When it comes to concrete particulars and how they persist through time, there are two different accounts: endurantism and perdurantism.
Endurantism: for a concrete particular to exist through time is for it to exist completely at different times.
Perdurantism: it is impossible for the same concrete particular to exist at different times - a concrete particular is made up of different temporal parts.
Two Theories of Persistence - Endurantism and Perdurantism
In the first section on concrete particulars (chapter 3), it was just assumed that concrete particulars are entities with temporally bounded careers. They come into existence at some point, they pass out of existence at a later time, and they exist at all the times in between. This is the general everyday view most people would agree with.
The endurantists believe that concrete particulars exist whole and completely at each of several different times. The NoLasagna of yesterday and NoLasagna of today are the same particular. The perdurantists believe in temporal properties, therefore the Nolasagna of yesterday and NoLasagna of today are not the same thing. The endurantist doesn’t believe in these temporal parts. They simply believe in a simply three dimensions.
We have concrete particulars that exist in the three spatial dimensions and the only things that count as the concrete particular is the parts that make up that spatial area; such as hands, legs, etc. I exist wholly and completely at a time and persistence through time is merely existing at different times. Perdurantists view concrete particulars as four dimensional beings. In addition to the spatial dimensions there is also a temporal extension - concrete particulars take up time as well as space.
Persistence and the Nature of Time
How do these theories of persistence relate to the discussed views on the nature of time?
B-Theory really meshes quite well and naturally with persistence. Some claim that endurantism also works with B-theory, but this requires some definitional changes. In B-theory, it is viewed that the world is four dimensional and view that all times and their contents are equally real. And the view is that concrete particulars are like a spacetime worm. There are other people that view A-theory as something that is also compatible with perdurantism.
The Ontology of Perdurantism
So this is going to get a little wild with views. When it comes to temporal properties that can be divided up, such as NoLasagna of yesterday and NoLasagna of today - it is viewed that these divisions are arbitrary in how the pieces are divided up and analyzed. This is similar to earlier views that we have a concrete particular of ‘man’ that it is made up of arms, legs, etc, but these divisions are arbitrary since you could have finger nails, skin, or atoms and molecules.
When it comes to this view we can see how far the cuts can go with times. We can claim there is a thing ‘blah1’, that is Jim Carrey in July 12 1992, the Sears Tower bottom half on May 5th 1968 and other things that most of us would associate with unrelated.
Essentially we are talking about gerrymandering of both spatial and temporal slices of matter.
An Argument for Perdurantism - Change in Properties
A big argument against endurantism is that it doesn’t account for change. Take my car. Brand new it is in good shape, it works well and running optimally. When it hits 10 years old, it has some different parts, there is some rust and it doesn’t seem to run the same as it used to. Endurantists contend that concrete particulars exist wholly and completely through time, but the car has changed.
Perdurantists contend that this is a violation of Identity of Identical. If the properties are different, they can’t be the same thing. Since perdurantism has temporal properties, it accounts for the changes that occur, without actually violating this principle.
A Second Argument for Perdurantism - Change in Parts
Another view can be summed up in an example of someone, NoLasagna, losing a hand. Let’s say I lose my hand at time t. t+ is time after t, and t- is time before t.
Perdurantists claim that endurantists will hold the following:
(1) NoLasagna t- is numerically identical with NoLasagna t+.
Let’s make another part, the NoLasagna part that is everything except my hand as NoLasagna-Minus.
(2) NoLasagna-Minus t+ is numerically identical with NoLasagna-Minus t-.
(3) NoLasagna t+ is numerically identical with NoLasagna-Minus t+ is true.
The view here is that endurantists have to agree with (1), (2) and (3).
(4) NoLasagna t- is numerically identical with NoLasagna-Minus t-.
The argument is that (4) is obviously false that NoLasagna with a hand isn’t the same as NoLasagna without a hand, but if you agree with (1), (2) and (3) you must be committed to (4). Endurantists reject that they agree with all the truths listed. One of these arguments is mereological essentialism, where they deny that objects remain identical through a change in their parts. Another argument is from Chisholm who has views on something that is ‘strict and philosophical’ and something more casual ‘loose and popular’ - so when we speak of NoLasagna we are not merely speaking of all these parts that make up this human, but an essence of what he is.