Thursday, September 13, 2012

Thompson and Mann: "Perceived Necessity Explains the Dissociation Between Logic and Meaning" (1995)

Under which conditions do people think that If A, then B can be paraphrased as A only if B? This paper by Valerie Thompson and Jacqueline Mann is an empirical investigation of the question, checking a couple of relevant parameters.

As it turns out, two factors play a major role: The temporal order between A and B, and whether we perceive A and B to be equivalent in the concrete case at hand.

By contrast, the type of discourse relationship between A and B plays no role. It thus doesn't matter whether the relationship between them is causation, permission, co-occurrence, definition, etc.

Independent Variables

Let me just fix some terminology. What I here call the discourse relationship is what Thompson and Mann call "pragmatic relations." I just dislike this term because it's not quite consistent with the jorgon of linguistics.

The two most important discourse relations that they are dealing with are causation and permission:
  • Butter melts if it's heated. (causation)
  • You may enter if you're over 18. (permission)
They introduce a couple more (p. 1557), but since disourse relationship turns out to have no effect, this is of a minor importance.

Second, when Thompson and Mann talk about "necessity" relationships, they are really talking about condtional perfection. This is the backwards conditional If B, then A that we sometimes infer when we hear the forward one:
  • If water is heated to 100°C, it boils (… and vice versa).
  • If it rains, the pavement will be wet (… but not necessarily vice versa).
The effect is a conflation of implication and bi-implication. This "logical" difference does, unsurprisingly, turn out to have an effect on the acceptability of paraphrases.

Lastly, the notion of temporal succession is the most interesting one, and it interacts in some non-trivial ways with the psychology undergraduates' intuitions about synonymy:
  • If a plant has received enough care, it grows. (A before B)
  • If a plant grows, it has received enough care. (A after B)
In terms of the relationships visible to classical logic, these sentence mean very different things: The first one rules out rules out externalities that could hinder growth even in the event of care; the second one rules out other sufficient causes of growth. However, from an intuitive perspective, the sentences seem to point towards the same underlying causal relationship.


Thompson and Mann's main concern is whether their subjects think that a sentence of the form If A, then B is synonymous with A only if B, and whether it is synonymous with B only if A. As I mentioned above, it turns out that this depends strongly on whether the (inferred, perceived) temporal order of A and B, and the (inferred, perceived) equivalence of A and B.

Thompson and Mann used a super-weird scoring scheme in which their subjects had to assign a 1 to a perfect match and a 7 to a complete mismatch. "For ease of comprehension," they report the transformed score 8 – x instead of x (p. 1557; why didn't they just use the easy one in the first place?).

This gives means between 1 and 7. I've transformed these means into percentages to make it easier to see how far the various means are from the maximal and minimal scores. I did this by computing 100/7 * (y – 1) from the reported y = (8 – x). So let's look at a couple of snapshots from the results of Thompson and Mann's experiment 2b.

First, causal relationships with forward-moving time and no conditional perfection. An example of this is the following:
  • If the car runs out of gas, then it will stall.
    1. The car only runs out of gas if it stalls (13% — equivalent)
    2. The car only stalls if it runs out of gas (50% — not equivalent)
In this case, subjects do not like the actually equivalent form (which suggests a modus tollens inference schema). Note that the percentages are the average scores for this class of sentences, not the specific example.

Now a causal relationship with backward-moving time, but still no conditional perfection:
  • If the car drives, then there is gas in the tank.
    1. The car only drives if there is gas in the tank (79% — equivalent)
    2. There is only gas in the tank if the car drives (21% — not equivalent)
So this reversal of time completely turns the intuitions upside-down: Now, the equivalent paraphrase seems more consistent with the order of terms (STATE only if PRECONDITION), and the non-equivalent seems less natural.

If we put these two sets of statistics together, we get the following chart of acceptabilities:

Lastly, a forward-moving example with conditional perfection:
  • If water is heated to 100°C, it boils.
    1. Water is heated to 100°C only if it boils (26% — equivalent)
    2. Water only boils if it is heated to 100°C (75% — not equivalent)
On a very coarse level, this is the pattern of forward-moving time without conditional perfection; there is an intensity effect, but no reversal of judgments.

The Role of Time

So it seems that the single most predictive factor about intuitions of synonymy and inference is the distinction between forward-moving and backward-moving time. Certain ways of construing a causal situation highlight the potential for following the actual causal direction in your thoughts, and other ways highlight the possibility of following the order of inference rather than the order of events.

If this is true, then it would have some consequences for how difficulty various inference types are, as well as how they errors will occur through "normalization." For instance, denial of the antecedent can be seen as a natural thought to have if we follow the order of events in a case where the literal meaning of the premises requires us to follow the order of inference.

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