Who is Jacques Derrida and what does he want?? In one sense, we all 'know' who Jacques Derrida is. Derrida is the idealist who thinks that the whole world is a text. Derrida is the guy who thinks that philosophy is just another type of literature. Derrida is the fellow who claims that writing comes before speech.
So many false assumptions and second hand opinions circulate in relation to Jacques Derrida and the intervention popularly known as deconstruction, that it's difficult to know where to begin. I can only ask you to perform a sort of 'bracketing' of everything you think you know about deconstruction, in order to focus on what Derrida actually says.
There are a number of reasons why we should pay attention to Derrida. For if deconstruction is right, then we have yet to think collectively. We have yet to draw the full consequences from our social being. And we have yet to theorise praxis from a position that is not tied to what Derrida calls the metaphysics of subjectivity.
Derrida also exposes the political consequences of some apparently marginal philosophical assumptions. One of Derrida's arguments is that we should not underestimate the power and rigour of philosophy. All attempts to 'defend' philosophy by attacking the 'irrelevance' of Derrida's interventions would in fact reflect rather poorly on the standards of logical argument we presume philosophers to have. Another one of Derrida's arguments is that these assumptions are not 'mistakes' that can be corrected, but in fact are vital to the logical consistency and argumentative power that we expect from philosophy.
Deconstruction is not about writing, or difference. Nor is it about how any totality is surrounded by "an irreducible surplus of meaning". Deconstruction involves an inquiry into the conditions of possibility and impossibility of philosophy. It is a question of uncovering what Derrida calls "a type of 'structural unconscious' ... which seems alien, if not incompatible with [philosophy] given its current axiomatics".  This 'structural unconscious' - différance - provides the transcendental conditions of possibility and impossibility for philosophical rigor. Yet it is not a question of a critique in the Kantian sense - a delimitation of the legitimate employment of reason - nor a project of landing in some region 'beyond metaphysics' (say, for instance, science). For Derrida, philosophy - including speculative totalisation - is both rigorous and necessary. It is also erected upon a series of blindspots that render the quest for truth of philosophy deeply problematic. These problems are intractable. There is a politics associated with the solutions to these problems. It is therefore a question of inscribing philosophy within a field that exceeds it, that makes it possible as an activity and simultaneously undermines its foundations, and that explains the political stakes involved in the apparently natural gestures by which philosophy produces concepts. Derrida somewhere says that this field - différance - could be called history, were it not for the teleological resonances of that term.
This would be, for instance, a non-totalisable history. That is not to say that totalisation - as an operation involving a summing up relative to the expectation of meaning from some interpretation or a determination of the factors essential to some project - is not a valid and necessary procedure. Derrida remarks in Of Grammatology that the point of intervention of a deconstructive reading is the outcome of an historical hermeneutics, ie. a determination of the meaning of a region of history for the purposes of intervening against injustice. It is simply that this totalisation is never the totality.
This is the main reason why deconstruction views Hegel as the key antagonist. Hegel's work, Derrida argues, occupies an ambivalent position within the history of Western philosophy. On the one hand, "he undoubtedly summed up the entire philosophy of the logos. He determined ontology as absolute logic; he assembled all the delimitations of philosophy as presence; he assigned to presence the eschatology of parousia [spirit], of the self-proximity of infinite subjectivity".  At the same time, however, Hegel announces the advent of the closure of metaphysics. Hegel is the philosopher who begins to think irreducible difference and tries to hold this difference within the logic of the unfolding of an "identity of identity and difference". With the Hegelian argument that it is only in the medium of language that intersubjective community is possible, language begins to invade the heart of the problems of philosophy. This will make possible a thinking which will seek to no longer be governed by the search for a 'transcendental signified' guaranteeing the transmission of meaning, knowledge and truth without remainder. Hegel therefore appears as "the last philosopher of the Book and the first philosopher of writing".  This determines the strategic character of deconstruction's intervention into speculative dialectics. "If there were a definition of différance," Derrida notes, "it would be precisely the limit, the interruption, the destruction of the Hegelian dialectical synthesis wherever it operates". 
Derrida's concern is ethical. In the words of Simon Critchley: "can philosophical dialectics approach the otherness of the other, that is to say, can it entertain an alterity that cannot be comprehended or reduced to an object of cognition or recognition?".  Or, as Derrida puts it in Of Grammatology, "logocentrism is nothing but the most original and powerful ethnocentrism".  This ethnocentrism is expressed principally in the persistent tendency for philosophy to ratify as de jure what is in reality de facto. In the context of the 'will to totality' of philosophy - including the drive to logical coherence and rhetorical consistency that constitute philosophy as rigorous and necessary - this means the triumph of the positivity of knowledge and being over the negativity of dispersion and non-existence. Hegel's dialectic - with its guarantee that within the 'rememoration of world history,' that is to say, the recuperation of the meaning of history from the fragments of historical events - represents a prime exhibit of this tendency. Within the dialectic, negation as determination preserves the totality of meaning and transmits it from one moment to the next, without remainder.
But for Derrida there is something laughable about the pompous seriousness of the Hegelian negative. In, for instance, the master/slave dialectic, this negative huffs and puffs with the business of the 'struggle to the death for recognition' whilst secretly guaranteeing that real death, death as finitude and the simple absence of meaning, is excluded from the start, since "death is the natural negation of consciousness, negation without independence, which thus remains without the required significance of recognition".  Death fails to signify meaningfully and is therefore excluded from the dialectical synthesis. Like the peoples 'without history' and those with a non-phonetic writing, it simply drops out of the equation, enabling the speculative totalisation of world history and the condition of mutual recognition. At the same time, it allows philosophy to be both the agency of death and the vehicle for immortality, that is to say, to speak the master discourse of the overcoming of human finitude.
Central to this 'structural unconscious' driving the axiomatics of philosophy is the assumption of the priority of speech over writing, which underpins what Derrida has called 'logocentric metaphysics'. To think logocentrically, according to Derrida, is to dream of a 'transcendental signified,' a meaning outside and beyond the differential play of language that would stop the potentially infinite process of interpretation and guarantee the transmission of meaning. The assumed priority of speech is based on the myth of the complete coincidence of meaning and intention in the moment of 'hearing/understanding oneself speak,' where the living voice guarantees the mutual understanding (and self-understanding) of persons. By contrast, the dead letter of writing - where the author is no longer present to govern the transmission of the meaning of the text via the voice of authorial intention - can only, for philosophy, present the disastrous spectacle of a meaning that permanently threatens to go astray. This works itself out in Hegel's philosophy as the privilege granted to phonetic script over other forms of writing.
Spirit, for Hegel, must externalise itself in its other (nature and humanity) to truly know itself. The medium for this self recognition is language. Hegel's treatment of language is not a subjective mistake under the influence of his time, but completely consistent with the tradition of Western philosophy since Plato and internally necessary to his system of absolute idealism. Hegel determines speech as the natural state of language and concludes that phonetic writing is a faithful transcription of the voice, while non-phonetic writing - hieroglyphics, for instance - as that which has no clear relation to the living voice and requires deciphering, is beneath the interest of philosophy. For it is only in spoken language, and the phonetic writing that faithfully records the intentions of the author, that there is this apparently ideal coincidence of meaning and intention. Hieroglyphics fails to make this passage by way of the 'natural' bond between voice, self-present intention and the meaning of a discourse.
Hegel is confusing the natural attitude where intention governs meaning with the logical basis for communicative acts. But there is in phonetic writing that which is non-phonetic: an irreducible graphic component, including a differential spacing, which is marked by the arbitrariness of notational conventions. This worries Hegel. When he comes to Leibniz's project of a logical calculus expressed in written form, Hegel dismisses this as an exaggeration of the 'practical mind'. What the 'practical mind' fails to grasp is the necessity for the concept to pass by way of the natural link between sound and sense as captured by phonetic language ie. the speculative and idealist aspect of Hegel's treatment of language.
In order to deepen this appreciation of what Derrida is driving at and its implications for dialectics, we have to pursue him further into the deconstruction of the idealism of the bond between speech and intention. For Derrida is not trying to 'rehabilitate' writing. He is delving into what grounds the difference between speech and writing and makes this opposition possible whilst simultaneously undermining it.
In Derrida's engagement with 'ordinary language philosophy' we encounter again the elevation of the natural attitude into a metaphysics of communication with normative overtones. In response to Derrida's demonstration of the lack of a transcendental signified at the center of any structure - and the consequent inability to make a final delimitation of context for any enunciation or an ultimate determination of the meaning of an utterance - the English philosopher John Searle accused Derrida of a destruction of meaning and a denial of the obvious pragmatic character of communicative acts. Any written or spoken interaction, Searle argued, is governed by the fact that it is an attempt to communicate a meaning. The very fact that there is meaning - that it can be spoken of - implies that the speaker's intention or the context of writing limit the possible spread of meanings. Indeed, Searle claimed, it makes it possible to determine the meaning of a discourse.
But this is to miss entirely the point of Derrida's intervention. For ordinary language philosophy, the 'pragmatic character of communicative acts' is famously separable into the 'performative' element - the practical action performed by an utterance - and the 'constative' element - the substantive meaning conveyed by the signifying chain. 'I baptise this ship Titanic' performs the launching of the ship while announcing the constative meaning that its name will be 'Titanic'. This is supposed to fix speech-acts outside of any 'reduction' to a semiotic theory of meaning, for while the constative value of an utterance remains under the sign of the intention of the speaker, the performative value of the speech act has to be located within a precise context. (Speech act theory talks of the "total context".) Yet Derrida's argument is that this performativity of a speech act represents a kind of ritual that is the very definition of something that can be carried outside of any given context and repeated indefinitely. "The performative is a 'communication' which is not limited strictly to the transference of a semantic content that is already constituted and dominated by an orientation towards truth".  This argument can be applied to constatives as well, insofar as the act of speech is accompanied by the performative force of the gesture of communication. This 'iterability' of a speech act is not the deviant property of a handful of social rituals but the precondition for language to signify: for if speech acts were not in principle iterable, then the communicative value of words would be so context-dependent that only the speaker could know what was meant. It is this generalised iterability of all speech acts, however, that determines that no final delimitation of the context of an utterance can be made.
It is this 'generalised iterability' that makes the difference between performatives and constatives possible, while at the same time rendering the precise specification of that difference unsustainable. It is this 'generalised iterability' that I want to turn to now, since it is only the moment of the reinscription of the binary opposition within the field of these 'quasi-transcendental' structures - like arche-writing, supplementarity, différance and generalised iterability - that breaks with dialectics. This is what deconstruction is 'really' all about.
To grasp what is happening with the production of these 'conditions of possibility and impossibility' we have to turn to Derrida's early work, where he deconstructs the works of the philosopher who, for Derrida, is the "greatest since the Greeks" - Edmund Husserl. Husserlian phenomenology took a stand against the prevalent relativism of the first part of the twentieth century and the relegation of philosophy to a minor place in the field of the 'human sciences'. Husserl argued that there was a crucial distinction to be made between the fact that some empirical content was presented to consciousness and the essential characteristics of what was presented. By bracketing all natural assumptions and theoretical constructions of the phenomenon (even to the point of suspending belief in the existence of the external world) Husserl claimed to be able to zero in on the productive act of consciousness as it produced both cultural categories of experience and the perception of the empirical contents. Thus, whatever the causes of experience and belief discovered by scientific investigation, such discoveries cannot affect the intrinsic meaning of phenomena, as these are initially revealed to consciousness. This unprejudiced description of the essential structures of experience will constitute a new, rigorous science of philosophy that will place the empirical sciences and the humanities on a self-certain basis. Husserl claimed to be producing not a description of this or that culture's transcendental categories but of the transcendental act by which any culture could possibly conceive of a history, a culture and a science.
Now, Derrida, in his introduction to Husserl's Origins of Geometry agrees with the anti-relativist thrust of Husserl's procedure. Implicitly arguing against structuralism, with its objectivist reduction of meaning to an effect of the differential relationships between terms in a structure and its consequent flattening of the subject onto 'subject positions' within structural locations, Derrida argues that "the notion of structure presupposes at least a rigorous delimitation of prior regions [of experience], and this elucidation of the meaning of each regional structure can only be based on a phenomenological critique. The latter is always first by right ..." 
This approach is equally in evidence later on, for instance when Derrida accuses Foucault of failing to grasp that the Cartesian cogito has the status of a productive act of consciousness, as the "zero point where determinate meaning and non-meaning join in their common origin".  Or in Grammatology, where Derrida argues that the linguist Hjelmslev has failed to pose the question of the "condition of all linguistic systems". Hjelmslev remains on the terrain of the natural attitude and its contamination of philosophical rigor by the empirical materials of this or that linguistic prejudice. "The parenthesizing of regions of experience or of the totality of natural experience must discover a field of transcendental experience. This experience is only accessible insofar as after having, like Hjelmslev, isolated the specificity of the linguistic system and excluded all the extrinsic sciences and metaphysical speculations, one asks the question of the transcendental origin of the system itself."  As late as the 1974 interview Positions, Derrida is arguing that "what I first learned about this critique [of relativism] from Husserl ... seems to me to be valid in its argumentative schema". 
However, this is only a part of Derrida's argument, since he also directs his investigation towards the "un-thought out axiomatics of the Husserlian phenomenology". IN Husserl's Origins of Geometry, Husserl concludes that writing is a necessary condition for the transmission of the ideal objectivity of scientific principles. This is because it is only by the detachment from any actual subjectivity that writing makes possible that the objectivity and communicability that constitute the scientific status of science can be achieved. "Speech," Derrida writes, "is no longer simply the expression of what, without it would already be already an object, caught in its primordial purity: speech constitutes the object and is a concrete juridical condition of truth. Without the fall back into language and thereby into history, a fall which would alienated the ideal purity of sense, sense would remain an empirical formation imprisoned in as fact in an actual subjectivity - in the inventor's head. Historical incarnation sets free the transcendental instead of binding it. This last notion, the transcendental, must then be rethought." 
Indeed, for Derrida, the presence of speech in the constitution of ideal objectivity - entailing a relationship between the speaking subject and language, alterity and time - means the introduction of difference into the supposedly self-present origin of consciousness. Husserl's attempt to erase the 'external' and 'indicative' functions of language through a series of bracketings which culminate in a self-addressed inner voice of consciousness, is condemned to failure. There is no domain of 'phenomenological silence' prior to the representational (hence divisive) workings of language. Furthermore, this 'intrusion' of facticity is linked to the failure of present consciousness to be a point like apprehension of the "Living Present". When Husserl admits that present consciousness is inseparable from future and past - modes of awareness that are neither the representation of absence nor the intuition of presence, then the immediacy of self-presence, upon which Husserl's conceptions of evidence and truth depend, is revealed as an illusion ie the collapse of Husserl's project. The conclusion flows necessarily: "difference would then be transcendental". In other words, the permanent evidential gap within phenomenology itself, which appears as the result of the intrusion of facticity and historicity, is the effect of a transcendental structure more fundamental than consciousness. This, I would suggest, is what Derrida earlier in my presentation alluded to as a 'structural unconscious'.
Derrida calls this 'structural unconscious' différance, which is a neologism combining implications of differing and defering (amongst five possible functions), but which, is only a written mark, without meaning or direct existence. It is the movement of différance - and its other correlative quasi-transcendentals - that produces the transcendental subject as the subject in and of language and history. It is this chain of quasi-transcendentals that opens, "in one and the same possibility, temporalization as well as the relationship with the other and language".
Deconstruction proceeds by a "double gesture" - a phase of reversal and a phase of reinscription or displacement. Deconstruction starts with an interrogation of a variety of contradictions or aporias in the discourse of philosophy. These are not contradictions or aporias proper, however, since the discourse of philosophy accomodates them without difficulty. All these aporias, differences of levels, inequalities of development and disparities characteristic of the discourse of philosophy yet do not seem to disturb the logic of philosophy - indeed, they are necessary to the establishment of that (indispensible) logic. All the gestures of philosophy - reflection and transcendentality, especially themes of subjectivity, transcendentality, freedom, origin, truth, presence and the proper - are impossible without the differences and discrepancies that permeate the texts of philosophy. Yet these same disparities also limit the scope of these gestures and the purity and coherence of the philosophical concepts and themes.
Deconstruction is an attempt to account for these heterogeneous aprorias and discursive inequalities using quasi-transcendentals, like différance. These minimal structures are both the grounds of possibility of totalisation and the constitution of philosophical concepts, and their ungrounding in the play of signification within a non-delimited context. These structures limit what they make possible by rendering its rigor and purity impossible. Deconstruction does not merely set itself to destroy metaphysical concepts; it shows how metaphysics draws its possibility from that which makes it impossible.
Derrida demonstrates this through the movement of textuality that he calls 'dissemination'. Dissemination is not 'uncontrolled freeplay' but a carefully controlled demonstration of the repressed semantic possibilities of any 'text' - of any experience - which arises at the "zero point where determinate meaning and non-meaning join in their common origin'. This is different to hermeneutics, with its potentially infinite process of interpretation. For hermeneutics, the recovery of meaning always takes place within a horizon of the expectation of meaning. Derrida raises the possibility of bursting this semantic horizon with the possibility that non-meaning might be inextricably intertwined with meaning. There is a strongly existential overtone to this demonstration.
Likewise, dissemination is different to structuralist interpretation, which in Derrida's terms, reduces meaning to the effect of structure. Différance, Derrida has argued, is about what escapes the metaphysical reduction to language on the model of ideal communication. It is not about, as some have argued, a misrecognition of discourse as composed solely of diacritical marks, as if the positive existence of words whose historically sedimented (multiple) meanings might be the other of the differential structure of language, had gone over Derrida's head. Derrida insists, time and time again, that the purpose of deconstruction is precisely to pay attention to this historical and pragmatic character of language.
Finally, it is not the same as speculative totalisation through Hegelian dialectics. It is about what is heterogeneous to the ideality of meaning and to the assimilation of being to thinking. Its demonstration that language is not the inert medium for the transmission of thought but - as an intersubjective medium shaped historically and pragmatically - contains that which exceeds the intentions of the supposedly self-conscious subject. It explodes speculative totalisation.
It is closest to Marxism and psychoanalysis. This is not to say that the paradoxes identified by Derrida would simply vanish from a sociological perspective. For while the relationship to Husserl suggests that deconstruction is locating the effects of praxis at the level of consciousness, Derrida's point would surely be that the thinking of praxis can only proceed through Western metaphysics. It is at that level that praxis itself has to be rethought.