Sentence examples for numerical sentences from inspiring English sources

And since these numerical sentences contain no vague vocabulary, it would seem to follow that it cannot be indeterminate how many things there are.

(The restriction to concrete objects ensures that numerical sentences aren't trivially false simply on account of there being infinitely many numbers, sets, and so forth).

(A numerical sentence is a first-order sentence asserting the existence of some objects. For example, the numerical sentence that there exist at least two objects is: ∃x∃y(x ≠ y).) If van Inwagen is correct, it is indeterminate whether or not the relevant numerical sentence is true, in which case one of the constituent expressions—'∃', 'x', 'y', '~', '=' must be vague.

And consider the numerical sentence (see section 4) which asserts the existence of (at least) one-million and one things.

Now consider the numerical sentence that asserts the existence of (at least) one-million and one objects.

For any finite number, one can produce a "numerical sentence" saying that there are exactly that many concrete objects.

Here, for instance, is the numerical sentence for two: '∃x∃y(x≠y & Cx & Cy & ∀z Cz→(x=z ∨ y=z)))'.

The proto-hammer definitely exists, but it is a borderline case of composition: it is indeterminate whether the handle and head compose the proto-hammer or whether they instead compose nothing at all (in which case the proto-hammer has no parts).[20] Alternatively, one might resist C2 by pinning the vagueness on the quantifiers in the numerical sentence.

Alasdair Urquhart (1986, 108) stresses "the extremely artificial nature of the attaching of precise numerical values to sentences like … 'Picasso's Guernica is beautiful'".

So quantitative probability may be viewed as essentially just a way of placing a numerical measure on sentences that uniquely emulates the is no more plausible than relation specfied by qualitative probability.

In accordance with certain rules, the machine then displays the shape "4" in a certain location on the monitor, and perhaps, if it is implementing the rule "the values of column B are to be twice the values of column A", it tokens the sentence "numerical value 8 in cell B1" and displays the shape "8" in another location on the monitor.