An associative calculus with an unsolvable problem of equivalence

1970 ◽  
pp. 73-92
Author(s):  
G. S. Ceĭtin
Keyword(s):  
Unsolvable Problem

Linear sampling and the ∀∃∀ case of the decision problem

1974 ◽  
Vol 39 (3) ◽  
pp. 519-548 ◽  
Author(s):  
Stål O. Aanderaa ◽  
Harry R. Lewis
Keyword(s):  
Decision Problem ◽  
Combinatorial Problem ◽  
Finite Model ◽  
Unsolvable Problem ◽  
Sampling Problem ◽  
Solvable Class ◽  
Full Class ◽  
Infinite Model ◽  
Intricate Argument ◽  
Linear Sampling

Let Q be the class of closed quantificational formulas ∀x∃u∀yM without identity such that M is a quantifier-free matrix containing only monadic and dyadic predicate letters and containing no atomic subformula of the form Pyx or Puy for any predicate letter P. In [DKW] Dreben, Kahr, and Wang conjectured that Q is a solvable class for satisfiability and indeed contains no formula having only infinite models. As evidence for this conjecture they noted the solvability of the subclass of Q consisting of those formulas whose atomic subformulas are of only the two forms Pxy, Pyu and the fact that each such formula that has a model has a finite model. Furthermore, it seemed likely that the techniques used to show this subclass solvable could be extended to show the solvability of the full class Q, while the syntax of Q is so restricted that it seemed impossible to express in formulas of Q any unsolvable problem known at that time.In 1966 Aanderaa refuted this conjecture. He first constructed a very complex formula in Q having an infinite model but no finite model, and then, by an extremely intricate argument, showed that Q (in fact, the subclass Q2 defined below) is unsolvable ([Aa1], [Aa2]). In this paper we develop stronger tools in order to simplify and extend the results of [Aa2]. Specifically, we show the unsolvability of an apparently new combinatorial problem, which we shall call the linear sampling problem (defined in §1.2 and §2.3). From the unsolvability of this problem there follows the unsolvability of two proper subclasses of Q, which we now define. For each i ≥ 0, let Pi be a dyadic predicate letter and let Ri be a monadic predicate letter.

The Unsolvable Problem of Abortion

1987 ◽  
Vol 29 (2) ◽  
pp. 233-251
Author(s):  
H. B. Rothschild
Keyword(s):  
Unsolvable Problem

scholarly journals LEGAL NIHILISM: THE PROBLEM OF UNDERSTANDING

2020 ◽  
Vol 8 (3) ◽  
pp. 11-15
Author(s):  
Galina Lanovaya
Keyword(s):  
Scientific Knowledge ◽  
Conceptual Analysis ◽  
Philosophical Problem ◽  
Legal Language ◽  
Unsolvable Problem ◽  
Legal Science

The article analyzes the reasons why researchers fail to Express the essence of legal nihilism clearly and accurately. The article deals with such problems of interpretation of legal nihilism as filling the gaps in scientific knowledge about it with myths, rejecting conceptual analysis in favor of conceptual analysis, ignoring the multilayered concept of «legal nihilism» and its cultural conditionality, and verbalization of this concept by means of the philosophical and legal language, rather than the language of legal science. While emphasizing that these problems can be eliminated, the author emphasizes that along with them there is a fundamentally unsolvable problem: legal nihilism is an idea that is difficult to relate to empirically known reality, and this calls into question the very possibility of considering the formation of an understanding of legal nihilism as a scientific, rather than a philosophical problem.

scholarly journals Temporality and History in Spinoza

2021 ◽  
pp. 55-72
Author(s):  
Ericka Marie Itokazu
Keyword(s):  
Human History ◽  
Unsolvable Problem ◽  
Theory Of History ◽  
Sub Specie Aeternitatis

Spinoza’s philosophy is often characterized as a philosophy sub specie aeternitatis where time and temporality are notions without an expressive role. Consequently, understanding human history by means of the Ethics — using geometric demonstrations supported by metaphysical terms — and without the aid of the notion of time, can be considered as leading to an unsolvable problem. In this chapter, I draw upon Spinoza’s refusal of finalism to propose a renewed investigation about Spinozism and the issue of temporality, asking the question: could the absence of time in Spinoza’s work and his writings on efficient and immanent causality allow us to rethink a theory of history?

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