Santorio's Counterfactual Triviality Result

I recently presented a manuscript of Paolo Santorio's where he extends Lewis's well-known triviality results to counterfactual conditionals. Similar material was covered in Paolo and Justin Khoo's NASSLI course Probabilities of Conditionals and Conditional Probabilities. I essentially walk through the details in my presentation. If you're inclined to work through the details of proofs - to make sure they work - then you might enjoy this excursion here. 

Sketches of Love

What follows treats love as consisting entirely of desires and motivational profile:
x loves y just in case x desires goods for y up to and greater than what x takes y to deserve
We might have as a dual:
x hates y just in case x desires bad for y up to a greater than what x takes y to deserve

Clarification 1: When John loves Sally, John wants good things to happen to Sally in general. John might want goods for Sally even if John isn't involved in Sally obtaining said goods.

Clarification 2: When John merely likes Sally, John wants good things for Sally that Sally deserves. Note, John not wanting Sally to receive goods greater than what John thinks Sally deserves is not equivalent to John wanting Sally to not receive goods greater than what John thinks Sally deserves. The latter - but not the former - would lead to John being upset if Sally did receive such goods.

Clarification 3: One might hold - as Velleman does - that John desires goods for Sally out of respect for her capacity for practical reasoning. I would not accept this though. It seems to me love for another person is love of that other person's qualities, because that's all there is to the other person. I can't imagine a table absent extension, color, shape, etc.; I can't imagine Sally absent all her qualities, so how could I love such a thing?

  • Response 1: If one loves another only for their qualities, then since these qualities can be instantiated elsewhere, the beloved is not unique, and that seems counterintuitive.

  • Rejoinder: While true qualities can be instantiated elsewhere, quality combinations are rarer. There are many blue-eyed individuals, but fewer blue-eyed brown-haired individuals. Attending to the configuration of a beloved sharply restricts the likelihood of another individual exhibiting the same quality set. Moreover, everyone has a height, but each person has a specific height. For each quality, each person has both a determinable and determinate aspects. Focusing on the determinate aspect sharply restricts the likelihood of another exhibiting the same determinate quality set. It is not simply that Sally has blue eyes, brown hair, etc., but that Sally has this shade, hue, and saturation, along with her many other features, which make her rather rare.

  • Response 2: If a beloved perished but all the beloved's qualities were found in a duplicate, would we love the duplicate? Likely not, so there must be something beyond the mere qualities.

  • Rejoinder: I’m not sure what to make of this exotic thought experiment, but I’m inclined to say – if all the properties are the same, including memories, etc. – then ‘yes’. Cp. Hurka who asks if our beloved is replaced with a clone with all the same properties would we still feel a sense of loss. He infers from answering this affirmatively that there is something special about the beloved beyond properties. I think this inference is fallacious. Of course I’d still feel a sense of loss, someone has died. Death is a loss. This doesn’t yet show there’s something beyond the properties of my beloved.

Clarification 4: Some qualities we dislike are found in those we love. John might dislike when others interrupt him in general, but dislike it much less when one interrupts him in a charismatic or charming manner. Similarly, things we dislike in general we might even enjoy if done by our lover because we generally like when things are done, say, cleverly or charismatically, and we find our lover clever or charismatic.

For the Sake of Argument...

I had an instructor who thought hard about formal systems that might underwrite analysis of speech acts like supposition and asserting. He argued as a matter of logic, asserting entailed supposing, though supposing did not entail asserting. For example, the following would be counted as valid:

  1. John AST(The store is open)

  2. Hence, John SUP(The store is open)

While the following would not count as valid:

  1. John SUP(The store is open)

  2. Hence, John AST(The store is open)

I agree with the latter not counting as valid. Asserting seems clearly associated with a norm of truth in every case, while supposing does not. John might claim to know p while supposing not p, without intuitive conflict. In contrast, John claiming to know p while asserting not p, seems a misuse of asserting, i.e. a lie. He's surely asserted, but he's violated a norm.

Does this make trouble for the first argument too? Not obviously. John asserting p comes with a norm of assertion, and if it's entailed John supposes p as well, we might think John's supposing in this case comes with a norm of assertion as well. That doesn't mean John can't suppose without the norm, and indeed, in many cases he will do just that.

That said, I do think there's trouble holding the first entailment. Supposing as an attitude seems to me to involve - in every case - direction towards some further goal. John doesn't simply suppose the store is open. Rather, John supposes the store is open for a reason. This is clearest, I think, in situations where one might suppose something for the sake of contradiction, i.e. reductio proofs. John might suppose p with the intention of drawing out some inconsistency in a premise set combined with background logical constraints. This strikes me as how supposing works in natural language as well. When John supposes the store is open, it's natural to ask - if you aren't already party to reason for the supposition - why John is supposing such a thing, e.g. do you need milk? do you have a shift today?

This feature of supposing in mind, return to the first argument. If John asserts the store is open, then if this argument is valid, it follows John supposes the store is open. But if John supposes the store is open, then there is some goal X John has in mind which motivates this supposition. Hence, in every case of assertion, there is some goal X agents have in mind which motivates the assertion. I find this implausible.

I'll detail why in another post. In the meantime, what do you think?

2018 North American Summer School in Logic, Language, and Information

NASSLLI was a blast! I got to catch up with old friends (Anastasia!), make a few new ones (Anatha! Seth!) and - among other things - enjoy Rineke Verbrugge masterfully dissect shifts in rational knowledge attributions in the Friends episode The One Where Everybody Finds Out, using Kripke models. Other highlights include debating whether logic is the right tool to characterize counterfactual attitudes over lunch with Valentin Goranko, being mesmerized by Patrick Blackburn's entertaining and persuasive case for Hybrid Logic, and enjoying Paolo Santorio and Justin Khoo explore triviality results concerning conditionals and probabilities.

Also, the Carnegie Mellon campus is beautiful.  

Trust Logic, Not Tortoises

Carroll's note What Achilles Said to the Tortoise holds many lessons, many of which related to putative justification - or lack of justification - for basic logical inferences. Recently, Romina Padro, pulling from coursework and discussions with Kripke, has argued one more lesson should be added to the list, namely, that under certain conditions adopting basic logical inferences is impossible. I've a few thoughts on this new lesson, in particular how it might play with the old lessons. Check it out a recent draft here!

A Version of the Anti-Realist Manifestation Argument

Suppose sentence U is such that relevant experts currently have no effective procedure for determining whether what the sentence expresses is true or false. Semantic realism is the thesis that understanding U consists in grasping U's truth-conditions, and these conditions may obtain or not regardless of whether relevant experts are in principle able to recognize it. Semantic anti-realists agree that understanding U consists in grasping U's truth-conditions, but claims these truth-conditions are constrained by speaker evidence. Why accept this latter thesis over realism? Consider the following so-called Manifestation Argument against semantic realism a central tenet of which if found in the supposition in line (1):

(1)   SUPPOSE: U has evidence-transcendent truth-conditions
(2)  Relevant experts understand U
(3)  If speaker S understands sentence P then S grasps P’s truth-conditions
(4)  Hence, relevant experts grasp U’s truth-conditions
(5)  If S grasps P’s truth-conditions, this manifests in S’s use of P
(6)  Hence, experts manifest grasp of U’s truth-conditions in use of U
(7)  Hence, relevant experts manifest grasp of U’s evidence-transcendent truth-conditions in use of U
(8)  It is not the case relevant experts manifest grasp of U’s evidence-transcendent truth-conditions in use of U
(9)  Hence, U does not have evidence-transcendent truth-conditions

Since (9) conflicts with semantic realism, if the argument is sound this thesis is false. Come explore whether it is sound or not, as well as the delicate dialectic between realists and anti-realists in a paper I'm working on here!