Papers by Salvador Guzman
The Iterated Romance of Syntax, 2023
One of the greatest intellectual crimes to beset us in the 20th-century was the premature death o... more One of the greatest intellectual crimes to beset us in the 20th-century was the premature death of the formalist program. The millennia old dream of solving math was never realized as our efforts fell short of our ambition. David Hilbert, with all his grace, his effulgent brilliance, his professional magnanimity, and his unflinching dedication, was left with only disgruntled disappointment. The formalist program was a noble effort, held aloft by the unyielding conviction and charisma of the foremost mathematicians of the age. This forlorn vignette is rendered at least somewhat emotionally digestible by the developments that followed. The dream of syntax is all became partially realized by the contributions of Haskell Curry, Alonzo Church, Stephen Kleene, Moses Schönfinkel and others. With their syntactic approach to mathematics, we capture the compositional beauty of infinity in our humble symbol. And thus, we compile the syntactic face of God.
Truth as Process, 2021
**Abstract: Truth as Process**
In this paper, we explore the Halting Problem through a novel len... more **Abstract: Truth as Process**
In this paper, we explore the Halting Problem through a novel lens, examining its implications and deconstructing its perceived paradoxes. The Halting Problem posits the impossibility of creating an algorithm that can determine whether any given process will terminate. By reframing the problem, we propose that such paradoxes arise more from the constraints of our logical tools and the historical context of mathematical thought, particularly influenced by Platonic ideals of perfection.
We argue that paradoxes like the Halting Problem reflect the limitations of human-designed tools rather than intrinsic logical impossibilities. By understanding logic as a negotiable framework akin to a game, we emphasize the flexibility of our intellectual constructs. This perspective allows for innovative approaches to seemingly intractable problems.
The concept of truth as a process is introduced, suggesting that solutions to problems like the Halting Problem can be dynamic rather than static. This approach aligns with practical scenarios in distributed computing and statistical confidence intervals, where truth evolves over time and context.
Ultimately, we advocate for a more adaptable view of mathematical truth, encouraging the development of tools that reflect the fluid nature of logical inquiry. This paradigm shift has the potential to enrich the field of mathematics and logic, fostering progress through a more pragmatic and less dogmatic approach to intellectual challenges.
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Papers by Salvador Guzman
In this paper, we explore the Halting Problem through a novel lens, examining its implications and deconstructing its perceived paradoxes. The Halting Problem posits the impossibility of creating an algorithm that can determine whether any given process will terminate. By reframing the problem, we propose that such paradoxes arise more from the constraints of our logical tools and the historical context of mathematical thought, particularly influenced by Platonic ideals of perfection.
We argue that paradoxes like the Halting Problem reflect the limitations of human-designed tools rather than intrinsic logical impossibilities. By understanding logic as a negotiable framework akin to a game, we emphasize the flexibility of our intellectual constructs. This perspective allows for innovative approaches to seemingly intractable problems.
The concept of truth as a process is introduced, suggesting that solutions to problems like the Halting Problem can be dynamic rather than static. This approach aligns with practical scenarios in distributed computing and statistical confidence intervals, where truth evolves over time and context.
Ultimately, we advocate for a more adaptable view of mathematical truth, encouraging the development of tools that reflect the fluid nature of logical inquiry. This paradigm shift has the potential to enrich the field of mathematics and logic, fostering progress through a more pragmatic and less dogmatic approach to intellectual challenges.
In this paper, we explore the Halting Problem through a novel lens, examining its implications and deconstructing its perceived paradoxes. The Halting Problem posits the impossibility of creating an algorithm that can determine whether any given process will terminate. By reframing the problem, we propose that such paradoxes arise more from the constraints of our logical tools and the historical context of mathematical thought, particularly influenced by Platonic ideals of perfection.
We argue that paradoxes like the Halting Problem reflect the limitations of human-designed tools rather than intrinsic logical impossibilities. By understanding logic as a negotiable framework akin to a game, we emphasize the flexibility of our intellectual constructs. This perspective allows for innovative approaches to seemingly intractable problems.
The concept of truth as a process is introduced, suggesting that solutions to problems like the Halting Problem can be dynamic rather than static. This approach aligns with practical scenarios in distributed computing and statistical confidence intervals, where truth evolves over time and context.
Ultimately, we advocate for a more adaptable view of mathematical truth, encouraging the development of tools that reflect the fluid nature of logical inquiry. This paradigm shift has the potential to enrich the field of mathematics and logic, fostering progress through a more pragmatic and less dogmatic approach to intellectual challenges.