Questions 40-67

Query 40. Whether it be not a general Case or Rule, that one and the same Coefficient dividing equal Products gives equal Quotients?

And yet whether such Coefficient can be interpreted by o or nothing? Or whether any one will say, that if the Equation 2 × o = 5 × o, be divided by o, the Quotients on both Sides are equal? Whether therefore a Case may not be general with respect to all Quantities, and yet not extend to Nothings, or include the Case of Nothing? And whether the bringing Nothing under the Notion of Quantity may not have betrayed Men into false Reasoning?

Query 41. Whether in the most general Reasonings about Equalities and Proportions, Men may not demonstrate as well as in Geometry? Whether in such Demonstrations, they are not obliged to the same strict Reasoning as in Geometry? And whether such their Reasonings are not deduced from the same Axioms with those in Geometry? Whether therefore Algebra be not as truly a Science as Geometry?

Query 42. Whether Men may not reason in Species as well as in Words? Whether the same Rules of Logic do not obtain in both Cases? And whether we have not a right to expect and demand the same Evidence in both?

Query 43. Whether an Algebraist, Fluxionist, Geometrician or Demonstrator of any kind can expect indulgence for obscure Principles or incorrect Reasonings?

And whether an Algebraical Note or Species can at the end of a Process be interpreted in a Sense, which could not have been substituted for it at the beginning? Or whether any particular Supposition can come under a general Case which doth not consist with the reasoning thereof?

Query 44. Whether the Difference between a mere Computer and a Man of Science be not, that the one computes on Principles clearly conceived, and by Rules evidently demonstrated, whereas the other doth not?

Query 45. Whether, although Geometry be a Science, and Algebra allowed to be a Science, and the Analytical a most excellent Method, in the Application nevertheless of the Analysis to Geometry, Men may not have admitted false Principles and wrong Methods of Reasoning?

Query 46. Whether although Algebraical Reasonings are admitted to be ever so just, when confined to Signs or Species as general Representatives of Quantity, you may not nevertheless fall into Error, if, when you limit them to stand for particular things, you do not limit your self to reason consistently with the Nature of such particular things? And whether such Error ought to be imputed to pure Algebra?

Query 47. Whether the View of modern Mathematicians doth not rather seem to be the coming at an Expression by Artifice, than the coming at Science by Demonstration?

Query 48. Whether there may not be sound Metaphysics as well as unsound? Sound as well as unsound Logic? And whether the modern Analytics may not be brought under one of these Denominations, and which?

Query 49. Whether there be not really a Philosophia prima, a certain transcendental Science superior to and more extensive than Mathematics, which it might behove our modern Analysts rather to learn than despise?

Query 50. Whether ever since the recovery of Mathematical Learning, there have not been perpetual Disputes and Controversies among the Mathematicians? And whether this doth not disparage the Evidence of their Methods?

Query 51. Whether any thing but Metaphysics and Logic can open the Eyes of Mathematicians and extricate them out of their Difficulties?

Query 52. Whether upon the received Principles a Quantity can by any Division or Subdivision, though carried ever so far, be reduced to nothing?

Query 53. Whether if the end of Geometry be Practice, and this Practice be Measuring, and we measure only assignable Extensions, it will not follow that unlimited Approximations compleatly answer the Intention of Geometry?

Query 54. Whether the same things which are now done by Infinites may not be done by finite Quantities? And whether this would not be a great Relief to the Imaginations and Understandings of Mathematical Men?

Query 55. Whether those Philomathematical Physicians, Anatomists, and Dealers in the Animal Oeconomy, who admit the Doctrine of Fluxions with an implicit Faith, can with a good grace insult other Men for believing what they do not comprehend?

Query 56. Whether the Corpuscularian, Experimental, and Mathematical Philosophy so much cultivated in the last Age, hath not too much engrossed Mens Attention; some part whereof it might have usefully employed?

Query 57. Whether from this, and other concurring Causes, the Minds of speculative Men have not been born downward, to the debasing and stupifying of the higher Faculties? And whether we may not hence account for that prevailing Narrowness and Bigotry among many who pass for Men of Science, their Incapacity for things Moral, Intellectual, or Theological, their Proneness to measure all Truths by Sense and Experience of animal Life?

Query 58. Whether it be really an Effect of Thinking, that the same Men admire the great Author for his Fluxions, and deride him for his Religion?

Query 59. If certain Philosophical Virtuosi of the present Age have no Religion, whether it can be said to be for want of Faith?

Query 60. Whether it be not a juster way of reasoning, to recommend Points of Faith from their Effects, than to demonstrate Mathematical Principles by their Conclusions?

Query 61 Whether it be not less exceptionable to admit Points above Reason than contrary to Reason?

Query 62. Whether Mysteries may not with better right be allowed of in Divine Faith, than in Humane Science?

Query 63. Whether such Mathematicians as cry out against Mysteries, have ever examined their own Principles?

Query 64. Whether Mathematicians, who are so delicate in religious Points, are strictly scrupulous in their own Science? Whether they do not submit to Authority, take things upon Trust, believe Points inconceivable? Whether they have not their Mysteries, and what is more, their Repugnancies and Contradictions?

Query 65. Whether it might not become Men, who are puzzled and perplexed about their own Principles, to judge warily, candidly, and modestly concerning other Matters?

Query 66. Whether the modern Analytics do not furnish a strong argumentum ad hominem, against the Philomathematical Infidels of these Times?

Query 67. Whether it follows from the abovementioned Remarks, that accurate and just Reasoning is the peculiar Character of the present Age? And whether the modern Growth of Infidelity can be ascribed to a Distinction so truly valuable?

FINIS.