We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
An Investigation of the Laws of Thought Published online by Cambridge University Press: 05 November 2011
EXAMPLE OF THE ANALYSIS OF A SYSTEM OF EQUATIONS BY THE METHOD OF REDUCTION TO A SINGLE EQUIVALENT EQUATION V = 0, WHEREIN V SATISFIES THE CONDITION V (1 − V) = 0.
1. Let us take the remarkable system of premises employed in the previous Chapter, to prove that “Matter is not a necessary being;” and suppressing the 6th premiss, viz., Motion exists,—examine some of the consequences which flow from the remaining premises. This is in reality to accept as true Dr. Clarke's hypothetical principles; but to suppose ourselves ignonorant of the fact of the existence of motion. Instances may occur in which such a selection of a portion of the premises of an argument may lead to interesting consequences, though it is with other views that the present example has been resumed. The premises actually employed will be—
If matter is a necessary being, either the property of gravitation is necessarily present, or it is necessarily absent.
If gravitation is necessarily absent, and the world is not subject to any presiding intelligence, motion does not exist.
If gravitation is necessarily present, a vacuum is necessary.
If a vacuum is necessary, matter is not a necessary being.
If matter is a necessary being, the world is not subject to a presiding intelligence.
If, as before, we represent the elementary propositions by the following notation, viz.:
x = Matter is a necessary being.
y = Gravitation is necessarily present.
w = Motion exists.
t = Gravitation is necessarily absent.
z = The world is merely material, and not subject to a presiding intelligence.
v = A vacuum is necessary.
To save this book to your Kindle, first ensure no-reply@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.
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.
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.