Stephen Barker argues that a possible worlds semantics for the counterfactual conditional of the sort proposed by Stalnaker and Lewis cannot accommodate certain examples in which determinism is true ...and a counterfactual Q > R is false, but where, for some P, the compound counterfactual P > (Q > R) is true. I argue that the completeness theorem for Lewis's system VC of counterfactual logic shows that Stalnaker—Lewis semantics does accommodate Barker's example, and I argue that its doing so should be understood as showing that the example is an exception to Lewis's Time's Arrow requirements.
Dretske's conclusive reasons account of knowledge is designed to explain how epistemic closure can fail when the evidence for a belief does not transmit to some of that belief's logical consequences. ...Critics of Dretske dispute the argument against closure while joining Dretske in writing off transmission. This paper shows that, in the most widely accepted system for counterfactual logic (David Lewis's system VC), conclusive reasons are governed by an informative, non-trivial, logical transmission principle. If r is a conclusive reason for believing p in Dretske's sense, and if p logically implies q, and if p and q satisfy one additional condition, it follows that r is a conclusive reason for believing q. After introducing this additional condition, I explain its intuitive import and use the condition to shed new light on Dretske's response to scepticism, as well as on his distinction between the so-called 'lightweight' and 'heavyweight' implications of a piece of perceptual knowledge.
Every Proposition is a Counterfactual Cross, Charles B.
Acta analytica : philosophy and psychology,
06/2016, Letnik:
31, Številka:
2
Journal Article
Recenzirano
I present and discuss two logical results. The first shows that a non-trivial counterfactual analysis exists for any contingent proposition that is false in at least two possible worlds. The second ...result identifies a set of conditions that are individually necessary and jointly sufficient for the success of a counterfactual analysis. I use these results to shed light on the question whether disposition ascribing propositions can be analyzed as Stalnaker-Lewis conditional propositions. The answer is that they can, but, in order for a counterfactual analysis to work, the antecedent and consequent must be related in a particular way, and David Lewis’s Time’s Arrow constraints on comparative world similarity must be relaxed. The upshot is that counterfactual analyses are easy to come by, in principle, even if not in practice. In that sense,
it’s easy to be iffy
.
New turbine engine designs requiring secondary flow compression often look to dual flow-path integrally bladed rotors (DFIBRs) since these stages have the ability to perform work on the secondary, or ...bypassed, flow-field. While analogous to traditional integrally bladed rotor stages, DFIBR designs have many differences that result in unique dynamic response characteristics that must be understood to avoid fatigue. This work investigates these characteristics using reduced-order models (ROMs) that incorporate mistuning through perturbations to blade frequencies. This work provides an alternative to computationally intensive geometric-mistuning approaches for DFIBRs by utilizing tuned blade mode reductions and substructure coupling in cyclic coordinates. Free and forced response results are compared to full finite element model (FEM) solutions to determine if any errors are related to the reduced-order model formulation reduction methods. It is shown that DFIBRs have many more frequency veering regions than their single flow-path integrally blade rotor (IBR) counterparts. Modal families are shown to transition between system, inner-blade, and outer-blade motion. Furthermore, findings illustrate that while mode localization of traditional IBRs is limited to a single or small subset of blades, DFIBRs can have modal energy localized to either an inner- or outer-blade set resulting in many blades responding above tuned levels. Lastly, ROM forced response predictions compare well to full FEM predictions for the two test cases shown.
Engine failures due to fatigue have cost the Air Force an estimated $400 million dollars per year over the past two decades. Damping treatments capable of reducing the internal stresses of fan and ...turbine blades to levels where fatigue is less likely to occur have the potential for reducing cost while enhancing reliability. This research evaluates the damping characteristics of magnesium aluminate spinel, MgO+Al
2
O
3
, (mag spinel) on titanium plates from an experimental point of view. The material and aspect ratio were chosen to approximate the low aspect ratio blades found in military gas turbine fans. In the past, work has generally been performed on cantilever supported beams, and thus the two-dimensional features of damping were lost. In this study plates were tested with a cantilevered boundary condition, using electrodynamic shaker excitation. The effective test area of each specimen was 4.5 in × 4.5 in. The nominal plate thickness was 0.125 in. Mag spinel was applied to both sides of the plate, at a thickness of 0.01 in, and damping tests were run at room temperature. The effect of the coating was evaluated at the 2nd bending mode (mode 3) and the chord wise bending mode (mode 4). A scanning laser vibrometer revealed the frequency and shape of each mode for the plates. Sine sweeps were used to characterize the damping of the coated and uncoated specimens for the modes tested. The coating increased damping nonlinearly for both modes tested in which the general outcome was similar to that found in beams.
A novel testing methodology has been developed to determine the fatigue limit strength of structural materials at high frequencies. The procedure involves the use of a base-excited plate specimen ...driven into a high frequency resonant mode which allows completion of a fatigue test in a few hours. The use of a step-testing method allows determination of the fatigue limit strength of the material corresponding to a very large number of cycles, 10
6 or 10
7 in this case. The methodology consists of a topological design procedure, incorporating a finite element model, to produce the shape of the specimen necessary to achieve the required stress state/pattern, and a forced vibration-based fatigue procedure for conducting the high cycle fatigue experiments with variable-amplitude loading. The successful application of the methodology is demonstrated by the experimental results from steel, 6061-T6 aluminum, and Ti-6Al-4V plate specimens subjected to fully reversed uniaxial and biaxial bending stress states. Results are compared with existing data produced using traditional fatigue test machines.
This essay corrects an error in the presentation of the Paradox of the Knowledge-Plus Knower (a variant of Kaplan and Montague's Knower Paradox) given in Cross 2001 ('The Paradox of the Knower ...without Epistemic Closure'). The correction adds a universally quantified transitivity principle for derivability as an additional assumption leading to paradox. This correction does not affect the status of the Knowledge-Plus paradox as a rebuttal to an argument against epistemic closure, since the quantified transitivity principle is true in the standard model of arithmetic and therefore innocuous.
In this essay I renew the case for Conditional Excluded Middle (CXM) in light of recent developments in the semantics of the subjunctive conditional. I argue that Michael Tooley's recent backward ...causation counterexample to the Stalnaker-Lewis comparative world similarity semantics undermines the strongest argument against CXM, and I offer a new, principled argument for the validity of CXM that is in no way undermined by Tooley's counterexample. Finally, I formulate a simple semantics for the subjunctive conditional that is consistent with both CXM and Tooley's counterexample.
In ‘Two Spheres, Twenty Spheres, and the Identity of Indiscernibles,’ Della Rocca argues that any counterexample to the PII would involve ‘a brute fact of non‐identity . . . not grounded in any ...qualitative difference.’ I respond that Adams's so‐called Continuity Argument against the PII does not postulate qualitatively inexplicable brute facts of identity or non‐identity if understood in the context of Kripkean modality. One upshot is that if the PII is understood to quantify over modal as well as non‐modal properties, the qualitative explicability of numerical distinctness requires not the PII but a principle of the identity of necessary indiscernibles.
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