# OSSA Day 3: Inference Claims

David Hitchcock, McMaster University

The organizing question: What does it mean for something to follow?

Tarski's answer- materially adequate notion of logical consequence has one condition such that X follows from some class K when it cannot be the case that all those in K are true and X false.

But what if the truth-preservation is trivial?  E.g.1, X being a necessary truth. E.g. 2, K being a contradiction.

Moreover what about arguments with non-formal support?

Another notion: truth-transmission.  The argument needs to have a form so that it satisfies Tarski's requirement, but also has it so that the premises can be false and the conclusion could be false.

But what about this case? Napoleon ruled France, Napoleon was exiled on Elba. Therefore, Napoleon was short.  The trouble is that it has counter-factual counter-examples (where N gets replaced by Jaques Chirac, who's tall).

Some others: Lincoln became US president in 1861, so he was at least 35 yrs old in 1861.

and

Lincoln became president in 1861, so he was a man in 1861.

There's a lawlike connection between the first, but not the second.

Ok, so we need to stipulate that there needs to be a lawlike/nomic relation there.  No contingent relation.  We need to revise the schematic articulation counterfactually (which may be indexed to whatever modality is appropriate to the argument — so it's legal possibility with the Lincoln case…)

In these cases, the issue is whether in Lincoln cases, we add the (suppressed) premises to K and test them, too, counterfactually.

But: Hitchcock argues that people don't actually argue that way.  People restrict the variables to some relevant domains. Acceptance is the issue, usually, not truth.  Conclusions aren't always declarative sentences, but other speech acts — so not always T or F.  Finally, people often reason according to rebuttable non-monotonic forms of inference.

The more effective account: an acceptable counter-factual supporting covering the generalization rules within the modally acceptable fields, if the premises are acceptable and the conclusion is acceptable, even though there can be cases where this is not definitive support.

What about gap-filling strategies?  We should supply the coordinate material conditional (again, remember the Lincoln cases).  The question is whether those conditionals are acceptable.  And so in these cases, we have a troubling case where we can't use the conclusion to show that the conditional is true, but it seems that when the conclusion is in question and the first premise is true, we aren't justified in believing the material conditional.  Presumably, this would only be provided by a background generalization, one that is pragmatically justified under the circumstances.

Another example:  AL: what time did we get back to the condo?  Betty: about 9:40.  AL: so it must be just about after 10, now.  (on any vacation day of this context where we arrive at our condo and take our time doing stuff, then it must be a little more than 20 min later….)

Q1: What about this?  Obama lives in the white house, so he lives in Washington DC.  But what about the counterfactual: If Vladimir Putin lived in the White House, he'd have moved it to Moscow?

Q2: Don't the counterfactual considerations make this too messy?  We'd do better to determine it as a feature of pragmatics.