1. Hobbes is significant in the development of modern thought insofar as he is one of the first to follow out with considerable consistency a position marked by:

a purely materialistic and atomistic metaphysics/ontology, coupled with

an empiricist epistemology, coupled with

a demand for mathematical certainty in knowledge.

This results in a characteristically modern reductionism, i.e., the project of reducing earlier pluralisms to a monistic view, e.g.:

a reduction of a spectrum of knowledges and their appropriate levels of uncertainty/certainty (both in, e.g., Aristotle and the Medievals) to only the certainty apparently found in mathematics; coupled with

a reduction of consciousness (including earlier notions of free choice) to the mechanical/deterministic interaction of atoms -- i.e., a reduction of psychology to physics; resulting in

the reduction of all human behaviors, including ethics and politics, to the ostensibly value-neutral interaction of matter -- an interaction marked by human atoms in competition, resulting in "the war of each against all," resulting in the need for an absolute monarch to impose (arbitrarily chosen) "values" by way of force.

Yet this philosophy also encounters grave inconsistencies, e.g.,

the problem of consciousness (how does a "knower" of the world emerge from the mechanical chain of atomistic, cause-effect interactions?);

the related epistemological problem with Hobbes' doctrine of phantasms: if our consciousness is not of "things as they really are in themselves" (i.e., atoms in the push-pull mechanical world) but of phantasms that somehow result from atoms impacting one another -- how do we arrive at a certain knowledge of the world as it is (i.e., of atoms impacting one another)?

the anthropological/political problem of beginning with a conception of human nature as self-interested, desire-driven, and thus arational -- only to appeal to the rational insight that it is better to relinquish one's natural rights in a state of nature to an absolute sovereign -- whose decrees, in turn, rest on no rational insight (e.g., into the good, justice, etc.) but simply on arbitrary will.

For this question, begin by explaining Hobbes' philosophy more fully -- and then explain more fully at least one of the significant problems with Hobbes' philosophy. To do this efficiently, content yourself with a general survey of Hobbes' views, but a more detailed exposition of those views which are pertinent to the problem you then turn to.

2. Descartes ostensibly sets out to achieve certainty in the swirl of uncertainty characterizing the religious and political upheavals of the Reformation and Renaissance. This project

begins with the acid bath of radical doubt, one which reduces all knowledge to either the absolutely certain or the false, which leads to

an epistemological (mythic?) journey in which Descartes soon leaves behind all the usual candidates for knowledge (sense, imagination, even reason) as these fail to stand up to the demand for absolute certainty (remember God as the evil genius!) -- so that

Descartes arrives at the (thinking) self as the (epistemological and ontological) center. The philosophical (mythic?) task is then to return to the world --

a return which entails, first, a proof for the existence of God, and then

secondly, the assurance that at least our mathematical conceptions of the world as revealed to us by the senses can be trusted.

In more abstract terms, however, this journey begins with

a radical epistemological dualism (a claim is either absolutely certain, or merely false), which issues in

a radical ontological dualism -- the unextended, thinking self as (problematically) divorced from the extended, thinking world of material substance.

OPTIONS:

a) Explain Descartes' philosophical journey more fully, with a view towards contrasting his philosophical idealism with Hobbes' ruthless materialism. This contrast should include comment on

i) their differences regarding ideas, including ideas of number

[i.e., the contrast we've discussed in terms of whether mathematical entities exist independently of the mind and are discoverd {idealism} or are arbitrary inventions imposed on the world {materialism}]

and such ethical and political notions as "good," "justice," etc.

[i.e., contrast Hobbes' nominalism, with the result that the absolute sovereign is free to impose any set of "values" arbitrarily upon a people, because "values" do not exist in any strong sense in a purely materialistic universe, vs. Descartes' {at least apparent} belief in a God, goodness, etc.]

b) Explain Descartes' philosophical journey more fully, with a view towards pointing out how Descartes, as "the father of modern philosophy," establishes

i) the epistemological foundations for modern science (as focusing first of all on mathematics and quantitative modes of knowledge as the only reliable source of certain knowledge), coupled with

ii) the ontological foundations for modern technology, as the human project of the mastery and possession of nature - a project resting on Descartes' strongly dualistic separation between the rational self and the world of the senses (including "nature"), and

the theomorphic theme of his philosophy, whereby the human self is reimaged in terms traditionally associated with God -- e.g., as possible creator of nature, as possessed of infinite will, etc.

and thereby lays the foundation for our contemporary environmental crisis. You may want to comment here how far you see folk around you and the culture at large as indeed assuming a Cartesian epistemology and ontology, and thus the rightness of the modern technological project of treating nature as an object to be mastered and possessed by a superior humanity.