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Simplifying the Indiscernibility of Identicals

equals - greenI’ve posted quite a few times here before about identity, and about the principle often called “Leibniz’s Law” – the Indiscernibility of Identicals. This is often put:

Necessarily, for any x and any y, x is identical to y only if for any P, x has P if and only if y has P. (Compare, e.g. Colin McGinn, Logical Properties (New York: Oxford University Press, 2000), 4-7.

I agree with other philosophers that this has apparent counterexamples, if “P” can stand either for any predicate or for any property.

But in my view, the underlying metaphysical intuition – that a thing can’t at one time be and not be a certain way – is undeniable. (And of course, it has important theological implications.)

I would restrict the “P” above to intrinsic properties, if I believed in properties. But I don’t. So I’ve been putting the principle like this:

The Indiscernibility of Identicals: Necessarily, any A and B are identical only if they (1) never have differed, (2) don’t differ, (3) will not ever differ, and (4) could not differ.

This formula doesn’t import any assumptions about property-theory, either for or against. Rather, it uses only a primitive concept of differing, or being different – as to qualitative aspect or way of being, not as to number. I think this well captures the intuition and fundamental conviction noted above.

But it now strikes me that the formula is needlessly complicated. Why not just this?Read More »Simplifying the Indiscernibility of Identicals

Constitution Trinitarianism Part 3: The Meaning of “Is”

Is the Son God? In the immortal words of Bill Clinton, “It depends on what the meaning of the word ‘is’ is.” Brower and Rea suggest the following classification of meanings of “is” (in logic, “is” is called “the copula” – that which connects the subject and what’s being said of that subject).

Um, no the Clintons aren’t in the original chart in their paper (71).
And yes, Bill is intrigued by the word “copula”. Read More »Constitution Trinitarianism Part 3: The Meaning of “Is”

three dancers - click for image credit

An eternal dance of Three?

Perhaps the greatest issue for Social Trinitarians with respect to the Holy Spirit is “his” personhood.

The Latin Trinity Chart 2 – a version of FSH modalism

 Let’s try this again.

Here’s a second application for my Latin Trinity chart (see the first post for what the letters designate). Let’s say that a state of affairs is a thing/substance having a property at a time or timelessly.

The “persons” here are just modes of D, that is, states of affairs involving D. So the Son just is D having Fi. And the Father just is D having P. And the Holy Spirit just is D having Sp. Regarding each of F, S, and H, each of them “just is” D – in the sense that in each of them, there is one and the same D.Read More »The Latin Trinity Chart 2 – a version of FSH modalism

Scott Williams’s new paper: Henry of Ghent on Real Relations and the Trinity

Congratulations to Scott Williams, trinities contributor and newly minted Oxford University PhD in Theology,  on his forthcoming paper:  ‘Henry of Ghent on Real Relations and the Trinity: The Case for Numerical Sameness Without Identity’, in: Recherches de Théologie et Philosophie Médiévales 79.1 (2012), will be published. Here is his abstract: I argue that there is a hitherto unrecognized connection between Henry of Ghent’s general theory of real relations… Read More »Scott Williams’s new paper: Henry of Ghent on Real Relations and the Trinity

SCORING THE BURKE – BOWMAN DEBATE – ROUND 5 – BOWMAN – PART 2

I still mean to comment on Bowman’s 5th round, but my inner logic nerd was drawn in by some action from round 5 here, comment 19: [Burke:] “This week I hope Rob will show Biblical evidence for the essential relationship formulae of Trinitarianism: 1. Father = ‘God’, Son = ‘God’ and Holy Spirit = ‘God’ 2. ‘God’ = Father + Son + Holy Spirit  .… Read More »SCORING THE BURKE – BOWMAN DEBATE – ROUND 5 – BOWMAN – PART 2

Hello from London

Dale Tuggy kindly set me up with an account here, so I will say a few words by way of introduction. As Dale notes here, I am a lazy fellow. Or as I say, just as a thing is more noble and perfect, so the longer it takes to reach perfection. I am still working on a book I began in 1984, and perhaps I can use… Read More »Hello from London

Arius and Athanasius, part 2 – Producing something with ‘ingredients’ (JT)

Well Dad, I just don't understand why we had to make them so small.
Well Dad, I just don't understand why we had to make them so small.

As I said last time, Arius maintains that the Son is created from nothing (ex nihilo), but Athanasius denies this. Much of the discussion depends on what these authors mean by ‘creation’. Before we go any further then, it will be helpful to establish a working definition for ‘creating something from nothing’. This requires some care, because we’re after a definition that both Arius and Athanasius would agree to. But so long as we make the right qualifications, I think that Arius and Athanasius do agree on what it means to create something from nothing.

Just so we have a rough idea of what we’re talking about, let me begin by describing creation in the following way: something is created from nothing if it’s produced without any pre-existing ingredients. Now, that’s a very loose way of putting it, but it makes the basic idea clear enough. We know that things get produced with pre-existing ingredients all the time. Masons build walls with bricks and mortar, cavemen make charcoal with fire and wood, humans procreate with sperm and eggs, and so on. But none of that counts as a creation. Something is created from nothing only when it’s produced without any pre-existing ingredients.

Read More »Arius and Athanasius, part 2 – Producing something with ‘ingredients’ (JT)

Did Jesus have faith in God? – Part 5

Continuing the conversation, apologist Tom Gilson stands by his claim that the NT doesn’t teach that Jesus had faith during his earthly life, and indeed, tellingly declines to say that. He says, in part, So the NT clearly comments on, and specifically names, many of Jesus’ virtues. If Dr. Tuggy is right, and the reason Jesus’ faith is not named as such is just because… Read More »Did Jesus have faith in God? – Part 5

Flocanrib – a parable

Irene was the only little girl in her whole extended family, and everyone loved giving her girly gifts. Three of her uncles liked to give her certain gifts every birthday. Uncle John always gave her a flower, uncle Jack always gave her a box of candy, and uncle Jerry always gave her a hair ribbon. They always gave together, and in secret. The night before… Read More »Flocanrib – a parable

Don’t think/write like a contemporary theologian – Part 4 – rubber doctrines

A prominent Christian scholar is criticizing some of his peers for their discussions of Jesus-era Jewish monotheism: [these blokes work] with only two possibilities: monotheism could either have remained intact or been broken. Commendably, [one of the blokes] pictures developments stretching or even distending Jewish monotheism, but he too seems not to consider the possibility of significant reformulations and new adaptations of a religious commitment… Read More »Don’t think/write like a contemporary theologian – Part 4 – rubber doctrines

Is every Orwell an Orwell?

Can we justify a distinction between the ‘is’ of identity and the ‘is’ of predication

Dealing with Apparent Contradictions: Part 8 – Rational Reinterpretation, cont.

Moses Stuart (1780-1852), professor at Andover Theological Seminary,
and NOT a fan of Rational Reconstruction (image credit)


What, if anything, is wrong with with the strategy of Resolution through Rational Reinterpretation? And why are most theologians so cold towards this strategy, while most Christian philosophers love it? Consider this quote by Moses Stuart on one of Leibniz’s takes on the Trinity:

The celebrated Leibniz was requested by a Loefler, who had undertaken to refute the writings of a certain English Antitrinitarian, to give him an affirmative definition of the persons in the Godhead. He sent for answer the following: – “Several persons in an absolute substance numerically the same, signify several, particular, intelligent substances essentially related.” On farther consideration, he abandoned this, and sent a second, which was, – “Several persons, in an absolute substance numerically the same, mean relative, incommunicable modes of subsisting.”

If Leibniz actually understood this, I believe he must have been a better master of metaphysics than any person who has ever read his definition.Read More »Dealing with Apparent Contradictions: Part 8 – Rational Reinterpretation, cont.