Note: this post is out of date. An updated reply to Koons' Grim Reapers argument can be found here.

**A
brief reply to Koons' Kalam Argument: the Grim Reapers **

**1.
Introduction**

The question of whether there are infinitely many past times is central to the Kalam Cosmological Argument.

In a 2011 paper[1], [2], Robert Koons uses a 'Grim Reapers' argument to support the hypothesis that the past is finite, and moreover, the hypothesis that time is not dense, in the sense that a finite temporal interval can only be divided in finitely many subintervals.

In this article, I will argue that Koons' Grim Reapers argument fails to support either hypothesis.

**2.
Intrinsicality**

Koons' gives the following two definitions of 'intrinsic' in two versions of his paper; one is in terms of propositions, the other one in terms of properties.

**Koons:
**[1]

A
property P is *intrinsic
*to
a thing x within region R in world
W if and only if x is P throughout R in W, and every counterpart of x
in any region Rﾒ
of
world Wﾒ
whose
contents exactly duplicate the contents of R in W also has P
throughout Rﾒ.

**Koons:**
[2]

A proposition P is intrinsic to spatiotemporal region R if P consists of a finite conjunction of atomic propositions ascribing simple powers and dispositions to things located entirely within R at times wholly within R.

In any case, applicability of the principles of binary patchwork and infinitary patchwork require that the powers and dispositions of each of the reapers be intrinsic. I will use the first definition above, but the second wouldn't affect the objections I will raise.

**3.
Binary Patchwork and Infinitary Patchwork **

Koons' proposes two principles, binary patchwork and infinitary patchwork.

**Koons:
**[1]

**Binary
Patchwork. **If possible world W_{1}
includes spatiotemporal region R_{1},
possible world W_{2} includes
region R_{2}, and
possible world W_{3} includes
R_{3}, and R_{1
}and R_{2}
can be mapped onto non-overlapping parts of R_{3}
(R_{3.1} and
R_{3.2}) while
preserving all the metrical and topological properties of the three
regions, then there is a world W_{4}
and region R_{4} such
that R_{3} and R_{4
}are isomorphic, the part of W_{4}
within R_{4.1 }exactly
duplicates the part of W_{1 }within
R_{1}, and the part
of W_{4} within R_{4.2}
exactly duplicates the part of W_{2}
within R_{2. }

**Koons:
**[1]

**P2.
Infinitary Patchwork (PInf). **If
S is a countable series of possible worlds, and T a series
of regions within those worlds such that T_{i} is part of W_{i
}(for each i), and f is a function from T into the set of
spatiotemporal regions of world W such that no two values of f
overlap, then there is a possible world W' and an isomorphism f' from
the spatiotemporal regions of W to the spatiotemporal regions of W'
such that the part of each world W_{i }within the region T_{i
}exactly resembles the part of W' within region f'(f(T_{i})).

**4.
Grim Reapers **

Grim
Reaper#n (henceforth, GR_{n}) is an entity that checks
whether there is a Fred particle at some designated position at a
distance d/2^{j} from a plane P, for some j >n.

If
there is one such particle, then GR_{n} does nothing.

If
there is no such particle, GR_{n} places one particle at a
specific location, at a distance d/2^{n }from plane P.

Also,
GR_{n} exists at a region R_{n} in W_{n}, and
there is a world W and a function from the series {R_{n}}
into the spatiotemporal regions of W such that no two values of f
overlap.

Each
region Rn has a temporally closed boundary in the direction of the
future, and an open one in the direction of the past; also, the
regions are temporally adjoining, and there is an infinite series
towards the past: for instance, if R_{n}
is extended over an
interval (t_{n+1},t_{n}],
R_{n+1}
is extended in
(t_{n+2},t_{n+1}].
[3]

According to Koons', patching those worlds would result in a contradiction.

However, the following scenario is apparently not contradictory.

Let's say that, at world W', the following obtains:

For
every n natural number n, in the interval (t_{n+1},t_{n}],
there is a reaper GR_{n} and a Fred particle F_{n} at
the specified location, at a distance d/2^{n }of plane P.

GR_{n}
and F_{n} do not exist at any other time in W'.

There appears to be no contradiction in the previous scenario, so it seems that patching them is possible after all.

**5.
Grim Signalers **

Koons' considers an objection such as the one raised above, and says that what matters is that a signal of some kind has to persist, and so the Grim Reapers (or Grim Signalers) would have an intrinsic power to send a signal to a following reaper, and to receive a signal from a previous ones.

Also, sending and receiving those signals would be intrinsic powers of the reapers or signalers, with the corresponding intrinsic dispositions.

Moreover, he avoids the objection that powers and dispositions may fail by saying that whether powers and dispositions are used successfully is intrinsic to the situation in which they're used.

However,
adjoining non-overlapping intervals aren't good enough. The power to
send the signal to the next signaler is akin to the power to make the
particle last *into
the next interval*.
That seems to defeat the argument, because the intervals would have
to overlap.

**6.
Conclusion **

Given the previous considerations, we can tell that the fact that Koons obtains a contradiction from the scenario he constructs is not related to the issue of whether time is dense or whether there are infinitely many past non-overlapping temporal intervals, and generally not related to infinities, since a similar contradiction can be obtained in the binary case.

So, in particular, Koons' 'Grim Reapers' (or Grim Signalers) scenarios fail to establish any conclusions about whether time is dense, or whether there are infinitely many past non-overlapping temporal intervals.

**Notes
and references **

[1] Source: http://www.robkoons.net/media/83c9b25c56d629ffffff810fffffd524.pdf

[2] Source: http://www.lastseminary.com/cosmological-argument/The%20Grim%20Reaper%27s%20Revenge%20-%20A%20New%20Kalam%20Argument.pdf

[3] That the regions have a temporally closed boundary towards the future and an open one towards the past, plus the conditions that the regions are adjoining are mentioned by Koons' in his reply to the 'vanishing particle' objection.

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