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Abstract

In the article I present and criticize the view of classical compatibilism on freedom, i.e. the view according to which free subjects and free actions can exist in the world ruled by universal, exceptionless causality. I claim that compatibilism does not solve the problem of freedom and determinism, but avoids and disregards it. Compatibilism pretends to accomplish the task by playing with semantic tricks that create a misleading impression of ‛compatibility’.

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Authors and Affiliations

Andrzej Nowakowski
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Abstract

In the article I discuss the modal version of the so‑called ‘consequence argument’ for incompatibilism. I quote and review critical remarks that predominate in the literature, and try to answer them. I show that the main strategy employed with the view to undermining the consequence argument revolves on the meanings of expressions used in it. The premises are allegedly false, the conclusion is not strong enough, and the rules are incorrect. I object to this kind of strategy and claim that the consequence argument should be assessed on its merits and declared as correct. It is a strong reason in favor of the truth of incompatibilism.
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Bibliography

Beebee H. (2013), Free Will. An Introduction, Basingstoke: Palgrave Macmillan.
Beebee H., Mele A. (2002), Humean Compatibilism, „Mind” 111, s. 201–223.
Campbell J.K. (2007), Free Will and the Necessity of the Past, „Analysis” 67, s. 105– 111.
Campbell J.K. (2010), Compatibilism and Fatalism: Reply to Loss, „Analysis” 70, s. 71–76.
Ginet C. (1966), Might We Have No Choice?, w: K. Lehrer (red.), Freedom and Determinism, New York: Random House, s. 87–104.
Grobler A. (2006), Metodologia nauk, Kraków: Aureus – Znak.
Huemer M. (2000), Van Inwagen’s Consequence Argument, „The Philosophical Review” 109, s. 525–544.
Kane R. (2007), Libertarianism, w: J.M. Fischer, R. Kane, D. Pereboom, M. Vargas, Four Views on Free Will, Oxford: Blackwell Publishing, s. 5–43.
Lewis D. (1979), Counterfactual Dependence and Time’s Arrow, „Nous” 13, s. 455– 476.
Lewis D. (1981), Are We Free to Break the Laws?, „Theoria” 3, s. 113–121.
McKay T.J., Johnson D. (1996), A Reconsideration of An Argument Against Compatibilism, „Philosophical Topics” 24, s. 113–122.
Speak D. (2012), The Consequence Argument Revisited, w: R. Kane (red.), The Oxford Handbook of Free Will, Oxford Handbooks Online, www.oxfordhandbooks.com.
Van Inwagen P. (1975), The Incompatibility of Free Will and Determinism, „Philosophical Studies” 27, s. 185–199.
Van Inwagen P. (1983), An Essay on Free Will, Oxford: Clarendon Press. Van Inwagen P. (2000), Free Will Remains a Mystery, „Philosophical Perspectives” 14, s. 1–19.
Vihvelin K. (2000), Libertarian Compatibilism, „Philosophical Perspectives” 14, s. 139–166.
Warfield T.A. (2000), Causal Determinism and Human Freedom are Incompatible: A New Argument for Incompatibilism, „Philosophical Perspectives” 14, s. 167–180.
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Authors and Affiliations

Andrzej Nowakowski
1

  1. Uniwersytet Marii Curie‑Skłodowskiej w Lublinie, Wydział Filozofii i Socjologii, Pl. M. Curie‑Skłodowskiej 4, 20‑031 Lublin
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Abstract

The paper presents an analysis of factors influencing the accuracy of reproduction of geometry of the vertebrae and the intervertebral disc of the lumbar motion segment for the purpose of designing of an intervertebral disc endoprosthesis. In order to increase the functionality of the new type of endoprostheses by a better adjustment of their structure to the patient’s anatomical features, specialist software was used allowing the processing of the projections of the diagnosed structures. Recommended minimum values of projection features were determined in order to ensure an effective processing of the scanned structures as well as other factors affecting the quality of the reproduction of 3D model geometries. Also, there were generated 3D models of the L4-L5 section. For the final development of geometric models for disc and vertebrae L4 and L5 there has been used smoothing procedure by cubic free curves with the NURBS technique.

This allows accurate reproduction of the geometry for the purposes of identification of a spatial shape of the surface of the vertebrae and the vertebral disc and use of the model for designing of a new endoprosthesis, as well as conducting strength tests with the use of finite elements method.

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Authors and Affiliations

Paweł Kroczak
Konstanty Skalski
Andrzej Nowakowski
Adrian Mróz
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Abstract

We build a mathematical game model of pandemic transmission, including vaccinations of population and budget costs of different acting to eliminate pandemic. We assume the interactions among different groups: vaccinated, susceptible, exposed, infectious, super-spreaders, hospitalized and fatality, defining a system of ordinary differential equations, which describes compartment model of disease and costs of the treatment. The goal of the game is to describe the development disease under different types of treatment, but including costs of them and social restrictions, during the shortest time period. To this effect we construct a dual dynamic programming method to describe open-loop Nash equilibrium for treatment, a group of people having antibodies and budget costs. Next, we calculate numerically an approximate open-loop Nash equilibrium.
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Authors and Affiliations

Radosław Matusik
1
ORCID: ORCID
Andrzej Nowakowski
1
ORCID: ORCID

  1. Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, Łódz, 90-238, Poland
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Abstract

Use of the poroelasticity theory by Biot in the description of rock behaviour requires the value of the e.g. Biot coefficient α to be determined. The α coefficient is a function of two moduli of compressibility: the modulus of compressibility of the rock skeleton Ks and the effective modulus of compressibility K. These moduli are determined directly on the basis of rock compressibility curves obtained during compression of a rock sample using hydrostatic pressure. There is also a concept suggesting that these compressibility moduli might be determined on the basis of results of the uniaxial compression test using the fact that, in the case of an elastic, homogeneous and isotropic material, the modulus of compressibility of a material is a function of its Young modulus and its Poisson ratio. This work compares the results obtained from determination of the Biot coefficient by means of results of compressibility test and uniaxial compression test. It was shown that the uniaxial compression test results are generally unsuitable to determine the value of the coefficient α. An analysis of values of the determined moduli of compressibility shows that whereas the values of effective moduli of compressibility obtained using both ways may be considered as satisfactorily comparable, values of the relevant rock skeleton moduli of compressibility differ significantly.
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Bibliography

[1] M.A. Biot, General Theory of Three-Dimensional Consolidation. J. Appl. Phys. 12, 155-164 (1941).
[2] M.A. Biot, Theory of elasticity and consolidation for a porous anisotropic solid. J. Appl. Phys. 26, 182-185 (1945).
[3] A. Nur, J.D. Byerlee, An Exact Effective Stress Law for Elastic Deformation of Rock with Fluids. J. Geophys. Res. 76 (26), 6414-6419 (1971).
[4] D . Fabre, J. Gustkiewicz J., Poroelastic Properties of Limestones and Sandstones under Hydrostatic Conditions. Int. J. Rock Mech. Min. Sci. 34 (1), 127-134 (1997).
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[6] J . Gustkiewicz, Compressibility of rocks with a special consideration given to pore pressure. In: Thismus et al. (Eds.), Poromechanics – A Tribute to Maurice A. Biot. Proceedings of the Biot Conference on Poromechanics, Louvain-la-Neuve (Belgium), 14-16 September 1998, Balkema, Rotterdam (1998).
[7] M. Lion, F. Skoczylas, B. Ledésert, Determination of the main hydraulic and poroelastic properties of a limestone from Bourgogne, France. Int. J. Rock Mech. Min. Sci. 41, 915-925 (2004).
[8] J . Gustkiewicz, Objętościowe deformacje skały i jej porów (Volume deformations of the rock and its pores). Arch. Min. Sci. 34 (3), 593-609 (1989) (in Polish).
[9] J . Gustkiewicz, Synoptic view of mechanical behaviour of rocks under triaxial compression. In: Rock at Great Depth. Proceedings International Symposium ISRM-SPE, Pau, 28-31 VIII 1989, V. Maury, D. Fourmaintraux (Eds.), Balkema, Rotterdam, 3-10 (1989).
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[11] J .C. Jaeger, N.G.W. Cook, R.W. Zimmerman, Fundamentals of Rock Mechanics. 2007 Blackwell Publishing, Malden-Oxford-Carlton.
[12] H .F. Wang, Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology. 2000 Princeton University Press, Princeton & Oxford.
[13] Z .T. Bieniawski, J.A. Franklin, M.J. Bernede, P. Duffaut, F. Rumpel, T. Horibe, F. Broch, E. Rodrigues, W.E. van Heerden, U.W. Vogler, I. Hansagi, J. Szlavin, B.T. Brady, D.U. Deere, I. Hawkes, D. Milovanovic, Suggested Methods for Determining the Uniaxial Compressive Strength and Deformability of Rock Materials. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 16 (2), 135-140 (1979).
[14] K . Kovári, A. Tisa, H.H. Einstein, J.A. Franklin, Suggested Methods for Determining the Strength of Rock Materials in Triaxial Compression: Revised Version. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 20 (6), 283-290 (1983).
[15] M. Długosz, J. Gustkiewicz, A. Wysocki, Apparatus for investigation of rock in three-axial state of stress. Part I. Characteristics of the apparatus and of the investigation method. Arch. Min. Sci. 26 (1), 17-28 (1981).
[16] M. Długosz, J. Gustkiewicz, A. Wysocki, Apparatus for investigation of rock in three-axial state of stress. Part II. Some investigation results concerning certain rocks. Arch. Min. Sci. 26 (1), 29-41 (1981).
[17] J . Nurkowski, An inductive strain sensor for operation in high pressure environments. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 41, 175-180 (2004).
[18] R . Ulusay, J.A. Hudson (Eds.), Suggested Methods for Determining the Uniaxial Compressive Strength and Deformability of Rock Materials. In: The Complete ISRM Suggested Methods for Rock Characterization, Testing and Monitoring: 1974-2006, 2007 Kozan Ofset Matbaacilik San. Ve Tic. Sti., Ankara.
[19] R. Přikryl, J. Prikrylová, M. Racek, Z. Weishauptová, K. Kreislová, Decay mechanism of indoor porous opuka stone: a case study from the main altar located in the St. Vitus Cathedral. Environmental Earth Sciences 76 (2017).
[20] J . Rychlewski, Note on the beginning of plastic deformation in a body under uniform pressure. Archives de Mécanique Appliquée 17 (3), 405-412 (1965).
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Authors and Affiliations

Andrzej Nowakowski
1
ORCID: ORCID
Janusz Nurkowski
1
ORCID: ORCID

  1. Strata Mechanics Research Institute of the Polish Academy of Science, 27 Reymonta Str., 30-059 Kraków, Poland

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