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Conditionals

Arcadia has a rich conditionals system. Some of the following aren't true conditionals in Arcadia, but they are listed here, as they are expressed via a conditional in many other languages.

  • Implications, which are used to express a direction implication:
    • If the water reaches 100°C in 1 atm, it boils
  • Definitions, which are used for definition:
    • A number bigger than 1 is called prime, if it's only divisible by 1 and itself
  • Anankastics, which are used to describe a necessity:
    • If you wanna be my lover, you gotta get with my friends
  • Biscuit conditionals, where the the truth of the then clause does not depend on the truth of the if clause:
    • There are biscuits on the table, if you want some
  • Counterfactuals, where the if clause is false or impossible:
    • If I were a rich man, all day long I'd biddy biddy bum
    • If I had studied more, I would have passed the exams
  • Anderson Case, which are used as part of an argument for the truth of its if clause:
    • If Adam had taken arsenic, he would not have shown just exactly those symptoms which he does show.
  • Predictive, where the if clause is a possibility:
    • If we work hard, we will finish the project on time

In Arcadia, conditionals follow a different paradigm.

We consider the following:

Factuality

The first distinction is based on the factuality of the if clause. Is it a possibility or is it counterfactual?

  • counterfactual, is an if clause that is or cannot be true.
    • an alternative past: If I had studied more (but I hadn't and I cannot change that)
    • an impossible situation: If I could land this spacecraft on the sun (but it's not possible)
    • an imaginary situation: If you were here (but you're somewhere else)
  • possibility, is an if clause that can be true
    • a future, unknown event: If I come home early (I may come early, I may not)
    • a "placeholder" case: If n in an even number (it depends on n)
    • an unknown: If you had been here (I don't know if you were, I'm trying to explore whether it's possible)

Necessity

The second distinction is the necessity of the if clause, ie whether the if clause is also a necessary condition for the main clause to happen. Anankastics are also expressed in the if clause. As in the other parts of Arcadia, we use the non-necessary form, unless we want to specifically include it. Essentially, we differentiate between:

  • If I work hard, I will be able to afford a new car

A complete conditional means that if I don't work hard, I won't be able to afford a new car, but an incomplete one indicates that I can still afford a new car, even if we don't work time, but with other means, for example by winning the lottery.

Implication strength

The third distinction is the strength of the implication of the conditional. If the if clause is true, how probable is for the then clause to happen? Consider the following sentences:

  • If the water reaches 100°C in 1 atm, it boils
  • If you exercise regularly, you'll live more
  • If I win the lottery, I'll buy a Ferrari

The first is a fact. If the water reaches 100°C in 1 atm, it has no other option that to start boiling. Maybe you can boil it in another way (eg in vacuum), but when the if clause is true then the then clause will necessarily happen.

The second is a strong association but not a necessity; you mean exercise, but not reach an old age from another reason. But the probabilities are with you.

The third one is a weaker association. Winning the lottery may change my priorities, although the most probable outcome is still that I'll buy a Ferrari.

Tenses

In Arcadia, the tense in all types of conditionals is the "true" temporal tense.