Some of the bitterest debates surrounding object-oriented ontology have unfolded around the idea of the reality of fictions. In all fairness, this has largely been my fault, rather than Graham’s. Harman has only maintained that fictions have the status of sensual objects rather than real objects. Within the framework of Graham’s object oriented philosophy, the claim that fictions are sensual objects is the claim that fictions can only exist on the interior of other, real, objects. For Graham, Popeye, for instance, can only exist on the interior of a real object such as my mind. Where I am able to exist independently, Popeye is only able to exist so long as I, the person who thinks Popeye, exists.
The thesis of my onticology, by contrast, has been that fictions are real entities in their own right. What I wish to claim, with my flat ontology, is that fictions are every bit as real as, for example, Popeye (or better yet, Twilight). This follows from my ontic principle developed in my article for The Speculative Turn. There I argue that any difference that makes a difference has a claim to reality. Clearly, when I’m claiming this, I’m not arguing that there is a physical entity like Popeye that eats, can punch people, gets strong when he eats spinach, etc. Popeye is real qua fictions. Nonetheless, Popeye the fiction is a real entity insofar as this fictional entity produces real differences within the world. In the case of Twilight, young women might model their amorous relations on these fictions. As a consequence, these fictions have real ontological efficacy in the world. They produce real differences. And honestly, why would we go to the trouble of critiquing so much myth and ideology if myths and ideologies were not genuinely efficacious in the world?
For me, the whole point of asserting the reality of fictions lies in theorizing the reality of the symbolic. My interest is not in fictions such as myths, novels, poems, and ideologies per se, but rather in theorizing how it is possible for symbolic entities such as money, social conventions, social identities, etc, can have a genuine reality. In my view, fictions provide a limit case for theorizing signs, symbols, and conventions in their purity. These entities, I believe, are irreducible to either the subjective (they’re never up to the whim of a particular individual mind), nor the objective. Put differently, they are neither physical objects like rocks, nor mental contents like mere imaginings. Money is not a thing nor is it merely an idea in the mind of a particular person.
Saussure, in his Cours, drove this point home with particular clarity when he wondered how it is possible for the four o’clock train to be late while remaining the four o’clock train. Clearly “being the four o’clock train” cannot be a physical quality of the four o’clock train because it is late yet remains the four o’clock train. Likewise, the four o’clock train can be a different physical train on Wednesday and Friday, yet still remain the four o’clock train. Finally, whether or not the four o’clock train is the four o’clock train has nothing to do with what individual minds believe. The four o’clock train is an objective reality independent of individual minds and physical properties, and therefore falls into a third class of entities: the symbolic. I outlined all of this long ago in 2006 in my post on the diacritical production of identity. My thesis now is that if we wish to theorize symbolic entities then we have to do so through a theory of fictions because fictions give us the most compelling case of symbolic entities that are neither physical entities nor subjective entities, but which nonetheless are real entities. Here I faithfully follow not only the Stoics and Epicureans in their claims about simulacra, nor do I simply follow Plato in his analogy of the divided line where he surprisingly grants images ontological reality, but I also follow Deleuze’s profound meditations on the reality of fictions in Difference and Repetition, The Logic of Sense, and Cinema II: The Time Image. As Deleuze argues in The Logic of Sense, it is above all necessary for us to discover a surface of sense, independent of propositional states and referents, that has a reality in its own right.
read on!
However, while drawing inspiration from all these trends, I also draw inspiration from symbolic logic. It is here that I draw particular inspiration from the logic or truth tables of material conditionals. A material conditional is an “if/then” statement. Here’s an example:
If Shamu is a whale, then Shamu is a mammal.
Shamu is a whale
Therefore Shamu is a mammal.
A material conditional has the form “P —> Q”. Now here’s what’s interesting about material conditionals: The only circumstance in which a material conditional is false is that circumstance in which its antecedent (P) is true and it’s consequent (Q) is false. In all other circumstances, material conditionals are true. Thus if the antecedent (P) is false and the antecedent is true the material conditional (P —> Q) is true. Likewise, if the antecedent of a material conditional is false and the consequent of a material conditional is false, then the material conditional as a whole (P —> Q) is true. I won’t bore you with all the details of why this is the case, as it involves a lot of logical equivalences between propositions. For the moment I will take it as face value.
Now there are a couple of points that follow from these points about material conditionals. First, the truth-functional logic that follows from the logic of material conditionals gives, at least, epistemological grounds for treating fictions as real. Ontologically fictions should be treated as real (not true) precisely because they are capable of producing truths despite being false. This entails that ideologies, delusions, fictions (works of art, narratives, novels, myths, religions) have a capacity to produce truth even though they are false. My second point is that this, in my view, calls into question the project of representational realism, eliminative materialism, or scientism where realist ontology is concerned. The representationalist, scientistic, or eliminativist wants to claim that truth can only be produced if the antecedent of a material conditional is true. If the truth produced by a literary work or a political movement based on fictional ideology, mythology, or religion (Martin Luther King’s religious belief for example) is false, the representational realist is necessarily committed to the thesis that such a political or ethical transformation can have no truth.
So here’s what I want to say: If the representational realist, the eliminative materialist, or the scientistic philosopher is truly committed to such a thesis, I want to see the thorough revision of symbolic logic that they develop to account for such a metaphysical position. In advancing such an argument, let’s remember that the so-called scientistic thinker and eliminative materialist is committed to rational account of inquiry, norms governing discourse, and all the rest. That’s what Brandom, after all, tells us. And this is what their “truth-functional” reason is committed to. So given the key role that material conditionals play in our foundations of mathematics (let’s remember all our Ladyman and Ross, our Sellars, our Brandom and how they wax on about norms and reason) and our sciences, are they willing to sacrifice the material conditional? Have they revised symbolic logic in such a way that they’re willing to sacrifice all the fruitful work that the material conditional and biconditional have accomplished? Will they rise to the challenge of giving us the new symbolic logic that refuses the possibility of a material conditional containing a false antecedent producing a true proposition? Inquiring minds want to know. So far I’ve only seen assertions, peppered with lots of truculent language and obscurantist reasoning (Laruelle) parading in the posture of rigor, but I have not seen this reworking of the basic principles of reason. So where is it?
I will also say that if these points about the material conditional are true– and it’s deeply painful for me to confess this –then our ideas of critique must be significantly transformed. If it is true that a false antecedent can produce a true proposition, then I can no longer inveigh against ideology, religion, mythology, fiction, etc., in the way I have in the past, and all the rest because all of these fictions (if they are fictions) have the power to produce the true. If that’s the case, then the question of whether or not something is an ideological mystification (a fiction, a myth, a religious belief) is largely irrelevant. The question then becomes that of whether or not that fiction is nonetheless capable of producing truth. I lack the resources to rework the foundations of mathematical logic, so I am unable to renounce the thesis that fictions can produce truth. Therefore, I am obligated to thoroughly– along Lacanian lines –rework the notion of what critique might be. I’ll stop there.
Larval Subjects . 
March 8, 2011 at 4:49 am
I would like to understand what you specifically mean by ‘capacity’, as in your statement: “This entails that ideologies, delusions, fictions (works of art, narratives, novels, myths, religions) have a capacity to produce truth even though they are false.”
Capacity = Potentiality? If so, what are these powers? Passive, active; both, neither? Static or dynamic capacities?
If an object in itself is a time-event or time-effect, then nothing is is ever itself or present; therefore, there can be no capacity in the sense of something passive awaiting to be awakened out of itself to produce an effect or affect other objects. Yet, if it is actual then there is no need for a potential or capacity, for it is already-always ready and able to deploy its force not as capacity but as movement, dynamic energia…
Since a fiction is an object-effect in movement, even if it is within certain minds, it is a material event that works against other material events, be they neurons, etc. Objects are actual and have effects on material things affectively without the need for a normative solution, or as Brassier recently stated a “capacity to understand meaning”… we do not need to know the differance between truth and falsity to see the effects/affects of objects, whether those objects be temporary ones within material minds or temporary one’s outside of those minds… we do not need an epistemology to help us understand how ontic things interact in any form or fashion.
I think your right you say: ” I have not seen this reworking of the basic principles of reason. So where is it?”
March 8, 2011 at 6:05 am
If the “semiotic entity” produces real differences it must be real. I get that. But how do we locate the difference-production in the “semiotic entity”, rather than in the mind? That is not clear to me.
March 8, 2011 at 6:16 am
Marcus,
I’m not sure how this is any difference than how biochemical processes make use of chemical processes in order to exist and maintain themselves. Just as the cell is a form of organization that is dependent upon but irreducible to those chemical processes (it’s the organization or emergence that matters) such semiotic entities would require minds to take place while being irreducible to mind.
March 8, 2011 at 7:33 am
First off, this post draws some really interesting, and troubling conclusions; all in all, I’m probably going to spend all of tomorrow fretting about it.
I haven’t gotten to your article in The Speculative Turn yet, so my confusion may be from that ignorance. I’d like to hear more about why you think of fictions as “false” in the example of symbolic logic.
The analogy seems unclear because the propositions utilized in symbolic logic tend to be expressed as properties, events, etc. E.g. “Adam loves Eve” or “Eve loves Adam”. We would not say “Popeye” is true or false.
I’m not entirely sure whether you are continuing an analogy or making a strict claim when you say that: “This entails that ideologies, delusions, fictions… have a capacity to produce truth even though they are false.”
In my reading of your post, this stops being an analogy somewhere in those passages. I’m even beginning to suspect it never began as an analogy, but then that begs the question I started this comment with: what do you mean by saying fictions can be “false”, and what “truths” do you suggest they can produce? Moreover, I’d like to know what you mean by “truths” here as well.
I’m inclined to understand “false” as “not real”, but clearly you are not arguing that. Does “false” simply mean “not physical”? I’m not inclined to believe that either.
Not knowing what you mean by “true” and “false” here, I cannot make sense of this idea of “producing” truths. False antecedents do not “cause” (P —> Q) to be true, at least not in any sense of “cause” that I understand. Rather, I see you using “truth” here in the sense which you discuss the difference produced by fictional objects.
Hope that made sense.
March 8, 2011 at 11:35 am
larvalsubjects:
The problem for me is that the semiotic entity only makes a difference to/for/in the (very real) object that interprets it as a semiotic entity. So is it the interpretation or the semiotic entity that makes the difference? This question does not arise with biochemical processes as I see it.
March 8, 2011 at 12:53 pm
We’re getting philosophically closer. At some point I think we’ll meet in the middle… :)
The idea that ontic fictions are “not real” purports a concept of reality that is antithetical to your claims to flat ontology. If you demand flatness, you must accept ontic fictions as “real”. This changes what “real” means. It is my claim that this change is essential, and that if object oriented ontology rejects this claim then it will always collapse into materialism of some kind (despite an agnosticism as to the ‘priority of the small’).
Best wishes!
March 8, 2011 at 1:51 pm
Thanks for the thought-provoking post. I appreciate your discussion of fictions and agree (not surprisingly perhaps since my training is in literary theory). I also appreciate your questioning of critique and believe that what you say in your final paragraph could tie in with performative theories of language (particularly indigenous theories, rather than conventional speech act although perhaps the latter, too).
March 8, 2011 at 6:51 pm
I kept looking for an example to discover the dilemma facing this for of symbolic logic and material conditionals. The closest I came was the Euthyphro dilemma which is more of the form a question about the good in which Socrates asks Euthyphro: “Is the pious loved by the gods because it is pious, or is it pious because it is loved by the gods?”
Now if we rephrase it or translate it into your terms of true or false antecedents of material conditionals productive/non-productive of truth we get:
“Is the fiction real because it is produced by the true antecedent of the material conditonal, or is it productive of truth because it is the product a true antecedent even though it is a false fiction?”
March 8, 2011 at 8:21 pm
I’m not sure that I understand the perceived problem for the eliminative materialist or scientist. Part of this connects to what S.C. Hickman and Roberto Pedroso said above, particularly the questions about what true and false mean in this scenario. But, at the same time, I do not understand how the e.m. or scientist or would have a problem with declaring fictions real?
Fictions are conglomerates of material bodies acting in a certain pattern. Per the train example, the four-o-clock train is able to transubstantiate itself onto multiple physical trains AND into multiple physical times because of its material existence in the fictions of its private “community of believers,” as well as in their cultural artifacts. So “the four o clock train” exists physically in their bodies and in their ledger-books, but is irreducible to any of these since it in its fullness (as in your cell-from-chemistry example above) is emergent. At the same time, it is not independent of these things, nor is it independent of certain truth-constraints within the world. If the “four-o-clock” train is consistently showing up hours from four o clock, usually around eight o clock, then it will eventually cease to be the four o clock train, OR the symbolic meaning of the four o clock train will become ironic through its own dissonance, altering the symbol and its use. The same is true if, one day, the four o clock train turns out to be a bus.
So is the issue here that eliminative materialism would deny emergence, arguing that the train IS reducible to all its constituent physical elements? If so, it just seems like that this eliminitavism is first of all, highly unscientific, and second, possibly a straw man, though there are doubtless those who WOULD argue this.
OR
Is this all about the truth and falsity? In this case, how exactly are fictions not “true” in the first place? They certainly “lie” about what they are–your picture of popeye “lies” about being composed of pixels on a screen, appearing to me as an actual small, strangely-proportioned man. But then again, I don’t believe popeye. I know that he is lying to me and that he is made of pixels. This maybe creates a helpful distinction when you bring up truths of religion, ideology and so forth, since, compared to fiction, the big difference is a tacit or shared knowledge of literal “falsity” accepted in fiction and denied in fundamentalist religion and especially denied in ideology. For instance: Every scientist operates within this realm every day–fully understanding that her theories effectuate change within the world though they are likely inadequate descriptions of the examined reality. But that in no way makes the “fictions” of science correlate to the fictions of religion or literature, since there are wholly different conditions for the production of these scientific “fictions.”
Overall, the issue is the same:
I do not see how the capacity of fictions to effect change within the world is at all a problem for scientific thought.
March 8, 2011 at 9:08 pm
Addendum: rephrase of the question, sorry!
Now if we rephrase it or translate it into your terms of true or false antecedents of material conditionals productive/non-productive of truth we get:
“Is the fiction real because it is produced by the true antecedent of the material conditonal, or is it productive of truth because it is the product of a true antecedent even though it is a false fiction?” (i.e., can a true antecedent produce false fictions? or not? If so then those false fictions created by true antecedents could produce truths even if they are in themselves false.)
March 9, 2011 at 12:24 am
I am not a man versed in formal logic so I can’t say I accept or reject the whole arguement, but I get the general idea. I am very fascinated by the idea of fictions producing truths. For instance, the events and teachings of the Bible may be a fiction but they have produced tremendous historical events, laws, institutions, and alter the behavior of billions of humans every day. Likewise, universal human rights are fictional, but they produce truth in that entire societies function around the concept of such rights and those who break such fictions are condemned as criminals. Surely many ‘moral’ or ethic commands began as simple social agreements that later reached a mythical-theological status/categorical imperative to such a degree that nobody can distinguish their truth from error. Likewise, who knows how many grew up and became plumbers, doctors, or soldiers because they idolized their favorite fictional character.
March 9, 2011 at 12:28 am
The eliminative materialist wishes to restrict claims to what is true and restrict what is true to what materially exists. So take a claim like the following found in Descartes: “If God is not a deceiver, then the claims of mathematics are true and certain.” If we suppose, for the sake of argument, that the claim “God is not a deceiver” (the antecedent of our conditional) is false (i.e., God does not exist, therefore it’s impossible for him to either be or not be a deceiver), then it would seem to follow, for the eliminative materialist, that this statement has to be strictly meaningless and false. For the logician, by contrast, the story is different. So long as the consequent of the conditional is either a) true or b) false, the conditional as a whole is true. Consequently, for the logician, the claim “If God is not a deceiver, then mathematics is true is certain” will be true. This seems to be exactly what the eliminative materialist is refusing: that a proposition containing a falsehood such as this can be false. I am basing my remarks here on Ray Brassier’s characterization of his own position on truth in his recent interview. Brassier’s position commits him to rejecting conditionals such as these and therefore to rejecting all sorts of true propositions. For the logician, by contrast, the only situation in which a material conditional will be false is when it has a true antecedent and produces a false consequent. For my own part, I think it’s necessary to distinguish the true and the real. In my view, a fiction can be real or have being without being true. It is a mistake to treat “true” and “real” as synonyms of one another. The former refers to existences, whereas the latter belongs to the domain of epistemology or statements about the world. A fiction can be a real existence in the world while being empty or false in terms of its representational content.
March 9, 2011 at 12:41 am
Right Drew,
That’s pretty much exactly what I’m getting at. Fictions, whether ideological, mythological, religious, or artistic, can produce truths regardless of the fact that they are false. This raises the question of why one would conclude that true representations are required to produce truths. Lacan put the point nicely, drawing on Bentham: “truth has the structure of a fiction.”
Stanley,
I think the question of whether an entity is material is entirely irrelevant to whether it is real. Following Marx and Deleuze and Guatteri, I believe there are incorporeal beings in addition to corporeal of material beings. This is the case with symbolic entities due to their iterability. This is why your money is able to be a dollar bill or a series of zeroes and ones in your bank account. It is not the matter of the train that makes the four o’clock train the four o’clock train. We know this because trains are often switched up from day to day (different material trains are used), yet the four o’clock train remains the four o’clock train. It is not matter that makes this train the four o’clock train that train, but the incorporeal symbolic.
March 9, 2011 at 2:05 am
Hi Levi,
I like the bold spirit of your attempt to pull ontological consequences out of the truth conditions of the material conditional, but I think that the whole idea gets tangled up in confusion right out of the gate. That *all* conditional statements with a false antecedent are true should be a warning sign here: what the semantics for the material conditional express is the fact that *from the false everything follows*. In other words, the false *implies everything, INDIFFERENTLY*, and this is why any theory subtended classical logic (most logics, in fact–the only exceptions I know of are called “paraconsistent logics”) cannot, strictly speaking, tolerate false assertions. No classical theory, for example, can assert both T and not-T as theorems. One or the other must be false (if nothing else “T and not-T” must be false”, and from a “false theorem” *everything follows*—ALL other propositions expressible in the language are then asserted as true.
This doesn’t sit well with your ontic principle, that it is of the essence of the real to “make a difference”. If you try to model the way in which fictions “make differences” in the real (and so qualify as real) in terms of the way in which false antecedents “make true conditionals”, you’re headed for disaster. Classical logic can’t tell the difference between two falsehoods. Both imply everything.
I’ve been soaking in Badiou again for the last few weeks, trying to get those dictionary entries done, and I’ve had a chance to read “Infinitesimal Subversion” again. There’s a great passage there, which captures the spirit of what I’m saying pretty well:
“If every statement is derivable, the system is inconsistent; if every constructible place is occupiable, the system, marking neither differences nor regions, becomes an opaque body, a deregulated grammar, a discourse dense with nothingness. The variable, as inscription which disjoins the constructible from the occupiable – governing which constants belong to the former but not to the latter – testifies to the intra-systemic trace of the system’s reality. The operator of the real for a domain, it in fact authorizes within that domain the writing of the impossible proper to it. The existent has as its category a being-able-not-to-be the value of a variable at the place it marks.”
At bottom, I don’t think it’s a good strategy to identify *fictional beings and their real powers* with *classical falsehoods and their logical power*. They differ in dramatic and fundamental ways. The logical “power of the false” is *absolute*, and that’s why it has to be left unasserted. If it’s important for your project to connect fictionality to some notion of logical falsehood, then it’s you, not Ladyman (who actually can accomodate Popeye without any difficulty—his (and Ross’) “Rainforest Realism” of “real patterns” does this in a very natural way. I recommend taking a look at that chapter in ETMG) who should look outside of classical logic. Take a look, for example, on some of the work being done on “paraconsistent” or “free” logics.
March 9, 2011 at 2:06 am
[…] Read his entry The Power of the False, here. […]
March 9, 2011 at 2:44 am
Levi,
I’ve thought for a while that fictions are Real, following a similar logic to the Saussaure reference you point to. What concerns me nowadays, training in mental health nursing (this is also why I remain anonymous), is precisely what to do with that insight with my client group.
There is the work of Marius Romme and Sandra Escher where they speak of delusions as real and the approach of the Hearing Voice Network that were inspired by their research. Yet I can’t help thinking that if we accept that delusions have their reality that psychiatry becomes a matter of ‘reality enforcement’, in a Philip K. Dick kind of sense.
March 9, 2011 at 6:22 am
I certainly understand that, against the materialist, any philosophy positing the non-corporeal as a possibility will have different options when it comes to determining truth and falsity. I think it’s equally important, though, that we don’t mischaracterize the materialist thesis. This thesis does not state that the material of the physical train makes it the four o clock train, because clearly it is iterable. The materialist would hold that it’s probably necessary for there to be a physical train or vehicle or SOMETHING at some point, however. But the material of the “4 o clock train” is MORE the material of the bodies of those who hold the narrative of the four o clock train and of the artifacts which compose the culture of those individuals–i.e., the ledger-books recording the movement of the train, the signs announcing its arrival and departure, the station built to accomodate its passage. Its iterability comes from the fact that the material of the symbol that is “4 o clock train” is not restricted to the four o clock train. The material is widely distributed, both in animate humans and inanimate objects. Now there are plenty of arguments to be made against that–though I think it’s something of a divergent issue here–but it is important that we not misportray it as “it is the matter of the four o clock train which makes it the four o clock train.”
I am also curious for an example of what kind of propositions a materialist like Brassier would have to reject based on the materialist logic.
March 9, 2011 at 8:28 am
“Have they revised symbolic logic in such a way that they’re willing to sacrifice all the fruitful work that the material conditional and biconditional have accomplished?”
Please tell me I’m not the only one who laughed at this bit of fey wickedness (given Fink’s use of Hegel’s “joke” about fruit with respect to sexuation in the 8-1-06 post).
Couldn’t help noticing in a recent post that you pronouncedly used the word “it’s” instead of “its” a few times, so I’ve been waiting with bated breath for a discussion where the action of contraction(s) (drawing together) might be central, and I’m intuiting that like the four o’clock train, it’s here, or a’comin’ real soon.
I’m genuinely happy; it’s really happening; you’re cracking jouissance. (And the rest, my friend, is spinach!)
March 9, 2011 at 12:59 pm
Hey Zachary,
Interesting point here, but also rather strange. Of course classical logics tolerate falso propositions. This is everywhere in the truth-tables, whether we’re speaking about disjunctions or material conditionals. When you speak of p and ~p, it’s not false propositions you’re referring to, but the law of non-contradiction and the excluded middle: it cannot both be the case that p and ~p are the true. The curious features of material conditionals arise from its logical equivalences. When I say p —> q I am saying “there cannot be p and not q” or ~(p & ~q). When you do the truth table for this you get these curious instances where a false proposition can entail a true proposition.
The point of this post is to call into question Brassier’s equation of the real and material with the true. If that move is made, I believe, you end up with some pretty devastating consequences for logic.
March 9, 2011 at 2:52 pm
Hi Levi,
I didn’t say that classical logic “cannot tolerate false PROPOSITIONS”—clearly, they’re among the basic artillery of any classical logic. What I said is that classical logic cannot tolerate false ASSERTIONS. But I didn’t explain the difference between these two terms, and so I see how I invited this confusion. An assertion is a proposition that’s taken to be true, or, better, provable. There are many different formalizations of classical logic out there, all essentially equivalent to one another, but the choice of which will constrain our way of speaking about these things. To keep it simple, let’s take the old Hilbert-style axiomatic presentation of logic as our framework here. In this framework, we start out with a stock of axioms (it doesn’t matter here what these axioms are; many alternatives are available), and (leaving quantifiers aside) two rules of inference:
(1) SUBSTITUTION, which lets us replace atomic propositions (letters in the formulae already asserted) with any other formula, provided that we replace all occurrences of that letter with the same formula; and
(2) MODUS PONENS, which bears directly on the material conditional. Modus ponens says that if we have
|- P –> Q
on one line of the proof, and
|- P
on another, then we can write
|- Q
on a subsequent line. (In other words, it says, “From ‘P –> Q’ and ‘P’, deduce Q”.)
I’m using the sign “|-“, here, to distinguish ASSERTED propositions (assertions) from bare propositions.
Now, let F be some false proposition. Following the truth table for the conditional, we know that
F –> X
is TRUE, for every formula X (whether or not X is true). This is absolutely correct.
Since F –> X is true, it is PROVABLE, that is, ASSERTABLE, in any complete axiomatisation of classical logic. (And classical logic does indeed have complete axiomatisations—Gödel’s incompleteness theorems don’t get in the way here since we’re not dealing with a system that can express arithmetic, and it was in fact Gödel’s COMPLETENESS theorem that established the completeness of the axiomatic presentation of classical logic.)
So, skipping the details, we know that we can, with a bit of work, write down
|- F –> X
in a classical proof.
Suppose now that we could assert F in its own right. This would mean that we could write
|- F
in the proof. So far, then, we have
|- F –> X
|- F
MODUS PONENS, the rule which expresses the “logical power” of the conditional, then lets us write
|- X
regardless of what X we chose. Since the choice of X has no bearing here, we can generalize this and see that “from the false everything follows”. (In the old days, this principle was called “ex falso sequitur quodlibet”.)
So, even though classical logic does make use of false propositions as raw material in its demonstrations, it does let them become assertions. A theory, subtended by classical logic, which does so, “explodes”: it implies EVERYTHING, indifferently, trivially, becoming a “discourse dense with nothingness”.
A theory which lets itself assert the false, moreover, is, for classical logic, a sense with no referent: NO structure is a “model” for that theory, there is nothing which that theory can be taken to “describe”.
I hope this clears things up.
Certainly, there’s no disputing that false propositions can be components of true propositions. To see this, we don’t even need to worry about the material conditional. Look at negation! If P is false, then not-P is TRUE.
As you must have realized by the time you wrote that P –> Q is equivalent to ~(P & ~Q), the principle of non-contradiction is already tangled up with the truth conditions for the material conditional, so these really aren’t separate issues. The principle of non-contradiction more or less expresses the assertability of ~(P & ~P), which is just another way of writing P –> P, so long as we stay within the scope of classical logic.
Now, let’s say that Brassier does in some sense “equate the real with the true”. What could this mean? Probably something like this: to be real, X must be the referent of a true proposition. (Not a proposition already uttered, of course, but a proposition that could be uttered, ideally.) (X, clearly, must be a state of affairs or a fact of some sort, since as someone has already pointed out, it’s states of affairs to which propositions refer, and not “things” in general.) It’s hard to argue with this, since a state of affairs that would be the referent of a false proposition DOES NOT EXIST. (Again, no (classical) theories which permit the assertion of false propositions have models. And it is classical logic which tells us this.)
It’s clear that Brassier (or whoever) does not mean that the real cannot be described by an assertion that makes use of false sub-propositions. Your blue mug, for example, which I assume is real, could certainly be described (rather, I should say “states of affairs in which your blue mug occurs can be described”) by a proposition which has as one of its components “Levi’s blue mug is red”. Like so:
It is not the case that [Levi’s blue mug is red].
If Levi’s blue mug is red, then I’m a monkey’s uncle.
And so on.
March 9, 2011 at 3:56 pm
Zachary,
Let me see if I’m understanding you correctly. When you write:
Your point is that my thesis about the reality of fictions and falsehood in classical logic don’t sit well with one another because falsehoods don’t produce a difference? Thus, insofar as I hold that in order to qualify as real something must produce a difference, falsehood would not qualify as real because it produces no difference. Is that right? Perhaps you could also say a bit more about Ladyman and Ross. I’m pretty skeptical of the thesis that the real can coherently be reduced to patterns. Their book strikes me as a lot of bombastic rhetoric that’s very thin on actual argument.
March 9, 2011 at 4:03 pm
Hi Levi,
Yes, that’s right. The only difference that asserting a falsehood in the field of classical logic could produce would be to obliterate all differences in that field—everything becomes equally assertable.
I’ll have to get back to you re: Ladyman & Ross. But do take a look at the “Rainforest Realism” chapter. It might not be so antagonistic to your platform as you suppose—which isn’t to say there aren’t any problems with the theory.
Cheers,
Luke
March 9, 2011 at 4:58 pm
Luke,
I think that’s a brilliant observation. I suppose what interests me is that fictions can still lead to true knowledge about the world, justice, etc. But you might be entirely right that this is a point independent of logic. I’ll have to think on it more.
March 9, 2011 at 11:49 pm
@ Drone Module
“Yet I can’t help thinking that if we accept that delusions have their reality that psychiatry becomes a matter of ‘reality enforcement’, in a Philip K. Dick kind of sense.
Well, the nuance to be made here is that OOO simply states that all objects equally exist, but this says nothing about the actual powers of such objects. A delusion is real, but it is still a delusion regardless of the whether the patient knows this or not. I may not know what the copy machine in front of me is made of or capable of but it is clearly different from other copy machines and it is clearly different from imaginary copy machines.
March 9, 2011 at 11:54 pm
Just an off-hand remark: Brassier’s recent comments have been causing a big uproar lately. I am hardly the first to say this, but there seems something rather absurd in submitting an article to an anthology called, of all things, The Speculative Turn, edited by (surprise, surprise) bloggers and Latourian-influenced thinkers like Bryant and Harman. I know his ‘Concepts and Objects’ article was strongly opposed to OOO and ANT, but that’s besides the point. If he didn’t appreciate the internet than he should have shut up and not submitted anything. It’s sad because I really enjoy Brassier’s work and see ways in which it can actually sync with OOO, not oppose it.
March 10, 2011 at 11:00 pm
It’s also important to note that some logicians have tried to eliminate those “paradoxes of the material implication” via the development of relevance logics. See:
http://plato.stanford.edu/entries/logic-relevance/
March 11, 2011 at 11:04 am
Someone pointed out to me that the pingback for my response to this post didn’t come through here, so here’s a link for anyone who is interested:-
http://deontologistics.wordpress.com/2011/03/10/stranger-than-fiction/
March 19, 2011 at 6:45 pm
This is a question about post number 20–what allows us to assert F if it’s false? Do you mean it becomes true, and then we’re stuck with X?
March 19, 2011 at 6:45 pm
That question was for Luke, I mean.
May 2, 2016 at 5:09 am
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