Elements of being: Reading Plato’s <i>Theaetetus</i> and <i>Sophist</i> as a critique of Wittgenstein’s <i>Tractatus Logico-Philosophicus</i>

In his Philosophical Investigations, Wittgenstein suggests that the logical atoms of his Tractatus Logico-Philosophicus are similar to the primary elements of Socrates’ Dream in Plato’s Theaetetus (P.I. §46). I explore the texts in detail and argue that there are two key similarities between the Tractatus and the Dream: they both propose the existence of a single type of logical ‘atom’ and they both reject the object-property distinction. I suggest that Plato’s Theaetetus and Sophist are effectively two parts of one larger dialogue which can be read as a critique of Tractatus-type theories – theories that have object-only ontologies. I argue that Plato demonstrates that any theory lacking the object-property distinction will be unable to explain how strings of words are transformed into meaningful propositions about the world. Such theories relegate all propositions and mathematics to the class of nonsense. Wittgenstein acknowledges that, strictly speaking, the propositions of the Tractatus are nonsense (TLP 6.54); I show that the inexpressibility problem that Wittgenstein references is the same problem that Plato shows is faced by Heraclitus in the Theaetetus (183b). At the time of writing the Tractatus, Wittgenstein did not realise that all propositions, not just those of philosophy, like those in the Tractatus, were reduced to nonsense by his theory. Plato, on the other hand, foresaw the issues that any Tractatus-type theory would inevitably face, and resolved them in the Sophist with the introduction of a second type of logical atom with a different (metaphorical) shape. Different shapes account for how logical atoms combine to create propositions with unity. I argue that the version of logical atomism that Plato presents in the Sophist looks more Fregean than Tractarian. I discuss Wittgenstein’s criticism of Frege, rejection of the idea of a second type of atom representing properties, and preference for necessarily featureless atoms. I conclude that this preference comes at too high a price

Bayesian calibration of fluvial flood models for risk analysis

Flood risk analysis is now fundamental to ood management decision making. It relies on the use of computer models to estimate ood depths for given hydrological conditions. The correct calculation of risks associated with di erent management options requires that the uncertainty in the computer model output is carefully estimated. There are several sources of uncertainty in flood models, including structural uncertainties in the model representation of reality, uncertainty in model parameters, and observation errors. We refer to the rst of these as "model inadequacy". The work described in this thesis concerns the calibration of computer models to describe fluvial flooding, taking into account model inadequacy and paying particular attention to the requirements of risk analysis calculations. A methodology which has had some success in other application areas is Bayesian model calibration, using Gaussian process representation both for the error arising from model inadequacy, and to emulate the computer model output. The e ectiveness of this methodology is demonstrated for steady state flood models, both of a series of laboratory experiments, and of a historical ood using a satellite image of flood outline for calibration. Extension of the methodology to calibration of dynamic models using gauged data is not straightforward, but is achieved for flood models by means of an emulator, which replaces the computationally expensive hydrodynamic model with a time-dependent transfer function. This permits calibrated prediction of floods using historical gauged data, both in the existing channel and after modelling potential modi cations to the channel. It is shown that calibration without inclusion of a model inadequacy function cannot match measured data. Finally, application of the methodology is demonstrated in the context of a calculation of probability of inundation in the channel, both with and without modi cation.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

High-level cognition during story listening is reflected in high-order dynamic correlations in neural activity patterns

Our thoughts arise from coordinated patterns of interactions between brain structures that change with our ongoing experiences. High-order dynamic correlations in neural activity patterns reflect different subgraphs of the brain’s functional connectome that display homologous lower-level dynamic correlations. Here we test the hypothesis that high-level cognition is reflected in high-order dynamic correlations in brain activity patterns. We develop an approach to estimating high-order dynamic correlations in timeseries data, and we apply the approach to neuroimaging data collected as human participants either listen to a ten-minute story or listen to a temporally scrambled version of the story. We train across-participant pattern classifiers to decode (in held-out data) when in the session each neural activity snapshot was collected. We find that classifiers trained to decode from high-order dynamic correlations yield the best performance on data collected as participants listened to the (unscrambled) story. By contrast, classifiers trained to decode data from scrambled versions of the story yielded the best performance when they were trained using first-order dynamic correlations or non-correlational activity patterns. We suggest that as our thoughts become more complex, they are reflected in higher-order patterns of dynamic network interactions throughout the brain

The Sudden Death of the Nearest Quasar

Galaxy formation is significantly modulated by energy output from supermassive black holes at the centers of galaxies which grow in highly efficient luminous quasar phases. The timescale on which black holes transition into and out of such phases is, however, unknown. We present the first measurement of the shutdown timescale for an individual quasar using X-ray observations of the nearby galaxy IC 2497, which hosted a luminous quasar no more than 70,000 years ago that is still seen as a light echo in `Hanny's Voorwerp', but whose present-day radiative output is lower by at least 2 and more likely by over 4 orders of magnitude. This extremely rapid shutdown provides new insights into the physics of accretion in supermassive black holes, and may signal a transition of the accretion disk to a radiatively inefficient state.Comment: 4 pages, 2 figures. Astrophysical Journal Letters, in pres