Truth, Proof and Gödelian Arguments : A Defence of Tarskian Truth in Mathematics

One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established to be true once we expand the formal system with Alfred Tarski s semantical theory of truth, as shown by Stewart Shapiro and Jeffrey Ketland in their semantical arguments for the substantiality of truth. According to them, in Gödel sentences we have an explicit case of true but unprovable sentences, and hence deflationism is refuted. Against that, Neil Tennant has shown that instead of Tarskian truth we can expand the formal system with a soundness principle, according to which all provable sentences are assertable, and the assertability of Gödel sentences follows. This way, the relevant question is not whether we can establish the truth of Gödel sentences, but whether Tarskian truth is a more plausible expansion than a soundness principle. In this work I will argue that this problem is best approached once we think of mathematics as the full human phenomenon, and not just consisting of formal systems. When pre-formal mathematical thinking is included in our account, we see that Tarskian truth is in fact not an expansion at all. I claim that what proof is to formal mathematics, truth is to pre-formal thinking, and the Tarskian account of semantical truth mirrors this relation accurately. However, the introduction of pre-formal mathematics is vulnerable to the deflationist counterargument that while existing in practice, pre-formal thinking could still be philosophically superfluous if it does not refer to anything objective. Against this, I argue that all truly deflationist philosophical theories lead to arbitrariness of mathematics. In all other philosophical accounts of mathematics there is room for a reference of the pre-formal mathematics, and the expansion of Tarkian truth can be made naturally. Hence, if we reject the arbitrariness of mathematics, I argue in this work, we must accept the substantiality of truth. Related subjects such as neo-Fregeanism will also be covered, and shown not to change the need for Tarskian truth. The only remaining route for the deflationist is to change the underlying logic so that our formal languages can include their own truth predicates, which Tarski showed to be impossible for classical first-order languages. With such logics we would have no need to expand the formal systems, and the above argument would fail. From the alternative approaches, in this work I focus mostly on the Independence Friendly (IF) logic of Jaakko Hintikka and Gabriel Sandu. Hintikka has claimed that an IF language can include its own adequate truth predicate. I argue that while this is indeed the case, we cannot recognize the truth predicate as such within the same IF language, and the need for Tarskian truth remains. In addition to IF logic, also second-order logic and Saul Kripke s approach using Kleenean logic will be shown to fail in a similar fashion.

Expected Performance of the ATLAS Experiment - Detector, Trigger and Physics

A detailed study is presented of the expected performance of the ATLAS detector. The reconstruction of tracks, leptons, photons, missing energy and jets is investigated, together with the performance of b-tagging and the trigger. The physics potential for a variety of interesting physics processes, within the Standard Model and beyond, is examined. The study comprises a series of notes based on simulations of the detector and physics processes, with particular emphasis given to the data expected from the first years of operation of the LHC at CERN.

Multivariate Techniques for Identifying Diffractive Interactions at the LHC

Close to one half of the LHC events are expected to be due to elastic or inelastic diffractive scattering. Still, predictions based on extrapolations of experimental data at lower energies differ by large factors in estimating the relative rate of diffractive event categories at the LHC energies. By identifying diffractive events, detailed studies on proton structure can be carried out. The combined forward physics objects: rapidity gaps, forward multiplicity and transverse energy flows can be used to efficiently classify proton-proton collisions. Data samples recorded by the forward detectors, with a simple extension, will allow first estimates of the single diffractive (SD), double diffractive (DD), central diffractive (CD), and non-diffractive (ND) cross sections. The approach, which uses the measurement of inelastic activity in forward and central detector systems, is complementary to the detection and measurement of leading beam-like protons. In this investigation, three different multivariate analysis approaches are assessed in classifying forward physics processes at the LHC. It is shown that with gene expression programming, neural networks and support vector machines, diffraction can be efficiently identified within a large sample of simulated proton-proton scattering events. The event characteristics are visualized by using the self-organizing map algorithm.

Central Diffraction at ALICE

The ALICE experiment is shown to be well suited for studies of exclusive final states from central diffractive reactions. The gluon-rich environment ofthe central system allows detailed QCD studies and searches for exotic mesonstates, such as glueballs, hybrids and new charmonium-like states. It wouldalso provide a good testing ground for detailed studies of heavy quarkonia. Dueto its central barrel performance, ALICE can accurately measure the low-masscentral systems with good purity. The efficiency of the Forward MultiplicityDetector (FMD) and the Forward Shower Counter (FSC) system for detectingrapidity gaps is shown to be adequate for the proposed studies. With thisdetector arrangement, valuable new data can be obtained by tagging centraldiffractive processes.