Skip to main content Accessibility help
×
Hostname: page-component-7bb8b95d7b-dtkg6 Total loading time: 0 Render date: 2024-09-13T23:19:32.558Z Has data issue: false hasContentIssue false

2 - Modalities

Published online by Cambridge University Press:  05 June 2012

John Woods
Affiliation:
University of British Columbia, Vancouver
Get access

Summary

[T]he bold bridgeheads seized by intuition must be secured, by thorough scouring for hostile bands that might surround … and destroy them.

Morris Kline, Mathematics: The Loss of Certainty, 1980

As widely understood, a modal logic is one whose logical particles include sentential operators that in their well-formed use inhibit the generality of substitution procedures. Among these we find the alethic modals, “necessarily” and “possibly,” the deontic modals, “it is permissible that,” and “it is obligatory that,” the epistemic modals, “it is known that,” and “it is believed that,” the causal modals “because,” and “it is causally sufficient that,” and the temporal modals, “at t,” “before t”; and so on. Modal systems are intensional. It is largely a matter of etymological advertence that a full-blown equivalence between the two has not taken root in our taxonomic practice, no doubt a reflection of the fact that not every category of syntactic element that makes a system intensional is, in the schoolboy's grammar of such things, a modal term. Still, there is nothing against the equation for those who find themselves drawn to it. In this more broadly conceived sense, a modal logic is one that sanctions any constraint that precludes full-bore extensionality. Seen in this broader way, modal logics include those made intensional by the English modals they embed, those made intensional by constraints required for relevance, and those made intensional by their recognition of semantic relations among elementary sentences.

Type
Chapter
Information
Paradox and Paraconsistency
Conflict Resolution in the Abstract Sciences
, pp. 40 - 79
Publisher: Cambridge University Press
Print publication year: 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • Modalities
  • John Woods, University of British Columbia, Vancouver
  • Book: Paradox and Paraconsistency
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511614002.004
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • Modalities
  • John Woods, University of British Columbia, Vancouver
  • Book: Paradox and Paraconsistency
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511614002.004
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Modalities
  • John Woods, University of British Columbia, Vancouver
  • Book: Paradox and Paraconsistency
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511614002.004
Available formats
×