Hobbes saw the purpose of the Leviathan as explaining the concepts of man and citizenship; he conceved of the work as contributing to a larger, three-pronged philosophical project that would explain nature in addition to these two phenomena. To begin his project, Hobbes argues that to understand the state we first need to understand mankind, since the state is nothing but an artificial man. To extend the metaphor, the sovereign of the state is like the soul of a man; the magistrates of the state like a man's joints; and the rewards and punishments doled out by the state like the nerves of man. According to Hobbes, the proper way to understand all men is to turn our thoughts inward and study one man (namely oneself), for to understand the thoughts, desires, and reasons of ourselves is to understand them in all mankind.
The natural starting point for understanding the thoughts of man is sense, since "there is no conception in mans mind, which hath not at first, totally, or by parts, been begotten upon the organs of sense." In other words, all thought and knowledge is in some way derived from our sensing the objects and matter of the external world. Central to the idea of sense is motion, for as Hobbes has laid out previously in his work on nature, the external world is nothing but a series of motions where objects chaotically interact with each other. Human beings, ourselves parts of the external world, are no different than these objects and interact with the external world through such motion. Specifically, when we sense objects, we do so because the motions of an object "press upon" or interact with our sensory organs, which in turns sets off another set of motions within our body that eventually end at our brain, and leave us with a feeling of the object sensed being hot or cold, loud or quiet, light or dark, etc.
The concept of motion explains how Hobbes goes from sense to what he calls "imagination" or "decaying sense." According to the prevailing Aristotelian physics during Hobbes' time, an object's natural state was rest. Yet Hobbes argued exactly the opposite: objects are constantly in motion, or to put it in Newtonian terms (which was to be later formulated 1687), an object in motion will remain in motion unless acted upon by an outside force. Now, after an object induces motion (and hence, sense) within us is removed, the feelings or impression it left us with do not automatically disappear. The motion set off by originally sensing this object gradually goes away, or decays, over time when some other sense or offsetting motion occurs. For example, you can still picture the image of something you experienced when your eyes are closed, and can still imagine a stove being hot even when you are not touching it. In other words, just because we are not directly sensing something does not mean that we have lost the feeling or impression it originally left us with. We can imagine things we no longer directly sense, and have memories of feelings past, which make up our experience.
While animals have, in some respect, memories and imaginations of their own, what distinguishes humans from other animals, according to Hobbes, is understanding or thought. Thought, or the transition from one imagination or memory to another, is not as random as it sometimes seems, and can be divided into two types: guided and unguided. Unguided thoughts, like those in a dream, may appear to be disconnected, but in reality are quick successions of thoughts connected by experience. For example, you might pass a hair salon and start to crave meatloaf. This might seem random at first, but if you think hard about a hair salon you might remember having to sit quietly at the salon in your hometown while your mom got her hair done; and having spoken to your mother earlier in the day, you might remember the meatloaf she made for you back as a child.
Regardless of how outlandish and random a thought may seem, Hobbes argues it can be traced back to a perfectly logical train of thought (which goes along with Hobbes' thesis about constantly interacting motions in our mind). Guided thought concerns ends and means, and can itself be divided into two subsets: 1) when we begin with a desire - or end - and think of what means will bring about this desired end, and 2) when we are in possession of some general means, and then think about what sorts of ends we can achieve with it.
Thoughts are internal, and the way we express thoughts is through speech, which helps us to remember our past thoughts and express them to others. Hobbes identifies four main uses of speech: 1) to remember cause and effect relations, 2) to show others our knowledge, 3) to express our will and desire to others, and 4) for sheer pleasure. Note that in all four cases, speech is conceived pragmatically. It is a practical instrument for expressing our thoughts to others.
Speech is also the basis of truth, as "truth consisteth in the right ordering of names in our affirmations." For example, "A man is a living creature" is a true statement, but only insofar as people share the same definitions of what the meanings of the words, "man," "is," and "living creature." We can see from this definition of truth the necessity of settling upon agreed definitions. Hobbes believes that geometry, "the only Science that it hath pleased God hitherto to bestow upon mankind," provides a model that philosophy should emulate. Specifically, geometry begins first by establishing agreed upon definitions, and from these proceeds logically through reason to build further principles and conclusions.
Additionally, Hobbes argues that truth, or the validity of reason, which he defines as the "Reckoning (that is, Adding and Subtracting) of the Consequences of generall names agreed upon," is not established because a great number of people agree upon something, or (contrary to Plato and his Philosopher King in The Republic) because a particularly enlightened person says so. No man's reason is infallible, and so man's reason should be trusted without proof. Therefore, reason - proceeding from one statement to the next in a logical order - can only be verified by oneself individually.
Thus, since definitions, truth, first-principles and reason cannot be founded upon natural science, general consensus or a particularly enlightened person, Hobbes argues that there must be some agreed-upon judge or body that establishes such things. One should note that establishing an agreed-upon body does not contradict Hobbes' earlier argument against truth by consensus. Hobbes objects to inherited or traditional forms of truth. In other words, something is not true for Hobbes simply because many people believe it to be true, or because it has been traditionally considered true. Truth for Hobbes, rather, must follow from consent. When people consent to join a larger body of truth, that larger body is legitimated. Foreshadowing his argument for an agreed-upon sovereign, Hobbes claims that establishing sovereignty by consent is the only way to avoid conflict among people.
Throughout Leviathan, Hobbes argues against the "Scholastic" philosophy of Aristotle. This is particularly the case in the early parts of Leviathan, where Hobbes argues directly against Aristotle's' philosophy of essentialism. According to this school of thought, objects in the external world have a certain "essence" that gives them the qualities that humans experience through their senses. For example, when we see a red apple there is an inherent "redness" to the apple that is transmitted to us through sense. Thus, there is some objective essence or meaning to objects that we experience. Contrary to this, Hobbes argues that our sensory experience is entirely subjective. He argues that to speak of any sort of essence like "redness" in the absence of an object is absurd, since we can only experience that which we can sense. When we see an apple we are not privy to some ethereal "redness," but instead just see a color that we have come to call "red." Following from this, what gives an object meaning is not some essence inhering in an object, but our own subjective experience of external bodies.
Hobbes' discussion of speech and truth is in stark contrast to philosophers like Plato who espouse universalism with regard to truth. According to these schools of thought, there is an objective truth that humans can know, which should serve as the basis for any philosophical system. Hobbes' argument that truth is a social construct and founded upon language has a anti-elitist strain to it, particularly his claim that no man's reason is infallible, regardless of how esteemed the man is, or how entrenched in tradition their thoughts may be. Hobbes argues that a human being can only know the world through his or her own sensing organs. Thus he or she is the only standard through which rational social organization can be measured.
One might think that because Hobbes' argument starts with sense, his philosophy should begin with natural science - that is, with definitions and first principles derived from our knowledge of the external world. Yet in defining sense as he has, Hobbes implicitly denies humans access to objective truth. We experience the external world subjectively, and contrary to Aristotle, do not experience some objective "essence" of external bodies. Since our knowledge of the external world is entirely subjective, it may differ from one individual to another, and thus the external world, for Hobbes, serves as a poor foundation for philosophy.
Hobbes' argument that all experience, and hence, all knowledge comes from sense can also be seen as an argument against innate knowledge, and for the tabula rosa (blank slate) model of the human mind. This model proposes that we enter the world without knowledge, and accumulate knowledge only through contact with external stimuli. Yet if the mind is nothing but a blank slate, how can we imagine things that we have never sensed? To use a famous counter-example, surely we can all imagine a unicorn - just take a horse and put a horn on it - even though they do not exist. How can this be? Hobbes argues that such imaginative entities are the result of "compounded imagination": i.e., you take two objects or qualities you have direct experience with (which is a form of your "simple imagination") and combine them in your mind to create this new image. Horn plus horse equals unicorn.
Finally, it's important to note that Hobbes' argument in the early parts of Leviathan unfolds like a geometric proof. Hobbes carefully defines terms like sense, memory, and reason, and proceeds step-by-step, each definition building upon the last. He sees geometry as the model by which all logic can be judged, and so follows suit. Some readers might sense a contradiction in this approach: Hobbes argues that truth can only be established by a common authority, so how can he ask us to accept his argument, which proceeds without such an authority but only from one man's (Hobbes' own) mind? In this regard, Hobbes invites the reader to 'bear with him' for the duration of the argument, and then to see if the conclusions and principles he derives make sense. In other words, Hobbes hopes that he can attain "common authority" in retrospect, once his arguments have been weighed and argued by society. However philosophically imperfect this may seem, in the absence of objective truths, this is the only way for any theory to proceed: people must temporarily grant the argument clout and judge it 'after the fact'. Thus, it is all the more important that Hobbes not merely advance conclusions that readers agree with, but rather show the validity of his reasoning through careful logic.