Gödel`s Ontological Argument, Positive Properties, and Gaunilist Objection

The article is devoted to Gödel’s ontological argument, its place in the history of philosophy, and the current debate over the validity of ontological proof. First, we argue that Gödel's argument is a necessary step in the history of the development of ontological proof. Second, we show that Gödel’s argument (namely, its core concept of “positive property”) is based on implausible axiological principles (this fact raises many objections like Hajek’s counter-argument), but can be appropriately reformulated in terms of plausible axiological principles (Gustafsson’s argument). Also, we consider the debate over the validity of Gödel’s argument between contemporary neo-Gaunilist Graham Oppy and the advocate of Gödel’s ontological proof Michael Gettings. We conclude that Gödel’s ontological argument is immune to Oppy’s neo-Gaunilism. Finally, given the fact that Oppy’s parody is arguably the most fine-grained Gaunilo-style argument in the history of philosophy, we conclude that Gaunilist line of argumentation, even if successful in refuting Anselm’s ontological proof of God’s existence, does not work against Gödel’s ontological argument (what is evidenced by the results of the debate between Oppy and Gettings).

Survey on sedation-analgesia regimens, in particular the use of dexmedetomidine, among Dutch implanters of spinal cord neurostimulators

Background and aims During implantation of most spinal cord neurostimulators, patients need to be cooperative to give feedback during lead placement, and also be comfortable. Sedation and analgesia can support these conditions. This survey aimed to provide an overview of the sedation-analgesia regimens currently used among Dutch pain specialists. The survey focused on the sedative agent “dexmedetomidine” due to its attractive pharmacological profile and its promising results during awake procedures. Methods A 27-item survey was sent to the 65 pain specialists involved in neurostimulation in the Netherlands. The survey consisted of questions related to different aspects of sedation and analgesia during neurostimulation, e.g. the current regimen, the opinion on and experience with dexmedetomidine as a sedative agent, and preferences regarding different aspects of sedation (i.e. production of arousable sedation, pain management, quality of patient’s feedback and overall preference). Results Of 65 pain specialists, 45 (69%) completed the survey. Most commonly used sedative was propofol (91%) and most common used analgesic was remifentanil (78%). Of the 45 respondents, 21 (47%) considered the use of dexmedetomidine, whereas 13 (29%) had experience with dexmedetomidine during neurostimulation. The most frequently mentioned positive property of dexmedetomidine was the easy production of arousable sedation. Most respondents who used dexmedetomidine preferred dexmedetomidine sedation over propofol sedation regarding all aspects of sedation. Conclusions The most commonly used sedation-analgesia regimen is the combination of propofol-remifentanil during the implantation of a neurostimulator among Dutch pain specialists. Only a small percentage of respondents had experience with the use of dexmedetomidine, despite its reported advantages. Implications When implanting a spinal cord neurostimulator, dexmedetomidine could be considered as a sedative, given its allowance for and preservation of a state of easy arousable sedation.

The Argument from Perfections

A new ontological argument schema for the existence of a necessary being is presented. Several ways to fill in this schema are shown, based upon different conceptions of “positive property.” The argument is made that at least one of these senses matches an intuitive, prephilosophical concept on which the premises are plausible. This argument has certain advantages over ontological arguments for God. In particular, it is explained how one could find the premises in the argument plausible without being committed to premises that entail the stronger thesis that there must be a perfect being. There follows a discussion of an objection Oppy raises against an ontological argument for the stronger thesis, and an explanation of how the argument put forward in the chapter avoids that objection.

Cubic Trigonometric Nonuniform Spline Curves and Surfaces

A class of cubic trigonometric nonuniform spline basis functions with a local shape parameter is constructed. Their totally positive property is proved. The associated spline curves inherit most properties of usual polynomialB-spline curves and enjoy some other advantageous properties for engineering design. They haveC2continuity at single knots. For equidistant knots, they haveC3continuity andC5continuity for particular choice of shape parameter. They can express freeform curves as well as ellipses. The associated spline surfaces can exactly represent the surfaces of revolution. Thus the curve and surface representation scheme unifies the representation of freeform shape and some analytical shapes, which is popular in engineering.

Goedel's Property Abstraction and Possibilism

Gödel’s Ontological argument is distinctive because it is the most sophisticated and formal of ontological arguments and relies heavily on the notion of positive property. Gödel uses a third-order modal logic with a property abstraction operator and property quantification into modal contexts. Gödel describes positive property as "independent of the accidental structure of the world"; "pure attribution," as opposed to privation; "positive in the 'moral aesthetic sense.'" Pure attribution seems likely to be related to the Leibnizian concept of perfection.By a careful examination of the formal semantics of third-order modal logic with property abstraction together with a Completeness result for third-order modal logic with property abstraction for faithful models that I previously developed in 2000 in my work, Gödel’s Ontological Argument, I argue that it is not possible to develop a sufficient applied third-order modal semantics for Gödel’s ontological argument. As I explore possible approaches for an applied semantics including anti-Realist accounts of the semantics of modal logic compatible with Actualism, I argue that Gödel makes implicit philosophical assumptions which commit him to both possibilism (the belief in merely possible objects) and modal realism (the belief in possible worlds).

Questioning Gödel's Ontological Proof: Is Truth Positive?

In his “Ontological proof”, Kurt Gödel introduces the notion of a second-order value property, the positive property P. The second axiom of the proof states that for any property φ: If φ is positive, its negation is not positive, and vice versa. I put forward that this concept of positiveness leads into a paradox when we apply it to the following self-reflexive sentences: (A) The truth value of A is not positive; (B) The truth value of B is positive. Given axiom 2, sentences A and B paradoxically cannot be both true or both false, and it is also impossible that one of the sentences is true whereas the other is false.