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<p>In recent decades, plural logic has established itself as a well-respected member of the extensions of first-order classical logic. In the present paper, I draw attention to the fact that among the examples that are commonly given in order to motivate the need for this new logical system, there are some in which the elements of the plurality in question are internally singularized (e.g. ‘Whitehead and Russell wrote <italic>Principia Mathematica</italic>’), while in others they are not (e.g. ‘Some philosophers wrote <italic>Principia Mathematica</italic>’). Then, building on previous work, I point to a subsystem of plural logic in which inferences concerning examples of the first type can be adequately dealt with. I notice that such a subsystem (here called ‘discrete plural logic’) is in reality a mere variant of first-order logic as standardly formulated, and highlight the fact that it is axiomatizable while full plural logic is not. Finally, I urge that greater attention be paid to discrete plural logic and that discrete plurals are not used in order to motivate the introduction of full-fledged plural logic—or, at least, not without remarking that they can also be adequately dealt with in a considerably simpler system.</p>
</abstract>

In recent decades, plural logic has established itself as a well-respected member of the extensions of first-order classical logic. In the present paper, I draw attention to the fact that among the examples that are commonly given in order to motivate the need for this new logical system, there are some in which the elements of the plurality in question are internally singularized (e.g. ‘Whitehead and Russell wrote Principia Mathematica’), while in others they are not (e.g. ‘Some philosophers wrote Principia Mathematica’). Then, building on previous work, I point to a subsystem of plural logic in which inferences concerning examples of the first type can be adequately dealt with. I notice that such a subsystem (here called ‘discrete plural logic’) is in reality a mere variant of first-order logic as standardly formulated, and highlight the fact that it is axiomatizable while full plural logic is not. Finally, I urge that greater attention be paid to discrete plural logic and that discrete plurals are not used in order to motivate the introduction of full-fledged plural logic—or, at least, not without remarking that they can also be adequately dealt with in a considerably simpler system.

In Defence of Discrete Plural Logic (or How to Avoid Logical Overmedication When Dealing with Internally Singularized Pluralities)

Disputatio

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In recent decades, plural logic has established itself as a well-respected member of the extensions of first-order classical logic. In the present paper, I...

In Defence of Discrete Plural Logic (or How to Avoid Logical Overmedication When Dealing with Internally Singularized Pluralities)

Published Online: Aug 29, 2022

Page range: 51 - 63

DOI: https://doi.org/10.2478/disp-2022-0004

Keywords
Classical first-order logic, discrete plurality, singular logic, solid plural logic, solid plurality

© 2022 Gustavo Picazo, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In Defence of Discrete Plural Logic (or How to Avoid Logical Overmedication When Dealing with Internally Singularized Pluralities)

Published Online: Aug 29, 2022

Page range: 51 - 63

DOI: https://doi.org/10.2478/disp-2022-0004

KeywordsClassical first-order logic, discrete plurality, singular logic, solid plural logic, solid plurality

© 2022 Gustavo Picazo, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Classical first-order logic, discrete plurality, singular logic, solid plural logic, solid plurality