenge not only to the Big Data deluge, but also to the traditional assumptions that data generating processes are biased toward low algorithmic complexity. Even when one assumes an underlying algorithmic-informational bias toward simplicity in finite dataset generators, we show that current approaches to machine learning (including deep learning, or any formal-theoretic hybrid mix of top-down AI and statistical machine learning approaches), can always be deceived, naturally or artificially, by sufficiently large datasets. In particular, we demonstrate that, for every learning algorithm (with or without access to a formal theory), there is a sufficiently large dataset size above which the algorithmic probability of an unpredictable deceiver is an upper bound (up to a multiplicative constant that only depends on the learning algorithm) for the algorithmic probability of any other larger dataset. In other words, very large and complex datasets can deceive learning algorithms into a ``simplicity bubble'' as likely as any other particular non-deceiving dataset. These deceiving datasets guarantee that any prediction effected by the learning algorithm will unpredictably diverge from the high-algorithmic-complexity globally optimal solution while converging toward the low-algorithmic-complexity locally optimal solution, although the latter is deemed a global one by the learning algorithm. We discuss the framework and additional empirical conditions to be met in order to circumvent this deceptive phenomenon, moving away from statistical machine learning towards a stronger type of machine learning based on, and motivated by, the intrinsic power of algorithmic information theory and computability theory.

cs.IT↗