Thoughts on the "Conceptualist Argument"

[punkforchrist]

I’d like to hear everyone’s thoughts on this. Consider the following:

1. Abstract objects are either
   a. contingent (or non-existent),
   b. necessary and mind-indepedent, or
   c. necessary concepts of a mind.
2. Abstract objects are
   a. not contingent (i.e. they are necessary) and
   b. not mind-independent.
3. Therefore, abstract objects are necessary concepts of a mind.

Premise (1) should not be controversial, since most epistemologists and metaphysicians agree that abstract objects must contain the characteristics of one of the above-mentioned options.

We might argue in favor of (2a) by pointing out the necessity of certain propositions or laws of logic. For example, it is true in all possible worlds that there are no married bachelors. But what is true in all possible worlds is necessarily true. Therefore, the proposition, “there are no married bachelors”, is a necessary abstract object.

I find (2b) very interesting. There are various causal objections to the idea of necessary but mind-independent abstracta. If, in fact, “there are no married bachelors”, is true independently of any cognitive faculty, and yet abstract objects are causally inefficacious, then why do we have knowledge of them? For our own contingent cognitive faculties cannot be the source of a necessary truth. Since there are possible worlds in which we do not exist, then we cannot bring it about that we would have knowledge of such objects.

The argument, then, is that abstract objects must be both necessary and concepts of a mind. However, they cannot be concepts of just any mind. They must be the products of a necessary mind in order for them to exist in every possible world.

What is everyone’s take on this? Is there perhaps a more sophisticated way of defending (2b)?

 

[SeekingCatholic]

I’d like to hear everyone’s thoughts on this. Consider the following:

1. Abstract objects are either
   a. contingent (or non-existent),
   b. necessary and mind-indepedent, or
   c. necessary concepts of a mind.
2. Abstract objects are
   a. not contingent (i.e. they are necessary) and
   b. not mind-independent.
3. Therefore, abstract objects are necessary concepts of a mind.

Premise (1) should not be controversial, since most epistemologists and metaphysicians agree that abstract objects must contain the characteristics of one of the above-mentioned options.

We might argue in favor of (2a) by pointing out the necessity of certain propositions or laws of logic. For example, it is true in all possible worlds that there are no married bachelors. But what is true in all possible worlds is necessarily true. Therefore, the proposition, “there are no married bachelors”, is a necessary abstract object.

I find (2b) very interesting. There are various causal objections to the idea of necessary but mind-independent abstracta. If, in fact, “there are no married bachelors”, is true independently of any cognitive faculty, and yet abstract objects are causally inefficacious, then why do we have knowledge of them? For our own contingent cognitive faculties cannot be the source of a necessary truth. Since there are possible worlds in which we do not exist, then we cannot bring it about that we would have knowledge of such objects.

The argument, then, is that abstract objects must be both necessary and concepts of a mind. However, they cannot be concepts of just any mind. They must be the products of a necessary mind in order for them to exist in every possible world.

What is everyone’s take on this? Is there perhaps a more sophisticated way of defending (2b)?

Premise 1) is fine. Premise 2a) is fine if meant that there are some necessary abstract objects, as you gave an example. If meant that all abstract objects are necessary, more proof is required.

Premise 2b) is problematic though. It seems you’re confusing truth with knowledge of the truth. The truth is necessary, our knowledge and cognitive faculties only contingent. Our own contingent cognitive faculties can bring about knowledge of the truth in any world in which they exist since that knowledge is only contingent.

 

[punkforchrist]

Premise 1) is fine. Premise 2a) is fine if meant that there are some necessary abstract objects, as you gave an example. If meant that all abstract objects are necessary, more proof is required.

Exactly. (2a) is only meant to show that some abstracta are necessary.

Premise 2b) is problematic though. It seems you’re confusing truth with knowledge of the truth. The truth is necessary, our knowledge and cognitive faculties only contingent. Our own contingent cognitive faculties can bring about knowledge of the truth in any world in which they exist since that knowledge is only contingent.

Causal objections to Platonism refer to this, but unfortunately, I’m just not familiar enough with them to make up my mind about them yet. The argument says that it would be impossible to have knowledge of them (poor phrasing on my part earlier), since abstracta are causally inefficacious. I’m not sure exactly where the contradiction is, though.

 

[SeekingCatholic]

Causal objections to Platonism refer to this, but unfortunately, I’m just not familiar enough with them to make up my mind about them yet. The argument says that it would be impossible to have knowledge of them (poor phrasing on my part earlier), since abstracta are causally inefficacious. I’m not sure exactly where the contradiction is, though.

But saying that abstracta are the products of a mind doesn’t answer the question of how knowledge of them is possible, given that they aren’t products of our mind, does it?

Backtracking on what I said before, though, knowledge of some truths does seem to be necessary in a relative sense. Knowledge of the law of non-contradiction is necessary in any world in which we (rational beings) exist. Likewise for the knowledge that “logic and reason exist”. Whether these abstracta “caused” their knowledge is just too deep for me.

 

[Chad_McIntosh]

I’m glad to see this argument is catching on!

punkforchrist:

What is everyone’s take on this? Is there perhaps a more sophisticated way of defending (2b)?

punkforchrist:

The argument says that it would be impossible to have knowledge of them (poor phrasing on my part earlier), since abstracta are causally inefficacious. I’m not sure exactly where the contradiction is, though.

I try to outline a more sophisticated way of defending (2b) in my article. Particularly I try to draw out the contradiction you mention by formalizing the argument thusly: Where O is some object of knowledge (say, an abstract object)

(1) If O is external to S, S can have knowledge of O only if there is some causal relation R between S and O
(2) O is such that it cannot enter R
(3) If (1b) is true, then O is external to S
(4) Therefore if (1b) is true, then S cannot have knowledge of O
(5) But S has knowledge of O
(6) Therefore, (1b) is false

I also try to respond to relevant objections to this argument in the post itself and in the endnotes.

SeekingCatholic:

But saying that abstracta are the products of a mind doesn’t answer the question of how knowledge of them is possible, given that they aren’t products of our mind, does it?

No, it does not. That is a very good observation. I have not done much thinking on this yet, but my initial response to this would be to appeal to the imago dei within us, the blueprint of which includes knowledge of abstracta. Moreover, the inherent fallibility and error in our best efforts at reasoning with abstracta should not be surprising given the cognitive consequences of sin.

We should also be careful of talking about abstracta as products of a mind—Speaking of them as products seems to suggest they are not necessary and created.

Here is a link to the post:

doxazotheos.com/?p=66

 

[Dopey_Gigglz]

Is this kind of the same thing as an argument for universals?
It seems too metaphysically topheavy to reify all these kinds of things into eternal, non-spatial forms that kind of just float around.

 

[punkforchrist]

Hi DG,

Is this kind of the same thing as an argument for universals?
It seems too metaphysically topheavy to reify all these kinds of things into eternal, non-spatial forms that kind of just float around.

The CA does involve the notion of universals under the term “necessary”. The propositions “there are no married bachelors” and “2 + 2 = 4” are said to be true in all possible worlds; hence, they are universally and necessarily true. What you’re describing as entities that “just float around” is most similiar to Platonism, which is the name of the view found in (1b)–namely, that abstract objects are necessary and mind-independent. For a conceptualist, on the other hand, abstract objects are indeed necessary, but they exist in a mind.