Furthermore, on the main issue we affirm briefly--if matter is extended, it is measurable; if it is measurable, it must have definite limits; if it has definite limits, it can not be infinite. Now that which is finite, limited, quantitive, conditioned, can not be self-existent, can not be infinite. Infinitude is illimitation by kind, quantity, or degree--illimitation by temporal, spatial, or numerical relations. An "infinite series" is therefore a contradiction _in adjecto_. "As every number, although immeasurably and inconceivably great, is impossible without _unity_ as its basis, so every series, being itself a number, is impossible unless a _first term_ is given as its commencement.... Even if it should be allowed that the series has no _first term_, but has originated _ab æterno_, it must always at each instant have a _last term_; the series as a whole can not be infinite."[117] If one thing more can be added to the number of existing things in the universe, then it is not infinite in number or in extent. In short, a series implies a succession of terms, or members, or links; if there is a last term, there must be a first term; if there is a last link, there must be a first. Through an Unconditioned First Cause, originating and conditioning all the members thereof, is a series conceivable or possible. To apply to number or quantity the designation of infinitude is surely _the_ "absurdity" in presence of which all others pale. We grant that the term "infinite series" is employed by mathematicians in a loose manner, to denote that which exceeds our powers of mensuration or conception, but which nevertheless has bounds or limits--the _indefinite_, but not the infinite;[118] such loose use of terms in philosophy, however, is inadmissible. The final reply of Dr. Mahan, "that the series under consideration is one which by hypothesis has no first," is the extreme of absurdity. It is as though a man should talk of a "round square" or a "bilinear figure," and when remonstrated with as to the contradictory character of these phrases, should reply, "Yes, but the 'square' under consideration is one which by hypothesis is 'round,' and the 'figure' is one which by hypothesis is formed by 'two lines!'" Men may make all kinds of strange hypotheses, but the strangest of all is that of an infinite-finite.