identity, necessity and conditionals

numerical identity

they are one and the same thing - strict identity

• sometimes is is used to demonstrate numerical identity

qualitative identity

sameness in some (typically important) respects

• count how many things there are (if there’s one, numerical; if there are two, qualitative)

other types of identity

• ‘Changing one’s identity’

• ‘Losing its identity’

• ‘Identity theft’

• ‘Identity crisis’

• ‘Ethnic/national identity’

• ‘Personal identity’

These can generally be understood as properties that tell you something important about what someone (or something) is like

indiscernibility of identicals

If a=b, then every property of a is a property of b (and every property of b is a property of a)

• can argue for non-indentity = If a and b don’t share all properties, then a≠b

the identity of indiscernible

if a≠b, then a and b must differ in at least one property

• There is serious disagreement about this – it definitely cannot be assumed!

• The principle rules out the possibility of two perfect duplicates existing, whose only difference is that they are not identical to each other

worry 1: identity through change

•considerations of identity tell me that I cannot be identical to something that has different properties to me here and now

worry 2: different descriptions

Doechii is famous; Jaylah Hickmon isn’t; therefore Doechii ≠ Jaylah Hickmon

• But the problem is, they are identical! Does this show the Indiscernibility of Identicals is false?

• No: fame is tied to the way we are described, but the property isn’t any different – Jaylah Hickmon is famous, but isn’t famous under that name

worry 3: knowledge and belief

Lois Lane knows that Superman can fly; Lois Lane doesn’t know that Clark Kent can fly; therefore Superman ≠ Clark Kent

• But again, they are the same person!

worry 4: what’s in a name

The model Twiggy was named this because of her build so:

• Twiggy was so-called for her build, but:

• Lesley Hornby = Twiggy, so:

• Lesley Hornby was so-called for her build (?!)

But this seems false! Carefully rephrasing the above shows the mistake:

• Twiggy was called ‘Twiggy’ for her build, and Lesley Hornby = Twiggy, so Lesley Hornby was called ‘Twiggy’ for her build

The problem comes only if we make the different inference to Lesley Hornby was called Lesley Hornby for her build

substituting into opaque contexts

• where properties depend on how something is named, or what people believe, these are called opaque contexts

• in such situations, we get incorrect or strange-looking inferences if we carelessly move from one name to another

what is usually assumed

• Logical truths are necessarily true

• Logical truths can be known a priori

necessary/contingent distinction

metaphysical distinction - ways the world can, or must, be

contingent truth/fact

If something is true but could have been false

necessary truths/facts

things that could not have been otherwise – they had to be that way

eg Bachelors are unmarried, 2+3=5

nomological/physical necessity

truths which are necessary provided we keep the laws of nature fixed

metaphysical necessity

truths which are necessary given the nature of reality

perceived hierarchy

logical necessity → metaphysical necessity → nomological/physical necessity

F necessity

truths which are necessity provided we keep F fixed

a priori/ a posteriori distinction

epistemological distinction - how things are known

a posteriori

known from experience

a priori

know certain things without having to appeal to evidence

an a priori truth is a truth which is knowable a priori

eg I know that 2+2=4

• If I in fact reason without using evidence, then my knowledge is a priori

• if something could be reasoned without using evidence, then the truth itself is a priori

a priori complication

I in fact know these things without appeal to experience, but perhaps not everyone will know them that way

• eg they might do all maths via a calculator

innate knowledge and a priori knowledge

• Some philosophers (like Plato) have tried to explain a priori knowledge by saying that it is innate, but the two are not the same!

• Philosophers like Locke and Hume denied that we have any innate knowledge, but they didn’t deny that we had a priori knowledge

• Innate knowledge was unpopular for a long time, but it was partially resurrected by linguists like Chomsky in the 20^th century

necessity and a-priority

• If a truth is necessary, then it doesn’t matter how the world is, it’ll still be true – so I don’t need to check how the world is to know it’s true – it’s knowable a priori

• If a truth is knowable a priori, then knowing it doesn’t require checking the world, but that means specific features of the world don’t change it – it must be a necessary truth

Saul Kripke and Hilary Putnam in particular argued this – consider:

• Billie Holiday is Eleanora Fagan

• Water is H₂O

• Mary Shelley was the child of Mary Wollstonecraft

The ‘standard metre’ bar in Paris is 1 meter long

• Kripke claimed that this is a priori, since if I know what the object is, I know it’s 1 meter long, but it’s contingent, since we could have chosen a different bar, of a different length

indicative conditionals

We take some condition (the antecedent) and assert something else (the consequent) that we expect to accompany it

These can appeal to the past, present or future

• eg “If Otto is a dog, then he is a mammal”

Warning: if you see a ‘would’, then you very likely don’t have an indicative conditional – we’ll come back to this case

if and only if

• If ‘if’ is not preceded by ‘only’, what follows it is the antecedent

• If ‘if’ is preceded by ‘only’, what follows is the consequent

when do we assert indicative conditionals

when we strongly expect that something rules out, or makes unlikely, the combination “true antecedent, false consequent”

subjunctive conditionals

WOULD

they get us to consider an alternative situation, and say what else would be true in that case

Indicative conditionals and subjunctive conditionals can differ in truth value:

• If Lee Oswald didn’t murder JFK, someone else did”

• “If Lee Oswald hadn’t murdered JFK, someone else would have”

when do we assert subjunctive conditionals

• generally subjunctive conditionals are used where we know or strongly expect that the antecedent is false – for this reason they’re often called counterfactual conditionals

• more restricted in tense – we express them by appeal to the past

• when something is false, but we think it most plausible that a situation in which it was true would be one in which something else was true

material conditionals

a logical operation represented by the formal symbol →

• truth functional

• cant represent subjunctive in this way

• can appeal sometimes to indicative

equivalence thesis

against equivalence thesis

responses to paradoxes of material implication

• there is a difference between truth and assertability

eg “I’m in the solar system or dogs can’t look up” is true, but why would I assert it?

• even if “(P→Q)” doesn’t perfectly capture “If P, then Q”, it is the closest that we can come in TFL, and still allows us to understand many valid inferences