Perspective Shifters (original) (raw)
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Philosophical Studies
Certain passages in Kaplan’s ‘Demonstratives’ are often taken to show that non-vacuous sentential operators associated with a certain parameter of sentential truth require a corresponding relativism concerning assertoric contents: namely, their truth-values also must vary with that parameter. Thus, for example, the non-vacuity of a temporal sentential operator ‘always’ would require some of its operands to have contents that have different truth values at different times. While making no claims about Kaplan’s intentions, we provide several reconstructions of how such an argument might go, focusing on the case of time and temporal operators as an illustration. What we regard as the most plausible reconstruction of the argument establishes a conclusion similar enough to that attributed to Kaplan. However, the argument overgenerates, leading to absurd con- sequences. We conclude that we must distinguish assertoric contents from compositional semantic values, and argue that once they are distinguished, the argument fails to establish any substantial conclusions. We also briefly discuss a related argument commonly attributed to Lewis, and a recent variant due to Weber.
This The new interpretation of arithmetic operation symbols
We introduce the permutation group of arithmetic operations symbols by getting the permutations of all the common arithmetic operations symbols, with keeping the brackets out of ordering. We find 6 ways of doing the arithmetic operations. Therefore the output of any mathematical formulas depends on which one element of the arithmetical permutation group we work on. We find invariants by the reordering of the arithmetic operation x+y, xy. Working with the irreducible representation of the permutation arithmetic symbols group we define new arithmetic structures called arithmetic particles symbols.
How the appearance of an operator affects its formal precedence
Two experiments test predictions of a visual process-driven model of multi-term arithmetic computation. The visual process model predicts that attention should be drawn toward multiplication signs more readily than toward plus signs, and that narrow spaces should draw gaze comparably to multiplication signs. Although both of these predictions are verified by behavioral response measures and eye-tracking, the visual process model cannot account for patterns of early looking. The results suggest that people strategically deploy visual computation strategies.
The new interpretation of arithmetic operation symbols
viXra, 2014
We introduce the permutation group of arithmetic operations symbols by getting the permutations of all the common arithmetic operations symbols, with keeping the brackets out of ordering. We find 6 ways of doing the arithmetic operations. Therefore the output of any mathematical formulas depends on which one element of the arithmetical permutation group we work on. We find invariants by the reordering of the arithmetic operation x+y, xy. Working with the irreducible representation of the permutation arithmetic symbols group we define new arithmetic structures called arithmetic particles symbols.