A Very Strange Post on Truth and Implication

Levi Bryant has a VERY STRANGE POST on truth and fictional entities over at Larval Subjects. Pete Wolfendale has written a patient response over at Deontologistics which attempts to reconstruct Levi’s views from the perspective of Brandom-style inferentialism. Being somewhat under pressure work-wise at the moment, I’ll confine myself to this key passage:

“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 realismeliminative materialism, or scientism where realist ontology is concerned. Therepresentationalistscientistic, or eliminativist wants to claim that truth can onlybe 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”


1) It’s true that in the standard logic of material conditionals, P —> Q returns F only when P is T and Q is F (where T and F can be treated as the values ‘true’ or ‘false’ – though they need not be, of course: they could be 0 and 1 or {} and {{}}, a pig and a cat…). Most counter-intuitively P —> Q is true whenever P is false (leading, amongst other things, to the consequence that a contradiction implies any proposition since a contradictory antecedent is always false).

It implies (within the standard formalization of propositional logic) that all conditions with false antecedents are true. The falsity of the antecedent ‘produces’ truth only in the sense that the implication relation is a truth function which maps truth values of constituents onto the truth value of conditional sentence.

We could define a further truth functional expression: Not(P —> Q). This returns T whenever P —> Q returns F and F whenever it returns T. So now we have a truth function where the falsity of the antecedent within the negated conditional always returns F.

If Levi is right that the material conditional warrants the claim that falsity can produce truth, then this truth function warrants the claim that falsity is capable of producing falsity.

It implies neither, of course, since the term ‘production’ is misleading. Truth functions are mappings from sets of truth values onto sets of truth values. A mapping is not a dynamic relation of production but a relation from a Range to a Domain. This can be described in set-theoretical terms. For example, the mapping of sons onto fathers can be treated as a set of ordered subsets, the first term of which has a son as a member, the second a father and such that all son-father mappings are represented in the relevant subsets.

The existence of this ordering does not, pace Bryant, indicate that sons produce their fathers.

Moreover, even if we allow Levi free reign, the logic of truth functions does not entail that false statements are anything other than false. Of course, false beliefs can produce true beliefs in any number of ways. Belief in perfectly elastic molecules may help infer empirically true claims about the relationship between the temperature, volume and pressure of a gas. Belief in a nonexistent god may, for all I know, lead people to infer moral truths.

None of these psychological and epistemological commonplaces, though, have revisionary implications for the reality of fictional entities or the truth of fictional statements. The only reason I can imagine that Levi might think this is that he’s muddled about the vehicle content distinction. Belief tokens and sentence tokens are vehicles, what they express or represent as being the case is their content. An ideology qua social reality is a vehicle with a content (the way in which the ideology represents things). Clearly, an ideology qua vehicle can have all sorts of interesting causal and functional roles without ceasing to be false.

2)

“The representationalistscientistic, or eliminativist wants to claim that truth can onlybe produced if the antecedent of a material conditional is true.”

Well, the representationist realist believes that truth is a semantic relationship between representations and states of the world (facts, events, whatever). There is a sense in which Levi is right. If there are no true representations of the kind ‘Snow is white’ then there are no true representations whose propositions could figure as antecedents to conditionals. But it doesn’t follow, of course, that the representationalist is committed to false ideologies not producing truths or, indeed, to them being anything other than false. I can only believe that Levi is using ‘truth’ here in a non-semantic sense.

 


 


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5 thoughts on “A Very Strange Post on Truth and Implication

  1. Pingback: Stranger than Fiction « Deontologistics

  2. Yes, I read Levi’s post with an growing sense of disbelief. The most charitable explanation I can come up with is that he has read so much of Badiou going on about ‘mathematics is ontology’, that he has come to believe that formal logic necessarily carries ontological implications played out in some form of causal/productive nexus. However, that still leaves the fact that he seems to be under the impression that formal logic begins and ends with material conditionals.

    Pete W’s post is astonishing – I wonder how long it took him to write it?

  3. Pete’s response is quite excellent – well worth reading independently of Levi’s original post – I’m sure there’s a good journal article there!

    I can only note the spooky conjunction of Levi’s post on truth and Ray B’s excoriation of SR blogs. Maybe there’s a layer of irony that I’m missing here.

  4. I assume that Levi’s post was intended as a kind of response to Brassier (to the latter’s argumentative dismissal of OOO in the Speculative Turn volume as well as to his rhetorical dismissal of the OOO in the interview). It seems that at least Levi and Graham have agreed not to mention the interview directly.

    That all being said, Levi’s post basically proves RB’s point.

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